Joshua E. Freeh

Glenn Research Center, Cleveland, Ohio

Analysis of Stationary, Photovoltaic-Based Surface

Power System Designs at the Lunar South Pole

NASA/TM—2009-215506

March 2009

AIAA–2008–7810
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Joshua E. Freeh

Glenn Research Center, Cleveland, Ohio

Analysis of Stationary, Photovoltaic-Based Surface

Power System Designs at the Lunar South Pole

NASA/TM—2009-215506

March 2009

AIAA–2008–7810

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Space 2008 Conference and Exposition

sponsored by the American Institute of Aeronautics and Astronautics

San Diego, California, September 9–11, 2008
Acknowledgments

The author would like to acknowledge Thomas W. Kerslake, NASA Glenn Research Center, for his efforts in the early lunar 

surface power system studies in support of ESAS and LAT and his mentoring and support for this effort; Joseph J. Nainiger, 

Alphaport, Inc., for his effort and collaboration during the LAT studies; James Fincannon, NASA Glenn Research Center,

for support with the DEM data as well as his technical review of the paper; Patrick J. George, Robert L. Cataldo, and 

Jeffrey S. Hojnicki, NASA Glenn Research Center, for their technical reviews of the paper.

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Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
Combinations of solar arrays and either batteries or regenerative fuel cells are analyzed

for a surface power system module at the lunar south pole. The systems are required to

produce 5 kW of net electrical power in sunlight and 2 kW of net electrical power during

lunar night periods for a 10-year period between 2020 and 2030. Systems-level models for

energy conservation, performance, degradation, and mass are used to compare to various

systems. The sensitivities of important and/or uncertain variables including battery specific

energy, fuel cell operating voltage, and DC-DC converter efficiency are compared to better

understand the system. Switching unit efficiency, battery specific energy, and fuel cell

operating voltage appear to be important system-level variables for this system. With

reasonably sized solar arrays, the regenerative fuel cell system has significantly lower mass

than the battery system based on the requirements and assumptions made herein. The total

operational time is estimated at about 10,000 hours in battery discharge/fuel cell mode and

about 4,000 and 8,000 hours for the battery charge and electrolyzer modes, respectively.

The estimated number of significant depth-of-discharge cycles for either energy storage

system is less than 100 for the 10-year period.

Nomenclature

V voltage, V

I current, A

P power, W

J current density, A/cm2

R resistance, Ω

T temperature, K, ◦C

A area, m2

r radius, m

m mass, kg

N number

m ̇ molar flow rate, mol/s

Q heat, W

mf mass fraction

m ̄ mass per area, kg/m2

C1 solar array I-V curve term, from Rauschenbach1

C2 solar array I-V curve term, from Rauschenbach1

f factor

F Faraday’s constant

Voc

∆T

solar cell temperature coefficient for Voc, V/◦C

Vmp

∆T

solar cell temperature coefficient for Vmp, V/◦C

Analysis of Stationary, Photovoltaic-Based Surface 

Power System Designs at the Lunar South Pole 

Joshua E. Freeh 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

NASA/TM—2009-215506 1
Jsc

∆T

solar cell temperature coefficient for Jsc, A/(cm2◦C)

Jmp

∆T

solar cell temperature coefficient for Jmp, A/(cm2◦C)

Subscripts

cell single cell

packing packing

f c fuel cell

mp maximum power

oc open-circuit

op operating

rad radiator

ref reference

SADA solar array drive assembly

sc short circuit

H2 hydrogen

O2 oxygen

H2O water

Greek Symbols

η efficiency/effectiveness

 emissivity

σ Stefan-Boltzmann constant

Abbreviations

BOL beginning of life

CIC coverglass/interconnect/cell

ESAS Exploration Systems Architecture Study

LAT Lunar Architecture Team

NASA National Aeronautics and Space Administration

PEM polymer electrolyte membrane

PMAD power management and distribution

RFC regenerative fuel cell

SADA solar array drive assembly

I. Introduction

In 2004, the President announced the Vision for Space Exploration,2in which he detailed plans to

develop the Crew Exploration Vehicle and return to the Moon and ultimately send humans to Mars. This

announcement initiated several iterations of studies that are ongoing to evaluate how to get the Moon

and what is necessary to sustain a human presence there. The first major study, the Exploration Systems

Architecture Study (ESAS), established the initial designs for Orion, Ares I, Ares V, and Altair spacecraft

as well as the beginning of the lunar surface systems studies.3 After the ESAS completed, the Lunar

Architecture Team (LAT) was created to explore the surface architecture and its interactions with the

transportation systems in more detail. The first iteration of the LAT studies focused on refining the ESAS

results and was announced by NASA in December 2006.4 The second iteration of LAT studies expanded

the options to include a cargo lander and a mobile lander design. Its results were presented at AIAA Space

20075 and other forums.6, 7 The LAT studies are ongoing and continue to both refine and expand the

options in preparation for more detailed design efforts in the future. The latest results were presented in

support of a milestone entitled the Lunar Capability Concept Review in June 20088 and at other meetings

as well.9 NASA has also emphasized the opportunity for international and commercial partnerships in the

lunar surface architecture.10

NASA/TM—2009-215506 2
II. Illumination at the Lunar South Pole

Establishing a permanent human presence on the Moon introduces significant challenges beyond that of

the Apollo missions, which stayed no longer than about 75 hours on the surface.11 Longer missions will

experience some period of lunar night, depending on the location on the surface, and therefore require a

significant amount of energy storage and the capability to recharge the energy storage during the lunar day.

Staying throughout the lunar day/night cycle will also introduce greater temperature variation at the surface

that will require significant additional thermal management capability. Longer missions may also be more

adversely affected by dust, radiation, and micrometeorites, due to the additional time on the surface.

One approach that somewhat mitigates some of the challenges with longer duration stays is to establish

the outpost at one of the lunar poles. The incident sunlight at the poles is at a lower angle than at the equator

so the thermal profile is less variant, but colder. Also, elevated areas near the poles can have significantly

greater durations of sunlight compared to equatorial sites due to the orientation and libration of the Moon.

This can reduce the amount of energy storage needed as well as make photovoltaic arrays more effective at

these sites. Conversely, some lower elevations near the poles (such as crater interiors) may see little or no

sunlight, making these regions scientifically interesting as well. As a result, a site on the rim of Shackleton

Crater near the lunar south pole has been used as a possible site for an outpost.

At the elevated polar sites, the solar illumination profile is governed more by the horizon terrain than by

the orbital mechanics of the Sun-Earth-Moon system. The Sun is typically near the horizon at these sites

and can be occulted by hills and other terrain a significant distance away. Detailed topographical maps and

elevation models are lacking for the polar regions due the remote location and distance from past missions

to the Moon. In the past decade there has been significant work in this area to interpret the available data

and produce new elevation models. Summary of the past work has been documented in several papers by

Fincannon.12–14 These papers also produced digital elevation models for the north and south polar regions

as well as horizon profiles for specific sites near the poles. This paper focuses on one site identified as Site

4RS13 near the Shackleton Crater rim. Figure 1 shows an estimate of the horizon profile and Sun centerline

position for January 2020 at Site 4RS. For this time period and location, the Sun is completely unocculted.

01/01 01/03 01/05 01/07 01/09 01/11 01/13 01/15 01/17 01/19 01/21 01/23 01/25 01/27 01/29 01/31 !4

!3

!2

!1

0

1

Month/Day

Elevation Angle, deg.

January 2020

Lunar Horizon

Sun Centerline

Figure 1. Estimated horizon terrain and Sun centerline for Site 4RS,13 near the Shackleton Crater rim and

the lunar south pole, for January 2020. Data shown is from Fincannon.13

The time period shown encompasses an entire lunar rotation; the horizon can be seen to repeat itself near

January 31, 2020. Figure 2 shows a different time period, September - October, 2020, and the corresponding

interaction of the horizon and solar centerline profile. This timeframe shows the worst-case interaction, in

which the minimum Sun location is near a significant set of hills on the horizon. The resulting period without

sunlight can be seen to be multiple days; excluding the valley shown near October 1, 2020, the estimate is

about 120 hours of continuous darkness at this site. Expanding the data shown in Figs. 1 and 2 for the

period of years 2020 - 2030 and mapping the unocculted fraction of the Sun produces Fig. 3. This plot

shows the ’summer’ and ’winter’ periods for this site, where the elevation angle of the Sun is higher than the

NASA/TM—2009-215506 3
09/15 09/16 09/18 09/20 09/22 09/24 09/26 09/28 09/30 10/02 10/04 10/06 10/08 10/10 10/12 10/14 !4

!3

!2

!1

0

1

Month/Day

Elevation Angle, deg.

September/October 2020

Lunar Horizon

Sun Centerline

Figure 2. Estimated horizon terrain and Sun centerline for Site 4RS,13 near the Shackleton Crater rim and

the lunar south pole, for September - October, 2020. Data shown is from Fincannon.13

2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 !0.2

0

0.2

0.4

0.6

0.8

1

Year

Sun Fraction, (0 = Shadow, 1 = Full Sun)

Figure 3. Estimated Sun illumination fraction for Site 4RS,13 near the Shackleton Crater rim and the lunar

south pole, for the years 2020 - 2030. Data shown is from Fincannon.13 The Sun illumination fraction is

defined as the fraction of the unocculted solar disk at the site specified.

NASA/TM—2009-215506 4
Jun Jul Aug Sep Oct Nov Dec Jan !0.2

0

0.2

0.4

0.6

0.8

1

Month

Sun Fraction, (0 = Shadow, 1 = Full Sun)

June 2020 ! January 2021

Figure 4. Estimated Sun illumination fraction for Site 4RS,13 near the Shackleton Crater rim and the lunar

south pole, for June 2020 - January 2021. Data shown is from Fincannon.13 The Sun illumination fraction is

defined as the fraction of the solar disk not occulted at the site specified.

terrain or intermittently lower than the terrain, respectively. The ’summer’ periods are nearly six months

of uninterrupted sunlight while the ’winter’ periods are also approximately six months in duration but the

change is gradual, as shown in Fig. 4, where the early and late portions of the time shown still contain

significant lengths of time in illumination. It should be noted that the total cycle of illumination is less than

an Earth year and can be seen in Fig. 3, where the ’winter’ periods gradually become earlier each Earth year

over the twelve years shown.

III. Mathematical Models

A. Solar Array Subsystem

The solar array subsystem model is an attempt to account for some of the major inefficiencies between an

ideal photovoltaic cell and an actual solar array on the lunar surface for an extended period of time. The

photovoltaic cell data is based on a published datasheet for the EmcoreTM BTJ cell.15 This cell area is

26.6 cm2 with a specified efficiency of 28.5%. While this cell could be considered current technology, it can

be assumed that a better cell may be available by the time it is needed for this application. The sensitivity

to this improvement will be examined in Section IV.D of this paper.

The solar array operating temperature is assumed to be 95◦C. One relevant analog is from the solar

array on Surveyor VI, which recorded a maximum solar array temperature of 110◦C.16 This spacecraft was

located at 41◦ S, a warmer location, so the assumed value here could be expected to be lower than the 110◦C

measurement. The sensitivity to this value will also be evaluated in section IV.D.

The effect of temperature on cell performance is based on measured voltage and current values at a

reference temperature, temperature coefficients from the EmcoreTMdatasheet, and the following equations

from Rauschenbach.1 From the EmcoreTMdatasheet, Tref = 28◦C.

Voc,Top = Voc,Tref +

Voc

∆T

(Top − Tref ) (1)

Vmp,Top = Vmp,Tref +

Vmp

∆T

(Top − Tref ) (2)

Isc,Top = Acell 

Jsc +

Jsc

∆T

(Top − Tref )



(3)

Imp,Top = Acell 

Jmp +

Jmp

∆T

(Top − Tref )



(4)

NASA/TM—2009-215506 5
For the photovoltaic cell I-V curve, the third model described in Rauschenbach1

is used.

C1 = 1 −

Imp

Isc

e

−

V mp

C2Voc (5)

C2 =



Vmp

Voc

− 1



log 1 −

Imp

Isc  (6)

With a given Vcell value, Icell is found from

Icell = Isc,Top 

1 − C1



e

Vcell

C2Voc − 1

 . (7)

For this study, however, the solar array is assumed to operate at Vmp. Also, the solar array is assumed to

only operate when in full Sun (Sun illumination fraction = 1). While the solar array will continue to produce

power when illuminated by the partial solar disk, to be conservative, this effect was ignored.

Several additional losses are included. To account for dust accumulation on the solar array, a 1% loss per

year is subtracted from Imp and Isc. To account for losses due to radiation from both solar particle events

and cosmic background radiation, a 1.2% loss per year is included for both the current terms and Voc and Vmp

as well. The effect of these assumptions will be included in the sensitivity analysis. Other loss assumptions

include the cell mismatch loss, array flatness loss, coverglass/interconnect/cell (CIC) loss, misalignment loss,

and a voltage drop due to the blocking diode. The cell mismatch loss accounts for differences in performance

between individual cells and is assumed to be a 0.5% loss from Imp and Isc. The array flatness loss accounts

for differences in the angles of the individual cells and is assumed to be a cosine loss of 4◦from Imp and Isc.

The CIC loss accounts for losses due to integration of the cell with the interconnect and coverglass and its

spectral properties and is assumed to be 1% of Imp and Isc. The array is also assumed to have a 5◦cosine

loss from Imp and Isc due to misalignment with the Sun. Finally, the blocking diode imparts a voltage drop

of 2% from Voc and Vmp.

The number of cells in series determines the solar array voltage and the number of cells in parallel

determines the solar array current. There is a small resistance for each interconnect from the cell to the

string, assumed to be 0.01Ω. There is an additional resistance from each string to the array bus, assumed

here to be 0.05Ω. The solar array drive assembly (SADA) also has resistive losses that are assumed to be a

bulk 0.02Ω. The total number of cells is the product of the numbers in series and parallel and the array area

is the product of the cell area and total number of cells, plus a packing factor that accounts for array area

lost due to interconnects and packing inefficiencies of the shape of the cell. For the current work, a circular

array is assumed that most likely does not fit cells together as well as a rectangular array, and therefore a

packing factor of 0.85 is used.1

In equation form,

Istring = Icell (8)

Iarray = IcellNcells,parallel (9)

Rstring = RinterconnectNcells,string + Rstring−to−array (10)

Vstring = VcellNcells,string − IstringRstring (11)

Varray = Vstring − IarrayRSADA (12)

Ncells,total = Ncells,stringNcells,parallel (13)

Aarray =

AcellNcells,total

fpacking

(14)

rarray =

r

Aarray

π

(15)

Each solar array wing subsystem mass is assumed to be made up of the solar array wing itself, a SADA,

and some secondary support structure. For this analysis, each SADA is assumed to be 10 kg, and the

secondary structure is assumed to be 10 kg as well. The wing mass is assumed to be a simple function of its

area by using a specific mass of 2 kg/m2. The maximum circular array radius is assumed to be 4.5 m. For

requirements above this value, two smaller arrays are used. The total mass of the solar array subsystem is,

marray =  ̄marrayAarray + NarraysmSADA + Narraysmstructure (16)

NASA/TM—2009-215506 6
B. Battery Subsystem

The battery subsystem model is based on an assumed charge and discharge efficiency value. For this analysis,

charge and discharge efficiencies of 0.97 and 0.98 are used respectively. A degradation of 1% per year in

these values is included.

P(to battery) = ηchargeP(f rom array) (17)

P(to load) = ηdischargeP(f rom battery) (18)

The total battery energy is based on a maximum allowable depth-of-discharge, assumed here to be 90%.

While this value is high, for this application, the system will rarely be discharged that much. For the battery

subsystem mass, a specific energy of 150 Whr/kg at the battery system level is assumed. Sensitivities to the

specific energy will be included to account for the uncertainty in this value.

C. Regenerative Fuel Cell Subsystem

The regenerative fuel cell (RFC) subsystem is assumed to include polymer electrolyte membrane (PEM) fuel

cell and electrolyzer stacks, high pressure gaseous hydrogen and oxygen tanks, and the required plumbing,

controls, and other components necessary for a working fluid system.

The fuel cell and electrolyzer performance are based on the equations derived in Larminie and Dicks.17

The baseline cell voltages (Vcell) are assumed to be 0.85 V for the fuel cell and 1.6 V for the electrolyzer.

These values are degraded by 1% year (fuel cell voltage decreased and electrolyzer cell voltage increased) in

a similar way to the battery degradation. These values will be examined in the sensitivity analysis. The

molar flow rates are as follows,

m ̇ H2 =

P

2VcellF

(19)

m ̇ O2 =

m ̇ H2

2

(20)

m ̇ H2O =  ̇mH2. (21)

The heat produced by the fuel cell is estimated based on the lower heating value of hydrogen. The electrolyzer

will most likely also require cooling but is expected to be less than or similar to that of the fuel cell, so Qf c

is used to size the thermal subsystem.

Qf c = P



1.25

Vcell

− 1



(22)

The RFC subsystem requires some additional power load to account for fluid pumping and thermal management throughout the system. For this study a constant value of 100 W is used during both charge and

discharge of the subsystem.

The fuel cell and electrolyzer stack masses can be simplified to be functions of the nominal power requirements. For this analysis, a constant value of 35 kg is used for each fuel cell stack because the net fuel

cell power requirement is also constant at 2 kW. Each electrolyzer stack is assumed to be 50 kg because the

charge power can be significantly higher depending on the solar array size. A few options in the following

analysis have significantly larger solar array area and for these options, the electrolyzer mass is doubled.

The ancillary components may include gaseous or liquid pumps, gas driers, the fluid lines, valves, and other

components. For this study, a rough estimate of 30 kg is used for each fuel cell and electrolyzer stack ancillary

system.

The hydrogen and oxygen tanks are based on composite overwrapped pressure vessel technology. The

pressure of the tanks is assumed to be driven by the electrolyzer stacks and the maximum pressure most

likely will be between 13.8 and 20.7 MPa (2000 and 3000 psi). The tanks are sized to hold the necessary

hydrogen and oxygen including the amount needed to prevent greater than 90% ’depth-of-discharge,’ as in

the battery case. For this study, the dry mass of the hydrogen tank is calculated from an assumed constant

10% hydrogen mass fraction. Similarly, the dry mass of the oxygen tank is calculated from an assumed

constant 50% oxygen mass fraction. The equation used is

mtank,dry =

mf luid

mff luid

− mf luid. (23)

NASA/TM—2009-215506 7
While this does not account for the potential mass fraction improvement in larger tanks, it is sufficient for

this study. An additional 10 kg is added to each tank, regardless of the amount of fluid, for non-scaling

components such as the fluid interface and structural components.

The approach to RFC mass is coarse but the intent is to capture general magnitudes and the effect of

the changing amounts of hydrogen and oxygen depending on the overall system design. This is a primary

difference compared to a battery: only the fluids scale with energy for the RFC, where the entire battery

system scales with energy. As the energy storage requirements increase, the metric of overall mass per energy

should trend toward the RFC system because of this difference in scaling.18

D. Power Management and Distribution Subsystem

A top-level power management and distribution subsystem is included to account for the mass and losses

from the major components of the subsystem. This study assumes an energy storage bus voltage of 28 Vdc.

The solar array, because of its likely higher power production requirement, is assumed to have an output

voltage (Varray) of 120 Vdc. Therefore, a DC-DC converter is needed to step the voltage down to the 28

Vdc level. This converter is assumed to have a 90% efficiency. A second power management component

is a central switching unit that handles the channel routing and fault tolerance and protection for each

subsystem. This unit is also assumed to have an efficiency of 90% both for charging and discharging. Both

the converter and switching unit are estimated at 20 kg each, irrespective of power levels. The other major

components are the cables and their connectors. A placeholder of 20 kg is used for power system internal

cables and connectors. Voltage drops from the cables and connectors that are local to the power system are

accounted for through the efficiencies and resistances described above. Cables and related losses external to

the power system are not included. Finally, similar to the electrolyzer mass estimates, when significantly

larger solar arrays are used in the following analysis, the PMAD mass is doubled. Top-level schematics of

the lunar daytime and nighttime PMAD diagrams are shown in Figs. 5 and 6.

Figure 5. Power system schematic for lunar daytime operation.

Figure 6. Power system schematic for lunar nighttime operation.

E. Thermal Subsystem

A top-level radiator model is included to account for greater cooling needs of the RFC subsystem compared to

the battery subsystem. The battery subsystem most likely requires some thermal management, but the RFC

most likely requires a more significant thermal system including an active cooling loop. The approximate

NASA/TM—2009-215506 8
area is calculated from the radiation equation with an assumed effectiveness of 0.9, an assumed emissivity of

0.9, an assumed radiator fluid temperature of 320K and an assumed sink temperature of 250K. The radiator

fluid temperature is based on a PEM fuel cell operating temperature of between 330K and 350K. To convert

the radiator area into an estimate of radiator mass, a specific mass of 5 kg/m2is assumed.

Arad =

Qf c

ηradradσ(T

4

rad − T

4

sink)

(24)

mrad =  ̄mradArad (25)

F. Redundancy and Fault Tolerance

Decisions on subsystem redundancy or fault tolerance can be mission- and scenario-dependent but can have

significant effects on the overall system mass. Fault tolerance for solar arrays can be handled by using

multiple wings to provide some capability to recover from a SADA or deployment failure. Once the array is

deployed, it rarely entirely fails. Batteries, like solar arrays, consist of connected cells in series and parallel

configurations, so that if there is a failure, it may only disable a single string or subset of the entire subsystem.

Batteries are therefore not typically fully redundant but possibly oversized to handle a string fault.

A regenerative fuel cell subsystem may require a different approach to handle redundancy. The Space

Shuttle fuel cells are dual-fault tolerant, in which three completely independent stack assemblies are each

capable of meeting the nominal loads.19 This approach is used here for the RFC system and its ancillary

components. For an outpost with multiple modules, the redundancy could most likely be reduced with

modules delivered later. For the RFC tanks, two tanks each of hydrogen and oxygen are assumed.

G. System Load Profile

The load profile used here follows the Sun illumination profile shown in Fig. 3. When the site is illuminated,

the power load is assumed to be 5 kW. When in shadow, the power load is assumed to be 2 kW. These loads

are thought of as module-level power loads, with a larger outpost requiring multiple modules. Matching the

power loads to the illumination profile can simulate an actual outpost that is more active during illuminated

periods and allows only necessary power loads during shadowed periods. For the south pole site, this may

be realistic due to the short periods in shadow and the long, active ’summer’ period. During crew nighttime

periods in the ’summer,’ when the crew is sleeping, the additional power loads that makeup the 5 kW

assumption may come from recharging of mobile vehicles or ongoing scientific studies, for example.

IV. Results and Discussion

A. Solar Array and Battery System

The required battery energy is dependent on the capability of the solar array; a larger solar array provides

more charge power, enabling the battery to charge quicker and therefore be better prepared for the next

discharge period. For an essentially random charge/discharge distribution such as at this site, the effect of

a larger solar array is more pronounced. This effect is shown in Fig. 7. The nonlinearity can be explained

by comparing the state-of-charge profiles for Options 0 and 1, show in Figs. 8 and 9. In the latter part of

Fig. 8, the solar array is not able to recharge the battery subsystem before the next discharge period, thus

beginning that period with a less than fully charged battery. Since the energy storage is sized based on a

maximum 90% depth of discharge, this directly effects the overall battery subsystem size. The result can also

be seen in the early years, where the much larger battery subsystem in Fig. 8 has a lower depth-of-discharge

than that shown in Fig. 9. As a result, almost 80% of the larger battery subsystem is essentially not used

for the first six years because of an undersized solar array. It should also be noted that though degradation

of the battery and solar arrays are part of the reason for increased depth-of-discharge over the decade, the

ability to recharge before the next discharge period is a more dominant effect.

The four Options for combined solar array/battery systems shown in Fig. 7 are presented in Table 1. For

Option 0, the solar array size is relatively small, but the batteries are much too heavy. For Option 1, the

solar array size is chosen to be near the primary ’elbow’ in Fig. 7. For this case, the batteries still dominate

the overall system mass. Option 2 enlarges the solar array to the maximum diameter allowed (specified

earlier as 9 m). This slightly improves the overall system mass despite a heavier solar array subsystem.

NASA/TM—2009-215506 9
0 10 20 30 40 50

0

200

400

600

800

1000

1200

Solar Array BOL Electrical Power, kW

Total Battery Energy Storage, kWhr

Option 0

Option 1 Option 2

Option 3

Figure 7. Plot of total battery energy storage required for a given solar array size.

2020 2021 2022 202$ 2024 202& 2026 202( 2028 202* 20$0 0

0.2

0.4

0.6

0.8

1

,ear

0attery State

!o6

!7harge

Figure 8. Plot of state-of-charge for the battery subsystem for the entire 2020 - 2030 period. The total battery

energy is 1208 kWhr, the solar array area is 37.0 m2 and the BOL solar array power is 9.9 kW. This system

is Option 0 in Table 1.

NASA/TM—2009-215506 10
2020 2021 2022 2023 2024 2025 2026 202( 2028 2029 2030 0

0.2

0.4

0.6

0.8

1

,ear

0attery State

!o6

!Charge

Figure 9. Plot of state-of-charge for the battery subsystem for the entire 2020 - 2030 period. The total battery

energy is 362 kWhr, the solar array area is 43.6 m2 and the BOL solar array power is 11.7 kW. This system

is Option 1 in Table 1.

Adding another 9 m solar array is shown as Option 3. The battery subsystem is significantly reduced at

the expense of two large solar arrays producing 33.9 kW of BOL power where only 5 kW is required for

the daytime power load, which is probably unrealistic from an outpost perspective. Option 2 is chosen for

further analysis. Figures 10 and 11 show the Option 2 state-of-charge detail for years 2020 and 2029. These

plots show typical years and the changes over the decade for the battery subsystem. Figure 12 shows the

estimated charge and discharge rates for the Option 2 battery subsystem.

Table 1. Options for a Combined Solar Array/Battery System.

Parameter Option 0 Option 1 Option 2 Option 3

Total Solar Array Area (m2) 37.0 43.6 63.6 127

Solar Array Diameter (m) 6.9 7.5 9.0 2x 9.0

Total Solar Array BOL Power (kW) 9.9 11.7 16.9 33.9

Total Battery Energy (kWhr) 1208 362 320 214

Solar Array System Mass (kg) 94 107 147 294

Battery System Mass (kg) 8055 2411 2131 1428

PMAD System Mass (kg) 60 60 60 120

Total System Mass (kg) 8209 2578 2338 1842

The long periods of time spent fully charged may introduce a minor issue of the battery subsystem selfdischarging over these periods. To mitigate this issue, the solar arrays could be expected to trickle charge

the batteries throughout this period, but this would not impact the overall system significantly.

B. Solar Array and Regenerative Fuel Cell System

The approach for the solar array/RFC combination is similar to that of the solar array/battery approach

above. The system behaves in a similar manner, in which the solar array capability has a significant effect

of the energy storage of the RFC. This effect is shown in Fig. 13. The units of energy storage for the RFC in

this paper are moles of hydrogen. Plots similar to Figs. 8 and 9 are shown in Figs. 14 and 15. Comparing

Fig. 14 to Fig. 8, the RFC case shows a greater amount of time with a less than full hydrogen tank. Also,

the slope of the recharge portions of the RFC plot are lower, indicating a lower efficiency compared to the

battery system. The lower efficiency of the RFC requires additional solar array power to maintain a full

hydrogen tank. A larger solar array is used in Fig. 15 and the result is a much better ’state-of-charge’ profile.

NASA/TM—2009-215506 11
01/01 02/01 03/01 04/01 05/01 06/01 07/01 08/01 09/01 10/01 11/01 12/01 0

0.2

0.4

0.6

0.8

1

Month/Day

Battery State

!of

!Charge

Year 2020

Figure 10. Plot of state-of-charge for Option 2 of Table 1 for the year 2020.

01/01 02/01 03/01 04/01 05/01 06/01 07/01 08/01 09/01 10/01 11/01 12/01 0

0.2

0.4

0.6

0.8

1

Month/Day

Battery State

!of

!Charge

Year 2029

Figure 11. Plot of state-of-charge for Option 2 of Table 1 for the year 2029.

Figure 12. Plot of estimated charge and discharge rates for Option 2 of Table 1.

NASA/TM—2009-215506 12
0 10 20 30 40 50

0

5

10

15

20

25

30

35

40

45

50

Solar Array BOL Electrical Power, kW

Total Hydrogen Energy Storage, kmol

Option 0

Option 1 Option 2 Option 3

Figure 13. Plot of total hydrogen energy storage within an RFC system required for a given solar array size.

2020 2021 2022 2023 2024 2025 202' 2027 202) 2029 2030 0

0.2

0.4

0.'

0.)

1

,ear

Hydrogen 7an8 9State

!o<

!Charge9

Figure 14. Plot of hydrogen tank ’state-of-charge’ for the RFC subsystem for the entire 2020 - 2030 period.

The total amount of hydrogen is 85.7 kg, the solar array area is 37.0 m2 and the BOL solar array power is

9.9 kW. This system is Option 0 in Table 2.

NASA/TM—2009-215506 13
2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 0

0.2

0.4

0.6

0.8

1

Year

Hydrogen Tank "State

!of

!Charge"

Figure 15. Plot of hydrogen tank ’state-of-charge’ for the RFC subsystem for the entire 2020 - 2030 period.

The total amount of hydrogen is 16.8 kg, the solar array area is 52.3 m2 and the BOL solar array power is

14.0 kW. This system is Option 1 in Table 2.

This solar array size is chosen to be near the ’elbow’ in Fig. 13 similar to the Option 1 battery case. Option

2 increases the single solar array size to the specified 9 m diameter maximum. The Option 3 RFC system is

similar to Option 3 for the battery case, in which two 9 m diameter solar arrays are used in combination with

the RFC. For the RFC, however, the larger solar arrays are actually detrimental to the overall system mass:

though the fluids and their tanks decrease in mass, the solar arrays, PMAD, and electrolyzer subsystem get

heavier due to the higher power levels. These Options are shown in Table 2.

Table 2. Options for a Combined Solar Array/RFC System.

Parameter Option 0 Option 1 Option 2 Option 3

Total Solar Array Area (m2) 37.0 52.3 63.6 127

Solar Array Diameter (m) 6.9 8.2 9.0 2x 9.0

Total Solar Array BOL Power (kW) 9.9 14.0 16.9 33.9

Solar Array System Mass (kg) 94 125 147 294

Total Hydrogen Mass (kg) 85.7 16.8 16.2 12.8

Total Oxygen Mass (kg) 679 133 128 101

Total Hydrogen Tank Mass (kg) 791 171 166 135

Total Oxygen Tank Mass (kg) 699 153 148 121

Total Fuel Cell Subsystem Mass (kg) 195 195 195 195

Total Electrolyzer Subsystem Mass (kg) 240 240 240 480

Thermal System Mass (kg) 16 16 16 16

PMAD System Mass (kg) 60 60 60 120

Total System Mass (kg) 2860 1110 1116 1475

Figures 16 and 17 show the Option 2 hydrogen tank ’state-of-charge’ detail for years 2020 and 2029.

Option 2 for the RFC system is chosen for comparison with the Option 2 battery system, though the RFC

Option 1 may be a better choice due to its lower mass and smaller solar array. Figure 18 shows the estimated

charge and discharge rates in terms of hydrogen flow rate for the Option 2 RFC subsystem.

NASA/TM—2009-215506 14
01/01 02/01 03/01 04/01 05/01 06/01 07/01 08/01 09/01 10/01 11/01 12/01 0

0.2

0.4

0.6

0.8

1

Month/Day

Hydrogen Tank "State

!of

!Charge"

Year 2020

Figure 16. Plot of hydrogen tank ’state-of-charge’ for Option 2 of Table 2 for the year 2020.

01/01 02/01 03/01 04/01 05/01 06/01 07/01 08/01 09/01 10/01 11/01 12/01 0

0.2

0.4

0.6

0.8

1

Month/Day

Hydrogen Tank "State

!of

!Charge"

Year 2029

Figure 17. Plot of hydrogen tank ’state-of-charge’ for Option 2 of Table 2 for the year 2029.

2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 0

20

40

60

80

100

120

Year

Hydrogen Flow Rate (mol/hr)

Fuel Cell (Discharge)

Electrolyzer (Charge)

Figure 18. Plot of estimated charge and discharge rates in terms of hydrogen flow rate for Option 2 of Table 2.

NASA/TM—2009-215506 15
C. Cycle, Calendar, and Operating Life

Based on the assumption that such a power module would be required to operate over the entire 2020 - 2030

timeframe, one can estimate the number of charge/discharge cycles, operating time, and other requirements

using the above results. Looking at Figs. 10 and 11, there are only a few deep discharges of the battery each

year. For the entire decade, there may nominally be only 40 - 50 significant discharges for the system. There

are about 20 discharges in the 10% - 20% SOC range each year as well. The system is sized for the deep

discharges, but the majority of the time is spent fully charged or at least greater than 80% state-of-charge.

This has good implications for the potential life and reliability of the battery subsystem as well as potentially

greater performance that may be possible from a particular cell.

Figures 16 and 17 show that the number and magnitude of charge/discharge cycles for the RFC case to

be similar to that of the battery case. This is also good for life and reliability of the RFC subsystem since

the cycling of pressure and temperature can be problematic for composite tanks, PEM stacks, and other

components. The thermal cycling is also a reason why higher temperature fuel cells and electrolyzers may

not be ideal for this application.

The modeled operation of the battery, fuel cell, and electrolyzer subsystems in their Option 2 designs is

used to estimate operating life. These values are shown in Table 3. For both the battery discharge and fuel

Table 3. Estimated minimum annual operating time for discharge and charge periods for the Option 2 systems.

Battery Discharge/

Fuel Cell Battery Charge Electrolyzer

Year Operating Time (hr) Operating Time (hr) Operating Time (hr)

2020 1026 290 544

2021 1036 315 589

2022 1032 338 630

2023 1019 360 669

2024 1044 398 739

2025 1043 431 798

2026 1036 466 859

2027 1026 503 924

2028 1014 543 995

2029 1039 611 1116

Total 10315 4255 7863

cell operation, the total operating time of greater than 10,000 hours is high compared to existing systems.

This may either require technology development and/or delivery of additional modules as replacement units.

The battery charge operating time estimate is lower than the electrolyzer operating time, due to the lower

system efficiency of the RFC system. Beyond delivering more modules, the electrolyzer (or battery charge)

operating life requirement could be reduced by adding more solar array power, though this may also increase

the size of the electrolyzer.

Another consideration is calendar life. The energy storage portion of the system only operates for about

17 - 20% of the entire decade if both charging and discharging are included. The system is still exposed

on the lunar surface for the remainder of the time. This idle period may also have implications for system

design and sparing approaches.

D. Sensitivity Analysis

Much of the approach in this paper is an attempt to capture the primary effects of different system designs

with simplified models. One technique to mitigate some of the uncertainty from the models is a sensitivity

analysis of some of the most important variables. This approach can also capture the effect of new technology

such as a higher solar cell efficiency. It can also capture the relative risk of a uncertain estimate such as the

mass fraction of the fluid tanks.

NASA/TM—2009-215506 16
This sensitivity analysis studies the effect of a ±10% variation on the variables shown in Table 4. The

results are shown in Figs. 19 and 20. The baseline cases for the battery- and RFC-based systems are both

Option 2 in Tables 1 and 2, respectively. Some of the most sensitive variables for both systems include

Table 4. Variables used for sensitivity analysis.

Variable Symbol, if applicable

Solar Array Temperature Top

Solar Array Dust Loss

Solar Array Radiation loss

Solar Array Voltage Vmp

Battery Degradation

DC-DC Converter Efficiency

Switching Unit Efficiency

Solar Array Mass per Area m ̄ array

Battery Specific Energy

Maximum Battery Depth-of-Discharge

Fuel Cell Voltage Vcell

Electrolyzer Voltage Vcell

RFC Ancillary Power

RFC Degradation

Hydrogen Mass Fraction mfH2

Oxygen Mass Fraction mfO2

Maximum RFC Depth-of-Discharge

the switching unit efficiency and energy storage depth-of-discharge. The RFC sensitivities appear to be less

than the battery case because the RFC system is more diversified in component mass. The battery specific

energy is important, but for the RFC, several components including the fluid tanks and fuel cell subsystem

significantly impact the overall mass. The switching unit efficiency is important because it imparts a loss to

the energy storage system during both charging and discharging periods. The DC-DC converter is not as

sensitive because it only affects the solar array power to the loads and to charging the energy storage system.

The solar array efficiency (through Vmp) is an important variable because of the effect of higher solar array

power on the energy storage size explained above.

V. Conclusion

Comparing Tables 1 and 2, even with significantly oversized solar arrays, the battery subsystem is heavier

than a reasonably-sized solar array/RFC combination. However, system mass is only one figure-of-merit,

others include life, reliability, and flight experience, for example. This analysis is also based on fixed load

requirements and a single location. Other requirements and locations may change the outcome.

Beyond the mass comparison, this work identifies a relatively low number of cycles and overall depth-ofdischarge profile for both batteries and RFCs. Note that this result is for a stationary system; a mobile system

would most likely have a much higher number of cycles and average depth-of-discharge. The operational

life for the RFC and battery systems in this application are shown to be significant if expected to operate

for the entire decade. This requirement can be mitigated by delivering additional modules throughout the

decade, at the expense of additional mass needing to be delivered to the surface.

This paper also emphasizes the importance of PMAD component efficiency and the need for well-designed

interfaces between the different subsystems. In addition, the solar array size also has a significant impact

on energy storage because of the importance of fully recharging before the next shadowed period. This

implies that the solar arrays will most likely be required to produce much more power than just the daytime

requirement.

NASA/TM—2009-215506 17
!20 !10 0 10 20

Solar Array Temperature

Solar Array Dust Loss

Solar Array Radiation Loss

Solar Array Vmp

Battery Degradation

DC!DC Converter Efficiency

Switching Unit Efficiency

Solar Array Mass per Area

Battery Specific Energy

Max Battery Depth!of!Discharge

% Difference from Baseline

Sensitivity on Total Solar Array/Battery System Mass

+10%

!10%

Figure 19. Sensitivity of solar array/battery system variables on total solar array/battery system mass. The

baseline case is Option 2 of Table 1.

!20 !10 0 10 20

Solar Array Temperature

Solar Array Dust Loss

Solar Array Radiation Loss

Solar Array Vmp

Fuel Cell Voltage

Electrolyzer Voltage

RFC Ancillary Power

RFC Degradation

DC!DC Converter Efficiency

Switching Unit Efficiency

Solar Array Mass per Area

Hydrogen Mass Fraction

Oxygen Mass Fraction

Max RFC Depth!of!Discharge

% Difference from Baseline

Sensitivity on Total Solar Array/RFC System Mass

+10%

!10%

Figure 20. Sensitivity of solar array/RFC system variables on total solar array/RFC system mass. The baseline

case is Option 2 of Table 2.

NASA/TM—2009-215506 18
References

1Rauschenbach, H. S., Solar Cell Array Design Handbook: The Principles and Technology of Photovoltaic Energy Conversion, Van Nostrand, 1980.

2Speech by President George W. Bush, January 14, 2004, available at http://www.whitehouse.gov/news/releases/2004/01/20040114-

3.html.

3”NASA’s Exploration Architecture Study,” NASA-TM-2005-214062, 2005.

4NASA Press Release 06-061, 2006.

5Session 90-STSA-20, AIAA Space 2007, 2007.

6Toups, L., Kennedy, K.J., Tri, T., Smitherman, D., Dorsey, J., ”Lunar Architecture Team-Phase 2 Architecture Option-2

Habitation Concepts.” ASCE Earth & Space Conference 2008, 2008.

7Toups, L., Kennedy, K.J., Gershman, R., Wilcox, B., Dorsey, J., ”Lunar Architecture Team-Phase 2 Architecture Option4 Habitation Concepts.” ASCE Earth & Space Conference 2008, 2008.

8NASA Press Release 08-155, 2008.

9Toups, L., Kennedy, K.J., et al., ”Constellation Architecture Team-Lunar Habitation Concepts,” AIAA Space 2008,

AIAA-2008-7633, 2008.

10NASA Press Release 08-171, 2008.

11Apollo 17 Mission Report, NASA Document JSC-07904, 1973.

12Fincannon, H. J., ”Lunar South Pole Illumination: Review, Reassessment and Power System Implications,” 5th International Energy Conversion Engineering Conference, AIAA 2007-4700, 2007.

13Fincannon, H. J., ”Characterization of Lunar Polar Illumination from a Power System Perspective,” 46th AIAA Aerospace

Sciences Meeting and Exhibit, AIAA 2008-447, 2008.

14Fincannon, H. J., ”Lunar Polar Illumination for Power Analysis,” 6th International Energy Conversion Engineering

Conference, AIAA 2008-5631, 2008.

15Emcore Product Brief, available at http://www.emcore.com/assets/photovoltaics/Emcore BTJ DS May 07.pdf, 2007.

16Cloud, J. D., Mc Intyre, W. B., Van Horne, T. B., ”Surveyor spacecraft system - Surveyor 6 flight performance Final

report,” NASA CR-93495, 1968.

17Larminie, J., Dicks, A., Fuel Cells Systems Explained, John Wiley & Sons, Ltd., 2003.

18Burke, K.A., ”Fuel Cells For Space Science Applications,” NASA TM-2003-212730, 2003.

19NSTS Shuttle Reference Manual, Electrical Power System Section, NASA Document, 1988.

NASA/TM—2009-215506 19
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Analysis of Stationary, Photovoltaic-Based Surface Power System Designs at the Lunar South 

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Freeh, Joshua, E. 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

Combinations of solar arrays and either batteries or regenerative fuel cells are analyzed for a surface power system module at the lunar south 

pole. The systems are required to produce 5 kW of net electrical power in sunlight and 2 kW of net electrical power during lunar night 

periods for a 10-year period between 2020 and 2030. Systems-level models for energy conservation, performance, degradation, and mass are 

used to compare to various systems. The sensitivities of important and/or uncertain variables including battery specific energy, fuel cell 

operating voltage, and DC-DC converter efficiency are compared to better understand the system. Switching unit efficiency, battery specific 

energy, and fuel cell operating voltage appear to be important system-level variables for this system. With reasonably sized solar arrays, the 

regenerative fuel cell system has significantly lower mass than the battery system based on the requirements and assumptions made herein. 

The total operational time is estimated at about 10,000 hr in battery discharge/fuel cell mode and about 4,000 and 8,000 hr for the battery 

charge and electrolyzer modes, respectively. The estimated number of significant depth-of-discharge cycles for either energy storage system 

is less than 100 for the 10-year period. 

15. SUBJECT TERMS

Solar arrays; Fuel cells; Electric batteries; Moon; Lunar base 

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