Evaluation of the Value of the FlexibilityOffered by On-orbit Servicing:

Case of Satellite Upgrade

Carole Joppin∗ and Daniel Hastings†

Space Systems, Policy and Architecture Research Consortium (SSPARC)Massachusetts Institute of Technology

Cambridge, MA 02139

Abstract

Space systems are characterized by a large initialinvestment and 15-20 year design lifetime to increasethe return on investment. No maintenance capabil-ity is available for most space systems. Therefore, thetraditional approach adopted by space systems oper-ators is to build-in reliability in the satellite and toreplace the system in case of obsolescence or failure.This lack of flexibility may translate to risk for theoperator such as risk of system failure, risk of tech-nology obsolescence, risk of commercial obsolescencefor commercial missions or risk of a change in require-ments. Autonomous on-orbit servicing can change thisparadigm and bring flexibility to space systems.The case of satellite upgrade using on-orbit servicingis investigated in the particular example of commercialmissions. A dynamic framework, based on real optionstheory, is used to account for the flexibility offered byon-orbit servicing. The case of a commercial missionunder uncertain revenues is first studied. The effect ofthe upgrade on the revenue stream and the volatilityof the market are two major parameters. The valueof the flexibility can be a significant part of the to-tal value of the project, emphasizing the importanceof dynamic valuation techniques rather than conven-tional valuation techniques such as Net Present Value(NPV). The case of a Geosynchronous Earth Orbit(GEO) communication satellite facing uncertain de-mand with a limited capacity is presented as a morespecific example. Upgrading the solar panels wouldrestore the power level on-board the satellite, thus al-lowing to increase the satellite capacity. Three optionsare embedded in this case: the option to replace, toservice and to abandon the mission. Results on thevalue of the option to abandon are presented for abaseline silicon solar panel satellite with a payload de-signed for end of life power. Future work will focuson comparing a serviceable satellite with traditional

∗Research Assistant, cjoppin@mit.edu†Professor of Aeronautics and Astronautics and Engineering

System Division at MIT, AIAA fellow, hastings@mit.eduCopyright c© 2003 by Carole Joppin. Published by the Ameri-

can Institute of Aeronautics and Astronautics, Inc. with permission.

satellites, satellites with high radiation resistant solarcells and satellites designed for a shorter lifetime.

NomenclatureC CostsD(t) Actual demand at time tDth(t) Forecasted demand at time tGEO Geosynchronous Earth OrbitInP Indium PhosphideLd Solar cell degradation coefficientM(t) Actual revenues at time tMth(t) Forecasted revenues at time tNuser Number of simultaneous usersNPV Net Present Valuepτ (x) Lognormal distribution functionPBOL Power at beginning of lifePEOL Power at end of lifePpay Power available to size the payloadQup Risk-neutral probability in the binomial treer Risk free discount ratetpay Time for which the payload is sizeddt Time step in the binomial treeT Decision pointU UtilityV Value of the missionx Possible value of XX Uncertain parameter driving mission valuedY Variable step size in the binomial tree

α Uncertain parameter driftσ Uncertain parameter volatilityτ Time interval

IntroductionA need for flexibility in space systems

Space projects can be characterized as projects witha large initial investment and small operational costs.Therefore, current trends are to design space sys-tems for 15 or more years of operation. Since nomaintenance, repair or upgrade capability is currentlyavailable for most space systems, the current trendis towards long design lifetime with no possibility to

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American Institute of Aeronautics and Astronautics Paper 2003-6366

Space 200323 - 25 September 2003, Long Beach, California

AIAA 2003-6366

Copyright © 2003 by Carole Joppin. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

physically modify the system once in orbit.Space systems operate in a somewhat uncertain envi-ronment. The lack of flexibility in initial design cantranslate to risk for the operator. Risks are:

• Risk of system failure: The performance of thesystem over a long lifetime is uncertain and fail-ures may occur. A common practice is to eitherbuild redundancy or very high reliability in thesystem to prevent a loss of performance resultingfrom a component failure, leading to added mass,complexity and therefore increased cost of the ini-tial system.

• Risk of technology obsolescence: The time scalecharacterizing the evolution of technologies islikely to be smaller than the lifetime of the satel-lite. Technology obsolescence can have majorconsequences on the level of performance of thesatellite: this in turn could cause threats to mil-itary assets or could, for commercial missions,translate to a loss of market share to competi-tors (satellites newly launched including the moreadvanced technology or new ways of completingthe same mission cheaper).

• Risk of commercial obsolescence: For commercialmissions, the dynamics of the market the satel-lite is serving is highly uncertain and no marketevolution can be predicted 15 years in advance.Demand may drop or increase above predictions,the served market may not exist anymore or newmarkets may have emerged that the satellite isnot able to serve.

• Risk of change in customer requirements: In gen-eral, customer desires may evolve over time. Arigid system will not be able to adapt to varyingcustomer’s requirements.

Three options are currently available for space op-erators: 1) build in redundancy; 2) abandon thesatellite; 3) replace the satellite. Building an on-orbitserviceable satellite is a fourth option that is currentlynot much used. The new approach of autonomous on-orbit serviceable spacecrafts would allow embeddingflexibility in the initial system to adapt to an evolvingenvironment.Flexibility is defined in this work as ”the ability of asystem to adapt and respond to changes in its initialobjectives, requirements and environment occurringafter the system is in operation in a timely andcost-effective manner”.1 Because space systems maybe operating in a highly uncertain environment, thereis a real need for flexibility.

On-orbit servicing: a means to provide flexibility

On-orbit servicing has long been considered as hav-ing the capability of changing the way business is done

in space and providing flexibility to space systems.On-orbit servicing offers the capability to physicallyhave access to the satellite once in orbit, providinga maintenance, repair and upgrade capability. Threemain options are offered by on-orbit servicing in ad-dition to the currently available options to replace orabandon the mission:

• Life extension option: On-orbit servicing allowsextending the operational life of the satellite inits initial design through for example refueling orrepair.

• Upgrade option: On-orbit servicing can be usedto improve the operational system in meeting itsinitial goals.

• Modification option: On-orbit servicing is also ameans to change the mission the system is per-forming to adapt to a change in the market or thecustomer requirements.

On-orbit servicing is a way to allow space operatorsto mitigate risks. Because space systems could bereactive to changes in their environment, uncertaintywould not be a synonym for risk anymore and couldeven be a source of value by taking advantage ofpotential upsides without bearing the downsides.

Background

Many studies have been conducted on the servicingconcept looking both at the technological aspects ofon-orbit servicing (technologies needed to enable ser-vicing,2 servicer design,3 design modifications to makesatellites serviceable4 and servicing infrastructuredesign) and the evaluation of the value of servicing.5

Most cost effectiveness studies were considering theservicing of specific space systems such as the GPSsystem6,7 or satellite constellations.8 The traditionalapproach is to consider a particular space system, todesign a corresponding optimal servicing architectureand then to analyze the value of the on-orbit servicingconcept using net present value calculations. Thosestudies concluded that on-orbit servicing could offersignificant cost reductions but not sufficient to over-come risk and uncertainty in the analysis. However,traditional evaluation methods, such as the netpresent value method, are static and therefore fail tocapture the value of the flexibility offered by on-orbitservicing, which is believed to be a major advantageof on-orbit servicing. A new dynamic evaluationframework has been developed by Lamassoure, Salehand Hastings9 using real options to account for thevalue of flexibility. This framework has been appliedto the analysis of the refuelling operation10 usingon-orbit servicing. The present paper reuses the samemethod to study the value of upgrading satelliteson-orbit.

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Case of satellite upgrade

Upgrading a satellite is of particular interest toprevent technology obsolescence or degrading perfor-mance. Different techniques have been proposed tophysically upgrade a satellite on orbit. In one con-cept, the servicer containing the new modules wouldattach and stay attached to the satellite to be serviced.The modules to be upgraded would be disconnected onthe initial satellite, their functions being performed bythe modules on-board the servicer. Another conceptfavors a modular serviceable satellite in which emptyslots would be built in the initial design. The servicerwould attach the new module in one of the satelliteempty slots. The connection would be switched fromthe old to the new module to offer upgraded perfor-mance.On-orbit upgrading offers three main advantages.First, with regular upgrades, satellites can keep upwith the evolution of technology and limit the risk oftechnological obsolescence. Second, a degradation inperformance can be offset by replacing the degradedmodule. Finally, on-orbit upgrading offers the flexi-bility to tailor the satellite performance with the res-olution of the uncertainty in the customer demand orrequirements.There are still major limitations that must be consid-ered in the evaluation of satellite upgrade via on-orbitservicing. The risk of the servicing operation is a keyelement to the acceptation of on-orbit servicing andwill be very difficult to estimate. It must also be rec-ognized that the scope of the upgrade performed by aservicer is limited since the upgrade must be compati-ble with the initial systems not upgraded. Finally theservicing infrastructure will have an essential impacton the scope of the upgrade and the delays in the de-livery. The newness of the upgrade technology and thedelay to service will depend on whether the modulesare kept in on-orbit depots or launched on demand.

Objective

The objective of the present study is to evaluate thevalue of upgrading via on-orbit servicing from the cus-tomer’s point of view, taking into account the value ofthe flexibility. Three main questions are studied: 1)When is on-orbit servicing valuable, in particular com-pared to the current replacement option?; 2) What isthe actual value of the flexibility offered by on-orbitservicing?; 3) What are the main parameters affectingthe value of on-orbit servicing?. The framework usedand how it was applied to the upgrade of commer-cial missions is described briefly in the first section(more details about the framework can be found inreference9). Then, first insights on the upgrade of com-mercial missions under uncertain revenues are derived.Finally, the more precise example of the upgrade ofthe power system on-board a GEO communicationsatellite to compensate for solar cells degradation is

Fig. 1 Customer and provider points of view inthe evaluation of the value of on-orbit servicing.

analyzed: servicing is compared to other options suchas replacing the satellite, designing the payload for endof life power or initially building-in high radiation re-sistant solar cells.

Framework OverviewThe rationale for choosing the framework developed

by Lamassoure, Saleh and Hastings over traditionalevaluation methods such as NPV is first presented be-fore explaining briefly the basic principles and generalbuilding blocks of the method that will be common tothe two studies presented in the following sections.

Framework Principles

Two main principles have driven the choice of thismethod as the preferred analysis framework:

Separate value from costThe cost of servicing is difficult to evaluate because

cost estimation relations are highly uncertain and theprice of the servicing operation may be different fromthe cost of the servicing infrastructure. Therefore thisevaluation uses the cost of servicing as a separate vari-able to carry out the evaluation. The value of on-orbitservicing is calculated from the customer side by con-sidering potential cost savings and the value of theflexibility for the customer. Using this approach, anupper bound on the price the customer would be will-ing to pay for servicing is determined. The analysis onthe provider’s side then uses this information to deter-mine if a valid and profitable servicing infrastructurecan be developed. This concept is illustrated in Fig-ure 1. In addition, keeping the cost of servicing asa separate variable allows one to develop an analysisindependent from any servicing infrastructure so thatgeneral results can be found for the intrinsic value ofon-orbit servicing.

Dynamic strategy to account for flexibilityIn the analysis, the value of the space mission con-

sidered depends on an uncertainty parameter. It couldbe market demand for example. On-orbit servicing al-lows the satellite to be accessed after the system hasbeen fielded, at time T . The value of the flexibilitycomes from the fact that the decision to alter or not thesatellite can be delayed: the satellite operator can usethe additional information gained during this period

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on the resolution of the uncertainty parameter to takea better decision. Therefore, the value of the flexibilitycannot be taken into account in a static framework, inwhich the sequence of decisions concerning the satel-lite are set at the beginning of the lifetime. It mustbe noted that in the case of satellite upgrade the deci-sion at T is constrained by the design decisions madefor the initial satellite and the degree of serviceabilityand upgradability incorporated in the initial design.The chosen framework uses real options to create adynamic strategy that accounts for the fact that theoperator will take at each point in time the optimaldecision that maximizes future value.

Framework Description

This section defines the basic building elements ofthe framework as applied to the upgrade case and de-scribes the method of evaluation. The model has beenadapted to study the upgrade of commercial satellites.

Uncertainty parameter X ”In a world of certainty,flexibility has no value”.1 To evaluate the value of theflexibility, it is assumed that the value of the missiondepends on an uncertainty parameter X. This firstanalysis focuses on commercial applications with un-certain demand or revenues. The distribution chosento characterize this uncertainty is the geometric ran-dom walk process with drift α and volatility σ, whichis a typical assumption to describe stock options andmarket dynamics.11

Decision points A decision point is a point in timeat which a decision on the system configuration canbe made and a mode of operation is chosen for thesystem over the next periods until the next decisionpoint. In the current study, only one decision point Tis considered during the lifetime of the satellite.

Mode of operations A mode of operation is a pos-sible state of the system resulting from a decision ofthe operator. For the case of satellite upgrade, threemodes of operation are made available: (1) system inits initial state with no alteration to the satellite; (2)upgraded system after having chosen to service thesatellite; (3) upgraded system after having chosen toreplace the satellite.

Utility U The utility measures the benefit for thecustomer. In the commercial case, utility is synonymto revenues generated by the satellite.

Costs C Costs represent all the expenditures asso-ciated with the mission. A matrix of switching costis defined that corresponds to the costs incurred bythe decision to switch from one state to another. Inthe model, the cost of the servicing operation refers tothe price a customer would pay to a provider to get asatellite serviced. It does not include insurance costsor costs to design the satellite for serviceability.

Value V The value metric is a function of the typeof mission studied. In the specific case of commercialmissions, the value is defined as the difference between

revenues and costs.

Analysis process A distribution is defined to de-scribe the evolution of the uncertainty parameter withtime. The uncertainty is propagated over the lifetimeof the mission: at each point in time, a list of po-tential values of X with its associated probability ofoccurrence is derived. In particular, a distribution ofthe potential values of X at the decision point T isobtained. For each possible value of X, and for eachpossible decision made at T , the value of the missionover the rest of the lifetime is calculated. It is as-sumed that the operator will make at T the decisionthat maximizes the future value of the mission. Ap-plying this rule, the optimal decision is determined foreach possible value of X at T . This defines a strategythat dictates the optimal decision to take dependingon the value of the uncertainty parameter observed atthe time of the decision. The expected value of themission is then derived based on the assumption thatthe optimal decision is made at T . The value of theflexibility is the difference between this expected valueand the value of the mission for a static, unchangeableor not upgraded, strategy. The process is discretizedand the evolution of the uncertain parameter is repre-sented in a tree called the binomial tree. Risk neutralprobabilities are used for the evaluation instead of realprobabilities in order to use the risk free rate to dis-count revenues and costs.

Assumptions included in the model The model as-sumes a pre-launch operations of 2 years.12 Satelliteand launch costs are spread evenly over the pre-launchoperations period. Calculation of the profits include a40% corporate tax rate on revenues as commonly usedin industry.12 Satellite costs are depreciated over thelifetime of the satellite. It is assumed that the servicingoperation is done in the same period as the decision ismade (within 6 months after the decision) and there-fore impacts the revenues and costs of the period inwhich the decision is made. The impact of the de-lay in the servicing operation is not considered. Forthe replacement option, a 2-year pre-launch period isalso assumed: revenues are impacted by the upgradeonly 2 years after the decision is made and replacementcosts are spread over the 2-year period following thedecision point. Risk is taken into account through in-surance payments and the expected value is modifiedto take into account the risk of failure as illustratedin Figure 2. Insurance payments are calculated as theproduct of the probability of catastrophic failure of theoperation and the amount insured that would be paidout in case of failure. Catastrophic failure leads to theloss of the satellite. In the case of servicing, all furtherrevenues are lost since the only vehicle is lost. In thecase of the replacement option, the replacement satel-lite is lost but it is assumed that the initial satellite isstill in operation providing revenues.

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Fig. 2 Decision tree used in the analysis.

Mission Under Uncertain RevenuesFirst, the specific assumptions considered in this

model are discussed. In particular, the definition ofthe uncertainty parameter, the effect of the upgradeas modeled in this study and the options made avail-able to the operator are detailed. Some of the resultsand conclusions are then presented.

Assumptions

Uncertainty parameter We consider a commercialmission under uncertain revenues. The actual rev-enues, M(t), differ from the forecasted revenues,Mth(t) because of uncertainty in the market. We de-fine the uncertainty parameter X as the ratio of theactual revenues over the forecasted revenues:

X =M(t)

Mth(t)(1)

As defined, the uncertainty can be considered as exter-nal, meaning independent of the decisions taken by theoperator. X is further assumed to follow a geometricrandom walk process with drift α and volatility σ as itis often chosen in real options theory. Therefore, theprobability density function of X(t+τ)

X(t) is given by:

pτ (x) =exp

[− [ln(x)−(α−σ22 )τ ]2

2σ2τ

]

xσ√

2πτ(2)

This distribution is illustrated in Figure 3. From thisdistribution, the step size dY and the real probabilityof an upwards step in the binomial tree are derived inorder to reproduce the mean and variance of the dis-tribution. The risk-neutral probability of an upwardsstep Qup is then derived:

Qup =1 + r − exp(−dY )

exp(dY )− exp(−dY )(3)

dY being given by:

dY =√

σ2dt + (αdt)2 (4)

where r is the risk free rate, dY the step size in thebinomial tree, σ the volatility of the distribution, αthe drift of the distribution and dt the time step inthe binomial tree.

Fig. 3 Evolution of the uncertainty parameterX over time with the assumption of a geometricrandom walk process.

Effect of the upgrade When deciding to service thesatellite, the operator expects the upgrading operationto lead to an increase in revenues. The effect of theupgrade is therefore modelled as an increase in theforecasted revenues. Since the uncertainty is linked tounpredictable changes in the market and is externalto the operator decision, the same uncertainty appliesto revenues generated after the upgrade and the un-certainty parameter is not affected by the upgrade.The amount by which the upgrade can increase theforecasted revenues depends on which module of thesatellite is upgraded and what is the impact of thismodule on the mission performed by the satellite. Theserviceable satellite is supposed to be modular and amodule corresponds to a part of the satellite that canbe switched or added during a servicing operation. Inthis section, the satellite mission and the type of up-grade are not specified and the amount by which theforecasted revenues increase after an upgrade are leftas a parameter.

Options considered In this study, the operator isfaced with three possible decisions: 1) no alteration ofthe satellite; 2) servicing the satellite; 3) replacing thesatellite. The satellite can be in three possible states:1) Initial state; 2) upgraded state after the servicingoption has been chosen; 3) upgraded state after thereplacement option has been chosen.

Other assumptions In this section, we assume thatthe spacecraft is initially designed to be serviceableindependently of the decision taken later on at the de-cision point. In a later study, the impact of designingfor serviceability will be investigated. The insurancepayments are calculated as explained in the frame-work overview with the following assumptions on theamount insured. In the case of a satellite launch (ini-tial and replacement launch) the amount insured is the

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cost of the satellite launched. In the case of a servic-ing operation, the amount insured is the sum of thedepreciated value of the satellite at the time of the de-cision and the loss of revenues over the rest of the lifeof the satellite calculated on the basis of the forecastedrevenues.

Results

Dynamic strategy The framework used is dynamicand determines an optimal strategy rather than con-sidering a strategy set in advance at the time of launch.The optimal decision to make at T depends on theresolution of the uncertainty at T . Figure 4 illustratesthis concept and shows an example of an optimal strat-egy. The optimal decision is shown depending on thecost of servicing and the value of the uncertainty pa-rameter at T . The assumptions used in this calculationare summarized in Table 1. For this figure, the up-grade is assumed to increase forecasted revenues by a100%. Up to a cost of $100 million for the servicingoperation, upgrading is always the best solution in-dependently of the uncertainty parameter. For a costof servicing higher than $100 million, when actual rev-enues are far lower than the forecast, an upgrade is notdesirable. In those cases, the actual added revenuespotentially generated by the upgrade do not offset thecost of the servicing or replacement operation, includ-ing insurance costs. In the case shown in Figure 4, acost of servicing of $100 million and insurance costs forthe servicing operation are higher than the potentialextra revenues obtained by upgrading for low values ofX.On-orbit servicing appears more appealing than thereplacement option for lower cost of the servicing op-eration and for higher values of the uncertainty param-eter. For cost of servicing below $100 million, the costof servicing is a lot smaller than the cost of replacingthe satellite: therefore the best method to upgrade isalways on-orbit servicing. For costs of servicing above$200 million, the cost of servicing is so much higherthan the cost of replacing that the replacement optionis more attractive. In between those two zones, thechoice of the upgrade method depends on the valueof X at T . The replacement option is less expensivewhen taking into account the cost of servicing and in-surance costs for the servicing operations. However,upgraded revenues are only earned two years after thedecision is taken. For low value of X, two additionalyears of increased revenues do not offset the added costincurred by servicing; for high values of X, two yearsof added revenues makes on-orbit servicing more ap-pealing. This example illustrates the importance of anevaluation using a dynamic program that accounts forthe fact that an operator will use all the informationavailable at the time of decision to make an optimalchoice. The higher reactivity offered by on-orbit ser-vicing is an advantage over the replacement option.

Parameter ValueSatellite initial cost $95 M

Satellite lifetime 15 years

Operation costs 10% of expected revenues

Launch cost $97.5 M

Launch preparation period 2 years

Launch failure 15%

Decision time 2 years after launch

Upgraded module cost $2 M

Servicing failure 10%

Initial revenues w/o upgrade $52 M

Revenues drift 5.39%

Revenues volatility 10%

Discount rate 5.39%

Table 1 Assumptions used in the calculations forthe analysis of the upgrade of a satellite under un-certain revenues.

Fig. 4 Example of the determination of a dynamicstrategy in which the optimal decision at T de-pends on the value of the uncertainty parameterobserved.

Value of the flexibility The expected value of themission, assuming the optimal decision is made at T ,is shown in Figure 5 for the same assumptions shownin Table 1. The effect of the upgrade on forecastedrevenues is now considered as a variable. The valueof the upgrade option is the difference between themission value and the value of a mission for whichupgrade is never used, shown here as a 0% increase inforecasted revenues after upgrade. The value of theoption is a significant part of the value of the mission:for a 50% increase in forecasted revenues after upgrade,the option value amounts to almost 40% of the missionvalue with almost $130 million for a total mission valueof $330 million.

Servicing cost In Figure 5, the servicing cost atwhich the mission value flattens is the maximum ser-vicing cost for which on-orbit servicing is ever chosen.The maximum cost of servicing as previously defined

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Fig. 5 Total expected value of the mission dis-counted to 2 years prior to launch depending onthe cost of the servicing operation and the increasein forecasted revenues from the upgrade.

can be used as the maximum price a customer wouldbe willing to pay to have the satellite serviced and canbe useful to a potential provider when establishing theconditions of a profitable on-orbit servicing infrastruc-ture.

Effect of the upgrade on forecasted revenues The ef-fect of the upgrade is a major parameter in the studyof the value of upgrading a satellite. Figure 6 repre-sents the same data as Figure 5 shown on a differentperspective. The top of the bars corresponds to a zeroservicing cost and the bottom to a $350 million servic-ing cost. It can be noticed that a minimum increasein the forecasted revenues is required to make ser-vicing desirable because of risk and insurance costs.Low increases in revenues after upgrade (values cir-cled on Figure 6) do not overcome the insurance andupgrade development costs. Even for a zero-cost ser-vicing operation, risk will be a significant hurdle to thedevelopment of on-orbit servicing.

Volatility The volatility of the market is a key pa-rameter in the evaluation of the flexibility. Flexibilityhas no value without uncertainty since one can pre-dict what will happen and plan in advance for it. Thehigher the level of uncertainty, the higher the poten-tial upsides and downsides and therefore the higher thevalue of the flexibility to be able to take advantage ofthe new opportunities and protect against risk. Figure7 shows the same calculation as Figure 6 for a highervolatility of 50%. The mission value for a zero servic-ing cost has not been much modified by the volatilitybut the mission value for high servicing costs greatlyincreases when volatility increases. This is due to thefact that a higher volatility means that the market may

Fig. 6 Evolution of the expected value of the mis-sion depending on the effect of the upgrade on theforecasted revenues.

Fig. 7 Effect of the volatility on the expected valueof the mission.

offer a wider span of possibilities and therefore higherpotential upsides. Therefore the customer will be will-ing to pay a higher cost to upgrade the system if theresolution of the uncertainty seems to point towardshigh revenues.

Conclusion

The model of a commercial satellite under uncertainrevenues gives some insight on the critical parametersfor the analysis of on-orbit servicing. The risk of theservicing operation and the effect of the upgrade onthe satellite revenues appear as critical factors in thevaluation. The value of the flexibility seems to accountfor a large part of the value of on-orbit servicing, whichjustifies the use of a dynamic program in this analysis.There are three main limitations to this model. First,the impact of serviceability on the cost of the initialsatellite has not been explored in this model and willbe an important factor to investigate. Second, it isassumed that there is no limitation on the level of

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revenues the satellite can generate, implicitly assum-ing that any level of demand can be satisfied by thesatellite. The capacity limitation of the commercialsatellite has to be taken into account for more realis-tic results. Finally, the effect of the upgrade on thesatellite is key and should be refined. A more techni-cal model of the upgrade and how it affects the initialsatellite is needed in order to get a better estimation ofthe impact on revenues, on the cost of the initial satel-lite and on the development cost of the upgrade. In thenext section, a more detailed example will be studiedconsidering a power system upgrade on a GEO com-munication satellite. This example tries to account forsome of the first model limitations identified and con-siders the cost to design for serviceability, a limitedsatellite capacity and a more refined evaluation of theeffect of the upgrade on the stream of revenues.

Mission Under Uncertain Demand:Power Subsystem Upgrade

As solar cells degrade, satellite power declines overtime. Power is a key element and this degradationhas major consequences on the satellite mission. Forexample in commercial satellites, current communi-cation satellite payloads are designed for end of lifepower levels to ensure a constant capacity and there-fore may not fully utilize the power generated on-boardat beginning of life. The example of upgrading solarpanels on GEO communication satellites has been cho-sen as a potential mission for on-orbit servicing. Theupgrade operation would attach new sections on thesolar panels to compensate for the degradation of ini-tial solar cells and restore the beginning of life power.This in turns allows the payload to be designed fora higher power level and would increase the capacityof the communication satellite as illustrated in Figure8. This study aims at evaluating if the increase in ca-pacity generated by this process would be sufficient tooffset the costs of on-orbit servicing for a GEO com-munication satellite facing an uncertain demand. Theservicing option is compared to other potential solu-tions such as building-in high radiation resistant solarcells in the initial design or replacing the satellite. Theassumptions used for this analysis are first describedbefore presenting some of the conclusions of the study.

Assumptions

Uncertainty parameter The uncertainty in the mar-ket is modeled as an uncertain demand for the commu-nication satellite. The forecasted demand is referredto as Dth(t) and the actual demand as D(t). The un-certainty parameter is defined as:

X =D(t)

Dth(t)(5)

As for the study of a commercial mission under un-certain revenues, X is further assumed to follow a

Fig. 8 Increase in capacity due to servicing thesatellite to compensate for solar cells degradationalong the satellite lifetime.

random walk process with drift α and volatility σ.X(t+τ)

X(t) follows that same distribution characterized bythe density function shown in Equation 2.

Effect of the upgrade The upgrade will restore thebeginning of life power level on-board the satelliteby adding solar panel sections to compensate for thepower degradation. Unlike in the previous section, theupgrade does not directly affect the revenues but in-creases the capacity of the satellite. Depending on thelevel of demand seen on the market served by the satel-lite, the revenues will or will not be impacted by theupgrade. Revenues are defined as the maximum of theactual demand and the capacity of the satellite:

U = max(capacity, D(t)) (6)

Options considered Five different architectures arecompared by the model to compare various types ofsolar cells with different degradation coefficients andvarious patterns of payload sizing. Baseline 1 repre-sents a state of the art Silicon-solar cells satellite witha payload sized for end of life power. Baseline 2 is avariant of Baseline 1 that uses high radiation resistantInP solar cells. Baseline 3 corresponds to the samesatellite as Baseline 1 for which the payload is sizedfor the power level reached at the decision point T .All baseline satellites can be abandoned or replaced atT but no servicing operation can be performed. Theserviceable architecture corresponds to a satellite de-signed with state of the art Silicon solar cells and witha payload sized for the power level reached at T . It isthe only architecture that offers the option of a servic-ing operation. The last architecture corresponds to aSilicon solar cells satellite designed for a shorter life-time (T years) that can possibly be replaced at T . Thecharacteristics of the five architectures are summarizedin Table 2.

Baseline 1, 2 and 3 are static architectures that donot offer the flexibility of an upgrade. For those ar-chitectures for which servicing or replacement are notviable options, only two decisions are offered to theoperator: 1) do not alter the system; 2) abandon themission. Two states of the system are therefore vi-able: 1) initial state of the system; 2) non operational

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Architectures Baseline 1 Baseline 2 Baseline 3 Service/replace Replace

CharacteristicsSat Life 15 years 15 years 15 years 15 years T years

Solar Cell Type Si InP Si Si Si

Time for sizing payload EOL EOL T T T

Serviceability No No No Yes No

Replacement available Yes Yes Yes Yes Yes

Decisions availableStatus quo Yes Yes Yes Yes Yes

Abandon Yes Yes Yes Yes Yes

Service No No No Yes No

Replace Yes Yes Yes Yes Yes

Table 2 List of the architectures considered in the power subsystem upgrade model.

state. For the servicing and replacement architectures,the two previous decisions are still available to the op-erator. The replacement architecture offers a thirddecision which is to replace the satellite. The servic-ing architecture finally adds the possibility to servicethe satellite to the possibility of replacing the satellite.Therefore three states are possible for the replacementarchitecture: 1) initial state; 2) non-operational state;3) upgraded state after having chosen to replace thesatellite. The servicing architecture adds to those afourth state, which is the upgraded state after havingchosen to service the satellite.

Capacity calculation The capacity of the satellitehas a major importance in the evaluation of the valueof the upgrade. The capacity, defined as the num-ber of billable minutes per year a satellite can offer, iscalculated from the power available for the payload us-ing a model adapted from a LEO constellation modelderived by Chang.13 The model uses a MF-CDMAmultiple access technique with a Viterbi modulationcode and QPSK phasing. The process is as follow:

(1) The initial capacity is calculated from the satellitepower for which the payload is sized. It is assumedthat 60% of the satellite power is allocated to thesatellite bus. The power Ppay used to calculatethe capacity is therefore:

Ppay = PBOL ∗ (1− Ld)tpay ∗ 0.4 (7)

where PBOL represents the satellite power at be-ginning of life, Ld the degradation coefficient ofthe solar cells and tpay the time for which thepayload is sized. This power is then used as aninput to the communication model that outputsthe number of simultaneous users the satellite canhandle. The number of billable minutes is thencalculated as:

Capacity = Nuser ∗ 365 ∗ 24 ∗ 60 (8)

where Nuser corresponds to the number of simul-taneous users a satellite can handle.

(2) The capacity is constant until tpay is reached. Iftpay corresponds to the end of life of the satel-lite, the capacity of the satellite will be constantover its lifetime. If tpay is smaller than the satel-lite lifetime, the capacity will start to decreaseprogressively. The model calculates at each pe-riod the new degraded satellite power, the poweravailable for the payload and the new number ofsimultaneous users the satellite can handle usingthe same process as in (1).

(3) If the architecture offers the possibility of an up-grade and the upgrade is chosen at T , the powerwill be restored to PBOL and the capacity will beback to the initial capacity for a period of tpay.The same process is iterated after a period of tpay.

Satellite and upgrade costs The satellite cost hasbeen tailored to the architecture to take into accountthe fact that satellite costs depend on the design life-time, high resistance solar cells are more expensivethan regular solar cells and designing for serviceabilityhas a cost since it requires a change in the satellite de-sign to add modularity. The model used to derive themass of the baseline satellite depending on the chosendesign lifetime is adapted from the work of Saleh.1 Us-ing a Cost Estimation Relationship based on mass, anestimation of the cost is derived. The solar panels areevaluated separately: the surface of the solar panel isderived from the efficiency of the solar cells used andPBOL. A cost14 of $100,000 per m2 is assumed forregular solar panels. No precise data on the cost ofInP solar panels could be found so the cost of InP istaken as a percentage increase with respect to regularsolar cells. This parameter will be varied. The cost ofthe upgraded module placed on the servicer is derivedas the cost of the added section of solar panels nec-essary to compensate for the degradation and restorethe beginning of life power.

Other assumptions The insurance payments are cal-culated as explained in the framework overview withthe following assumptions on the amount insured. In

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the case of a satellite launch (initial and replacementlaunches) the amount insured is the cost of the satel-lite launched. The satellite launched is assumed to beidentical to the initial satellite. In the case of a ser-vicing operation, the amount insured is the sum of thedepreciated value of the satellite at the time of thedecision and a compensation for the loss of revenuesoccurring over the rest of the life of the satellite. Thecompensation for the loss of revenues is based on thecapacity at end of life and corresponds to the revenuesthat would have been generated over the rest of thelifetime if the capacity at end of life had been entirelysold.

Results

Implication of a limited capacity assumption Themain difference characterizing this model is the dis-symmetry introduced by the capacity limitation. Inthe previous case of a mission under uncertain rev-enues, it is implicitly assumed that any level of demandcan be satisfied. When considering the limited capac-ity case, the operator cannot fully take advantage ofthe upsides because of its limited capacity, while stillbeing faced with the downsides. Therefore, the projectvalue without any option is decreasing with volatility.

Abandon option The first option embedded in themodel is the option to abandon the project at T ifit is no longer profitable. The value of the abandonoption for the Baseline 1 architecture is shown in Fig-ure 9 for different levels of volatility. As expected,the abandon option is more valuable as volatility in-creases: the higher the uncertainty, the higher therisks and the higher the value of the flexibility thatallows to partially protect against the risks of uncer-tainty. The value of the abandon option finally reachesa plateau. The value of the option cannot exceed themaximum losses it allows to protect against. The max-imum losses correspond to the operation costs from thedecision time until the end of the satellite lifetime (dis-counted back to 2 years prior to launch). For the samevolatility, the value of the abandon option is lower asthe initial demand increases, as illustrated in Figure10. This can be explained by the fact that the opera-tion costs are fixed and as the initial demand increases,the revenues generated for a given value of the uncer-tainty parameter X increase. Therefore, at a fixedvolatility, for a higher initial demand, the range of theuncertainty parameter for which the mission is aban-doned and the losses are reduced. The value of theabandon option still reaches the same plateau value athigh volatilities.

Future work The servicing option will be studiedseparately to analyze the dependence on volatility, ini-tial demand level and initial power of the satellite. Theoptimal architecture to choose will also be studied de-pending on the conditions of the market in order toget insight on when on-orbit servicing is valuable.

0 0.5 1 1.5 2 2.5 30

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40Expected value of the option to abandon for Baseline 1

Volatility [%]

Exp

ecte

d o

pti

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val

ue

[$M

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Fig. 9 Expected value of the abandon option cal-culated for the baseline 1 architecture for differentlevels of volatility.

0 0.5 1 1.5 2 2.50

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Expected value of the abandon option for different levels of initial forecasted demand

Volatility

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$250M/year$350M/year$500M/year$750M/year$1000M/year

Fig. 10 Value of the abandon option calculatedfor the baseline 1 architecture for different levels ofvolatility and for different levels of initial demand.

Conclusion and Future Work

Conclusion The framework developed by Lamas-soure, Saleh and Hastings9 has been adapted tostudy the case of satellite upgrade. This frameworkallows accounting for the value of flexibility by usingdynamic programming and gives general insights onthe intrinsic value of on-orbit servicing by separatelyconsidering customer and provider.The case of a commercial mission with uncertainrevenues has been investigated. The main parametersaffecting the value of on-orbit servicing in this modelare the effect of the upgrade on revenues, the volatilityof the market, the cost, the reactivity and the riskof the servicing operation. The value of flexibilityaccounts for a large part of the value of the project

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in some cases emphasizing the advantages of dynamicvaluation techniques over traditional NPV methods.The value of on-orbit servicing for commercial satelliteupgrades depends largely on the effect of the upgradeon the satellite revenues. A more precise examplehas been chosen to quantify the effect of a technicalmodification on-board the satellite on the revenuestream. The case of the upgrade of the solar panelsof a GEO communication satellite has been modeled.The upgrade operation restores the beginning of lifepower and may allow increasing the satellite capacity.

Future work First, the power upgrade example willbe studied thoroughly. The value of the different op-tions to abandon, service or replace will be analyzed.The conditions for which on-orbit servicing appearsvaluable in comparison to other options will be deter-mined. The same example will be studied for multipledecision points: the effect of the time of decision andpotential successive satellite upgrades over the satel-lite lifetime will be investigated. The framework willthen be used to investigate other cases such as mili-tary missions or unpredictable events such as failuresor competitor entries.

Acknowledgments

This research is supported by DARPA Orbital Ex-press and the Air Force Research Laboratory (AFRL).The authors would like to thank Charlotte Gerhartand Major Jim Shoemaker for their help and supportin this research.

References1Saleh, J., Weaving Time Into System Architecture: New

Perspectives On Flexibility, Spacecraft Design Lifetime, AndOn-Orbit Servicing, Phd thesis, Massachusetts Institute ofTechnology (MIT), Cambridge, MA, June 2001.

2Chato, D. J., “Technologies For Refueling SpacecraftOn-Orbit,” AIAA paper 2000-5107, presented at the AIAASpace 2000 Conference and Exposition, Long Beach, California,September 2000.

3Lengyel, A., “Design Of A Small Spacecraft To PerformOn-Orbit Servicing Tasks,” AIAA paper 2001-4528, presented atthe AIAA Space 2001 Conference and Exposition, Albuquerque,New Mexico, August 2001.

4Reynerson, C. M., “Spacecraft Modular Architecture De-sign For On-Orbit Servicing,” AIAA paper 99-4473, presented atthe Space Technology Conference and Exposition, Albuquerque,New Mexico, September 1999.

5Reynerson, C. M., “Spacecraft Servicing - First OrderModel For Feasibility And Cost Effectiveness,” AIAA paper2001-4732, presented at the AIAA Space 2001 Conference andExposition, Albuquerque, New Mexico, August 2001.

6Leisman, G., Wallen, A., Kramer, S., and Murdock, W.,“Analysis And Perliminary Design Of On-Orbit Servicing Ar-chitectures For The GPS Constellation,” AIAA paper 99-4425,presented at the Space Technology Conference and Exposition,Albuquerque, New Mexico, September 1999.

7Hall, E. K. and Papadopoulos, M., “GPS Structural Mod-ifications For On-Orbit Servicing,” AIAA paper 99-4430, pre-sented at the Space Technology Conference and Exposition,Albuquerque, New Mexico, September 1999.

8N. Davinic, S. Chappie, A. A. J. G., “Spacecraft Mod-ular Architecture Design Study: Cost Benefit Analysis of On-Orbit Satellite Servicing,” IAF 48th International AstronauticalCongress (IAA-97-1.4.07), Turin, Italy, October 1997.

9Saleh, J., Lamassoure, E., and Hastings, D. E., “Space Sys-tems Flexibility Provided By On-Orbit Servicing: Part I,” AIAApaper 2001-4673, presented at the AIAA Space 2001 Conferenceand Exposition, Albuquerque, New Mexico, August 2001.

10Saleh, J., Lamassoure, E., and Hastings, D. E., “SpaceSystems Flexibility Provided By On-Orbit Servicing: Part II,”AIAA paper 2001-4631, presented at the AIAA Space 2001Conference and Exposition, Albuquerque, New Mexico, August2001.

11Trigeorgis, L., Real Options: Managerial Flexibility andStrategy in Resource Allocation.

12McVey, M. E., Valuation Techniques for Complex SpaceSystems: An Analysis of a Potential Satellite Servicing Market,Master’s thesis, Massachusetts Institute of Technology (MIT),Cambridge, MA, June 2002.

13Chang, D., d. W. O., “Basic Capacity Calculation Methodsand Benchmarking for MF-TDMA and MF-CDMA Communi-cation Satellites,” AIAA paper , presented at, 2003.

14Elbert, B. R., The Satellite Communication ApplicationsHandbook .

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