Optimal timing of the US breeder

Download Optimal timing of the US breeder

Post on 21-Jun-2016

218 views

Category:

Documents

4 download

TRANSCRIPT

  • Optimal timing of the US breeder

    Richard G. Richeis and James L. Plummer

    Optimal timing of the introduction of the FBR is very sensitive to factors such as the availability of l ow-cost u ran ium, fu ture energy demands and the possibility of the introduction of yet more advanced technology. To a lesser extent i t is also sensitive to the relative cap i ta l costs of fast breeder and thermal nuclear plants. The relationship between R & D costs and the programme t im ing is a lso cruc ia l in deciding opt imisat ion .

    Richard G. Richels is a member of the technical staff, Electric Power Research Institute, and James L. P lummer is Ch ie f Corporate Economist, Occidental Petro leum Corporat ion, USA.

    This study was completed while the authors were affiliated, respectively, to Harvard University and the National Science Foundation. The views expressed in this paper do not necessarily reflect the positions of either of those institutions or the organisations to which the authors are currently affiliated.

    The authors wish to thank Alan Manne for making the ETA model available to this study, and for his helpful comments on an earlier version of this paper.

    'General Accounting Office, Costs and Schedule Estimates for the Nation's First Liquid Metal Fast Breeder Reactor Demonstration Power Plant, RED-75- 358, May, 1975. 2 Atomic Energy Commission, Liquid Metal Fast Breeder Reactor, Proposed Final Environmental Statement, WASH- 1535, US Government Printing Office, Washington, DC, December, 1974.

    In the mid-1960s, the Atomic Energy Commission (AEC) selected the liquid metal fast breeder reactor (LMFBR) as its highest priority reactor development programme. In January 1975, the Energy Research and Development Administration (ERDA) came into being, and assumed responsibility for the AEC's former research and development functions, including those associated with the LMFBR programme. After reviewing the AEC's position, the Administrator of ERDA committed that agency to continuing the research, development and demonstration of the LMFBR concept. Despite large increases in federal spending on coal, geothermal, solar, and fusion R & D, roughly one-third of the ERDA budget for FY 1976 went to the LMFBR. The $492 million allocated to the LMFBR represents the largest expenditure for any single civilian R & D project. Moreover, according to a GAO report, more than $10 billion will be needed to carry the programme through to planned completion in 2020. j

    Proponents point to the LMFBR's potential for extending the supply of low-cost uranium. Today, oil and gas furnish nearly 80% of our energy needs. If we are to free ourselves from dependence on insecure and expensive foreign sources of energy, it will be necessary to reduce our dependence on oil and gas by conservation and by shifting to coal and nuclear fuels.

    The long-term advantages of nuclear fission may be severely constrained, however, unless improvements can be made in the efficiency of uranium use. With currently available nuclear reactors, we are able to take advantage of only 1-2% of the energy potential of uranium. This is because the light water reactor (LWR) only uses the relatively scarce uranium-235 isotope present in natural uranium. If LWRs were the only type of reactors available in the future, they could possibly use all our currently estimated low-cost uranium resources within the next 30-50 years.

    Breeder reactors offer .the largest opportunity for uranium conservation. When breeder reactors convert the abundantly available uranium-238 to plutonium-239, more plutonium is created than is fissioned. In this way breeders would be able to utilise more than 60% of the thermal energy available in uranium. No other nuclear alternative can have such an impact on long-term uranium availability.

    Among the various breeder concepts, the AEC chose the LMFBR for priority treatment because of 'its predicted performance, existing industrial support, established base of technological experience, and proven basic feasibility'. 2 The LMFBR is also being developed on this

    106 ENERGY POLICY June 1977

  • 3 The model used in this study differs from ETA as described in A.S. Manne, 'ETA: A model for energy technology assessment,' Bell Journal of Economics and Management Science, Autumn, 1976, in that it provides the following additional options: LMFBR availability in the year 2005; ERDA's optimistic and pessimistic uranium supply curves; $50/kW and $150/kW capital cost differentials between the LWR and LMFBR; and an exogenous demand component. The model differs from ETA in that: the ADV becomes available in 2015; we assume a breeding gain of 8% per year (consistent with an advanced oxide fuel); and the marginal cost of coal remains constant at $1 per million BTU for the first 25 quads (1 quad - 1015BTU) consumed annually and then rises linearly to $1.5 at 50 quads, $2 at 75 quads, etc. Note that this assumption is intermediate between the case of 'rising costs' and 'constant costs' in the original ETA model.

    Optimal timing of the US breeder

    basis in the UK, France, West Germany, Japan and the USSR. Although a number of benefit--cost analyses have economically

    justified a breeder research and development programme, the issue of optimal breeder timing has received surprisingly little attention. In its proposed-final environment statement for the LMFBR programme (WASH-1535), 2 the AEC did measure the impact of a delay in breeder availability. However, this was measured primarily in terms of a decline in gross breeder benefits. Although the shape of the gross benefits function is an important determinant of optimal timing, it is misleading to discuss breeder timing solely in those terms. Attention must also be given to the shape of the R & D cost-time function. Only then can it be determi~ned how net benefits change with the breeder's availability date.

    In this study, a programming model is used to calculate LMFBR gross benefits. Our results indicate that if optimal timing depended solely on the shape of the gross benefits function, early availability would always be at least as preferable as later availability. However, our R & D cost analysis shows that with a declining discounted R & D cost-time function, later availability is often preferalSle.

    The model

    A non-linear programming model is used to calculate LMFBR gross benefits. The model, called ETA (for energy technology assessment), was developed by Alan Manne and first used in his work on the interdependence between benefits from the fast breeder and from synthetic fuels. 3

    ETA differs from the WASH-1535 model (the model used by the AEC for its breeder benefits calculations) in two fundamental ways. First, the AEC model focused exclusively on the supply and demand for electric energy. The electric and non-electric energy sectors were completely decoupled. Such a formulation tends to underestimate breeder benefits. Coal, for example, is used in coal-fired fossil plants to produce electricity, but could also be used for coal-based synthetic liquids and gases.

    If the breeder technology decreases our dependence on coal for electric power, then the marginal costs of coal production could be affected - and hence the cost of coal-based synthetics. A model that looks only at electric energy will fail to capture these benefits. ETA, by contrast, covers the entire energy sector.

    Similarly, by concentrating on the electric energy sector, the WASH-1535 model is unable to capture the effects of breeder availability on inter-fuel substitution. For example, rising oil prices may make hydrogen via electrolysis an attractive source of non- electric energy. The competitiveness of this option, however, will depend upon the price of electricity, but this in turn depends on breeder availability. A model that decouples electric and non-electric energy will ignore this interdependence when calculating breeder benefits.

    A second distinguishing feature of ETA is the effect of own- and cross-price elasticities. In the WASH-1535 model, as in many other energy models, the demand for electricity is specified exogenously, and the optimisation is performed so as to meet these demands at minimum cost. ETA, on the other hand, incorporates both own- and cross-priced elasticities for electric and non-electric energy, and it

    ENERGY POLICY June 1977 107

  • OptOnal thning of the US breeder

    4 1Q unit ((luad) 1 0 TM British Thermal U~lits ~,~ 10 TM joules.

    calculates a market equilibrium for the whole energy sector. In this way, rising prices for one energy form can be offset by conservation of that fuel - and also through substitution of other fuels whose prices have risen less rapidly.

    Principal assumptions

    In a deterministic analysis, it is necessary to act as though all parameters are known with certainty. The following assumptions define our 'reference case'. Later we will determine how the results vary with different sets of values for the key parameters.

    Planning horizon ETA employs a 75-year timespan, and covers 15 sub-intervals, each 5 years long. A planning horizon of this length is required to analyse the exhaustion of limited natural resources (oil, natural gas, and low-cost uranium) and the introduction of new technologies (eg, the breeder, solar, and/or fusion). Unless otherwise indicated, the analysis employs a discount rate of 10% - as is recommended by the Office of Management and Budget for federal benefit-cost calculations. The discount rate and all costs are stated in terms of 'real' 1975 dollars, relative to the GNP deflater for that year.

    Demand assumptions Demand projections are based upon the following assumptions:

    GNP will grow at 3.5% per year from 1970 to 2000 and eventually slow down to 2.5% towards the end of the 75-year planning horizon;

    Total energy demands would have grown at the same rate as the GNP if prices had remained at their 1970 levels;

    Price elasticities for energy are as follows:

    Own price Cross price elasticity elasticity

    Electric energy -0.75 0.50 Non-electric energy -0 .50 0.25 Total energy -0.25

    Our initial set of assumptions leads to electrical energy demands of 6 trillion kWh in the year 2000.

    Resource availabilities and costs Oil and gas. It is assumed that a total of 2Q units 4 of oil and gas are available domestically at 1975 import prices - $12/bbl (or $2/million BTU). Approximately IQ falls into the highly speculative 'undiscovered recoverable resources' category (eg, outer continental shelf). As for imports, it is supposed that for political reasons - as well as because of limited foreign supplies - US dependence on oil and gas imports will be limited to its current level of 7 million bbl/d.

    Coal. It is assumed that diseconomies of scale appear when the annual consumption rate exceeds 25 quads (twice the 1970 level). Heavy dependence on coal, for example, will probably result in a further tightening of primary air quality standards, as well as

    108 ENERGY POLICY June 1977

  • Figure 1. U3 08 cost versus supply est imates.

    Source. ERDA, Reference 9, p 111, F-51.

    Note: The U 3 08 costs used in this study refer to production costs and are substantially less than current market prices.

    5 In 1970, hydroelectric and geothermal accounted for 16% of the electricity generated. It is assumed that these sources will expand at the annual rate of 2% in the future.

    200

    Optimal timing of the US breeder

    180

    16C

    14C

    120 el)

    0

    ,.- I00 0

    _o

    0 C)

    6O

    4O

    2O

    I I 1 1 1 0 2 4 6 8 I0

    Qu0ntify of U308 (million tons)

    , Pessimistic supply

    Opt imis t i c supply

    I I 12 14

    increased environmental costs from surface mining as we are forced to become less selective in our choice of sites. Moreover, sharp increases in demand will most likely result in spiralling labour costs, particularly in the case of labour-intensive underground mines. Therefore, it is assumed that marginal coal costs remain constant at the 1975 price level of approximately $1 per million BTU for the first 25 quads and then rise linearly to $1.5 at 50 quads, $2 at 75 quads, etc.

    Uranium. The reference case adopts ERDA's most recent 'pessimistic' uranium supply curve (see Figure 1). Here, only 3 million short tons of U3 08 are available at $100/lb. Later we shall explore the effect of switching to ERDA's 'optimistic' supply curve.

    Electric energy supply options Except for limited amounts from hydroelectric, geothermal and the remaining initial oil- and gas-fired units, future electricity demands will be satisfied by the following four sources: coal-fired fossil plants; LWRs; LMFBRs; and ADVs (an acronym for an advanced technology, eg, fusion, solar, or perhaps the breeder)P The cost assumptions for each technology are summarised in Figure 2. The

    ENERGY POL ICY June 1977 109

  • Optimal timing of the US breeder

    Figure 2. Electric energy costs.

    6 The model also allows for fixed rates of shale oil production: 1 million bbl/d in 1990, 2 million bbl/d in 1995, 3 million bbl/d in 2000, etc. We assume that shale oil development will be severely limited by the availability of water and the problems of disposal of spent shale waste. 7 The model has 300 rows, 700 columns and 2500 non-zero matrix elements. It is solved by a reduced gradient algorithm written by B.A. Murtagh and M.A. Saunders of the Systems Optimization Laboratory at Stanford University.

    20

    r -

    o~

    15-

    I0 -

    5-

    / / / / / / / / / / / ,

    Fossil

    ( Coal at

    $ I /mi l l i on BTU)

    /Uran ium at

    r" d"

    Uranium , /

    / / / /

    / / / / / / / /

    , t / / i / / / / / / / /

    1/ / / / / / /

    2;;; LWR FBR

    $ lO011b

    at $1511b

    / / ' J r

    //.// 1/ / I / / / I I I I L

    x / i v

    / / / / / / / / 1 / / ) / / / /

    Y// / / / / / / / /

    ADV

    following constraints are placed on the rates of introduction of new capacity.

    Coal-fired fossil plants. It is supposed that these constitute at least 40% of all new electric energy output added up to the year 2000. The reason for this restrictive ordering policy is that coal-fired plants are likely to be the least expensive means of satisfying demands outside the baseload portion of the load duration curve. Eventually, it should be possible to develop low-cost storage technologies, or to use LWRs for cycling duty. Hence, this constraint is gradually relaxed between the years 2000 and 2020.

    LMFBR. For the reference case, the first commercial breeder reactor (CBR-I) becomes available in 1995. The LMFBR is then limited to 20% of new electric energy capacity added in the year 2000, 40% in 2005, 80% in 2010, and unlimited thereafter. These ceilings on the rate of commercialisation are intended to reflect the reluctance of utility executives to invest massively in new technologies before they are thoroughly tested.

    ADV. For the reference case, the ADV becomes available in 2015 and is limited to 20% of new capacity in that year; 40% in 2020, etc. Thus, it follows the same timetable as the LMFBR except for a delay of 15 years.

    Non-electric supply options The ETA model contains three primary supply sources for non- electric energy (liquids and gases): PETG (petroleum and gas); SYNF (coal-based synthetic fuels); and ELHY (electrolytic production of hydrogen). 6 For these sources, the cost assumptions are summarised in Figure 3.

    Reference case results

    For each set of data inputs into ETA, it is possible to calculate an optimal mix and the timing of transitions between alternative supply sources . 7

    110 ENERGY POLICY June 1977

  • Figure 3, Non-electr ic energy costs.

    8 ETA approximates a competitive equilibrium by maximising the sum of producers' plus consumers' surplus. Alternatively, the objective function can be interpreted as minimising the sum of the costs of conservation plus interval substitution plus the costs of energy supply. We will adopt the latter interpretation,

    6 O0

    4.50 -

    z) I-.- (13

    .c_ o 30C -

    .5o1_

    0

    Optimal timing of the US breeder

    36.00

    PETG SYNF (Coal at $ I/million BTU)

    ELHY

    27.00

    18.00

    9.00

    0

    In each case, the optimisation is performed in such a way as to minimise economy-wide energy costs over the 75-year planning horizon. 8 Figure 4 relates to the 'reference' set of input data. Figure 4a shows the following sequence of events for electrical energy supplies: LWRs overtaking hydroelectric, etc. during the mid-1970s, overtaking fossil in the late 1980s, and then being replaced first by the LMFBR and later by the ADV.

    The non-electric side is presented in Figure 4b. Recall that domestic oil and gas (PETG) supplies are limited to 2Q (the area under the domestic PETG curve). As these supplies begin to decline, coal-based synthetic fuels (SYNF) are introduced. Then, with rising marginal coal costs, non-electric energy prices rise to the point where it becomes economical to produce electrolytic hydrogen (ELHY), using the LMFBR as the primary energy source.

    LMFBR gross benefits

    The reference case assumes that the first commercial breeder reactor (CBR-I) is completed in 1995. To calculate LMFBR gross benefits, the optimisation is re-run with the LMFBR unavailable during the planning horizon. Gross breeder benefits are then defined as the difference in economy-wide energy costs with and without the LMFBR. For the reference case, gross benefits are calculated to be $22.7 billion.

    Figure 5 presents the optimal mix and timing of transitions between energy sources for the no LMFBR scenario. Comparing Figures 4 and 5 gives us some insight into the nature of breeder benefits. On the electric energy side, the absence of the breeder results in heavy reliance on LWRs. Hence, our dependence on high-cost uranium ore increases considerably. With the LMFBR, we need not use ore costing more than $100/lb. Without the LMFBR, we must exploit ores costing $190/1b. A comparison of Figures 4a and 5a also shows that the higher electricity prices lead to decreased demand.

    On the non-electric side, electrolytic hydrogen is delayed by a decade in the absence of the LMFBR, and we are forced to rely more heavily on coal-based synthetic fuels. Thus, absence of the breeder

    ENERGY POL ICY June 1977 111

  • Optimal timing of the US breeder

    I00, - , " L

    8O

    Demand, excluding EL U /FBR ~DV

    -"ossil Hydro etc, "~

    0 ~" i . . . . I ...-.'t I" I . 1970 1980 1990 2000 2010 2020

    a

    ,. 60 Q

    "io

    ~= 4C c)

    lO0

    1500

    ~mond

    IO00 ~ CL

    U

    f -

    to 500 ~-

    (P

    t9

    0 20:50

    80

    60

    =", 40 - (domestic)

    O

    PETG 0 20 , - (imports)

    30 ~, Requirements for .~ o electricity generation "-

    2O g

    IO

    Figure 4. Reference case (a) electric energy (b) non-electric energy.

    o b 1970 1980 1990 2000 2010 2020 2050

    means increased dependence on high-priced coal as well as on low- grade uranium ore.

    Next, we examine how breeder benefits might vary, depending on alternative assumptions regarding uranium supply, electrical energy demands, the capital cost differential between the LWR and the LMFBR, and the availability of the ADV technology. Alternative assumptions include:

    ERDA's'optimistic' uranium supply curve; electrical energy demand growing at a faster rate than in the

    reference case - an exogenous component is added to electrical energy demand in the form of a quadratic function fitted so that additional demand is 2 trillion kWh in 2000 and 8 trillion kWh in 2030;

    112 ENERGY POLICY June 1977

  • Figure 5. Reference case without LMFBR (a) electric energy (b) non- electric energy.

    I00

    80

    ~. 6O 3

    o 40 0

    20

    a 100

    Optimal timing of the US breeder

    e,c,uOino EL%/ / / - / / rAov

    LWR

    0 0 1970 1980 1990 2000 2010 2020 2030

    1500

    )

    0

    ~000 ~ c

    if3

    5O0 "6 aJ

    Requirements for

    60 y f..~-i30 >, \ 20 -~

    20- PETG / ~ / -10 ~ / (imports) / ~ . . ~ . / , . . . . . /

    o , ~ , / , \ o b 1970 1980 1990 2000 2010 2020 2030

    electrical energy demand growing at a slower rate than in the reference case. Here the exogenous component is subtracted from electric energy demand. For example:

    Electrical energy demands in 2000 10 ~2 kWh

    Low 4.0 Moderate (reference) 6-0 High 8-0

    @ a $150/kW capital cost differential; and no ADV during the planning horizon.

    Table 1 presents gross benefits for each of the 24 possible combinations of these assumptions.

    With optimistic uranium supply, low energy demand, a higher capital cost differential, and the ADV, discounted gross benefits are

    ENERGY POLICY June 1977 113

  • Optimal timing of the US breeder

    Table 1. LMFBR gross benefits from 1995 introduction of CBR-1 ($ billion discounted to 1975 at 10% per year)

    Uranium Demand Capital cost ADV Gross benefits differential

    Pessimistic Low $50/kW Yes 8.8 Pessimistic Low $50 No 23.8 Pessimistic Low $150 Yes 4.3 Pessim istic Low $150 N o 15.1

    Pessimistic Moderate $50 Yes 22.7 Ref. case Pessimistic Moderate $50 No 47.5 Pessimistic Moderate $150 Yes 13.7 Pessimistic Moderate $150 No 33.5

    Pessimistic High $50 Yes 33.7 Pessimistic High $50 No 64.8 Max. Pessimistic High $150 Yes 22.7 Pessimistic High $150 No 47.8

    Optimistic Low $50 Yes 5.0 Optimistic Low $50 No 14'3 Optimistic Low $150 Yes 0.5 M in. Optimistic Low $150 No 5.6

    Optimistic Moderate $50 Yes 12.3 Optimistic Moderate $50 No 27.2 Optimistic Moderate $150 Yes 3.3 Optimistic Moderate $150 No 13.2

    Optimistic High $50 Yes 17.4 Optimistic High $50 No 36.5 Optimistic High $150 Yes 6.4 Optimistic High $150 No 19.5

    $0.5 billion. It will be shown below that these benefits would hardly justify the programme's discounted R & D costs. However, with moderate or high energy demands, the gross benefits from 1995 availability well exceed even the most pessimistic cost projections for the R & D programme in all but one case.

    Effect o f t iming on gross benefits

    In planning the LMFBR R & D programme, it is important to know how gross benefits vary with the breeder availability date. In the previous calculations, it was assumed that if the breeder was introduced at any time, the first commercial breeder reactor (CBR-1) will be available in 1995, and that LMFBRs will be able to supply up to 20% of new electrical generating capacity in 2000. In this section, we investigate how gross benefits change as breeder availability is delayed 10 years. This means that the CBR-1 would be introduced in 2005, and that breeders could supply no more than 20% of new capacity in 2010, 40% in 2015, etc.

    Figure 6 presents gross benefits for the reference case, and for those scenarios that differ from the reference case, varying one assumption at a time.

    For the reference case, it can be seen that a 10-year delay in breeder availability would result in a $5.4 billion decrease in gross benefits. That is, economy-wide energy costs would increase by $5.4 billion with later breeder availability. For the most part, the additional costs can be attributed to increased dependence on low-grade uranium ore and greater reliance on high-priced coal-based synthetic fuels.

    114 ENERGY POLICY June 1977

  • Figure 6. Effect of timing on gross benefits (reference case and one-a- time variations on reference case).

    ~ 5O 0

    u

    dD v

    ~40

    0

    B 3O b--

    0

    t'-

    0

    to

    '= I0 - tl)

    to to 0

    (.9"

    Optimal timing of the US breeder

    Reference case :

    - Pessimistic uranium supply No ADV Moderate demand

    $150/kW capital cost differential

    High demand

    Reference cese

    -

    Optimistic - uranium supply

    $ 150/kW

    Low demand

    1 I 1995 2005

    Introduction date of CBR-I

    With pessimistic uranium supply and high electrical energy demands, economy-wide energy costs increase by $11 billion with later breeder availability. Here, the already short supply of low-cost uranium ore is exhausted even earlier because of the increased demand.

    The loss in benefits is also higher for the no ADV case ($9.6 billion). With no ADV, breeders are required in greater numbers in the later part of the planning horizon. If CBR-1 is delayed until 2005, the breeder introduction constraint will still be limiting introduction to 2020. This constraint will be more costly if there is no ADV in 2015 to relieve dependence on the breeder.

    Because LWRs have a cost advantage over LMFBRs for uranium ore prices below $50/lb, it is possible for LMFBRs to be 'available' before they are commercially competitive. With abundant low-cost uranium ore, there is little need for early breeder availability. From Figure 6 we see that with the optimistic uranium supply curve, the drop in gross benefits is now only $0.2 billion.

    As with optimistic uranium supply, lower demand flattens the curve. The loss in gross benefits from a 10-year delay in breeder availability is only $0.8 billion.

    Finally, notice that the $150/kW capital cost differential curve is parallel to the reference curve in Figure 6. This indicates that the loss in benefits due to a delay in breeder availability is independent of the capital cost differential. That is, it is the same for the $50/kW and the $150/kW cases.

    Table 2 presents the costs of a 10-year delay for the complete set of 24 alternative assumptions. In general, the higher the absolute level of benefits, the higher the cost of a delay.

    ENERGY POL ICY June1977 115

  • Optimal timing of the US breeder

    Table 2. Effect of delaying CBR-1 from 1995 to 2005 ($ billion of loss in gross benefits, discounted to 1975 at 10% per year)

    Uranium Demand Capital cost ADV Loss in gross differential benefits

    Pessimistic Low $50/kW Yes 0.8 Pessimistic Low $50 No 2.3 Pessimistic Low $150 Yes 0.8 Pessimistic Low $150 No 2.3

    Pessimistic Moderate $50 Yes 5.4 Ref. case Pessimistic Moderate $50 No 9-6 Pessimistic Moderate $150 Yes 5.4 Pessimistic Moderate $150 No 9.6

    Pessimistic High $50 Yes 11.0 Pessimistic High $50 No 16.7 Pessimistic High $150 Yes 11.0 Pessimistic High $150 No 16-7

    Optimistic Low $50 Yes 0 Optimistic Low $50 No 0 Optimistic Low $150 Yes 0 Optimistic Low $150 No 0

    Optimistic Moderate $50 Yes 0.2 Optimistic Moderate $50 No 1.1 Optimistic Moderate $150 Yes 0.2 Optimistic Moderate $150 No 1-1

    Optimistic High $50 Yes 1.4 Optimistic High $50 No 3.7 Optimistic High $150 Yes 1.4 Optimistic High $150 No 3.7

    The availability date and the commercialisation date

    As discussed above, it is possible for the LMFBR to become 'available' before it is commercially competitive. How does premature availability affect gross benefits? As an example, suppose that LMFBRs do not become economical until 2010. In this case, the model will select the same mix of technologies whether CBR-1 is available in 1995 or 2005. Since gross benefits are simply the difference in economy-wide energy costs with and without the breeder, gross benefits would be the same for either availability date. Gross benefits decline with deferred availability only if the deferral prevents the introduction of commercially competitive breeders.

    Note, however, that gross benefits never increase with deferred availability. The only way that a deferral could ever result in increased gross benefits would be if non-competitive LMFBRs were mistakenly introduced because of early availability. This cannot happen with an optimisation model such as ETA. Hence, if optimal timing depended only on the shape of the gross benefits function, early availability would always be at least as preferable as later availability.

    The R & D cost-time function

    Optimal timing also depends, however, on the shape of the R & D cost-time function. Figure 7 compares the effect of different cost-time functions for R & D. Since the discounted gross benefits function in the three graphs is identical, the change in the optimal LMFBR availability date is due entirely to the difference in the R & D costs. If

    116 ENERGY POLICY June 1977

  • X3 c~

    c E 3 o

    ~N g}

    a

    ~ G r o s s Maximum benefits net benefits

    ~L~_______ . . , - .~ RSID costs

    I t [995 2005

    LMFBR availability date

    z~ m

    zg

    Q_

    b

    Max,mL m ~'~ ' '~ '~- - Gross net benefits benefits

    costs

    1995 2005 LMFBR availability date

    O

    O tn

    O

    C

    Gross~_ benefits

    ~ _ Maximum R 8~ D ~ net benefits COSTS

    I 1995 2005

    LMFBR availability date

    F igure 7. (a) Rising R & D costs: (b & c) Decl ining R & D costs.

    9Energy Research and Development Administration, Final Environmental Statement - Liquid Metal Fast Breeder Reactor Program, ERDA-1 535, December 1975. 1This view of the cost-t ime function might be thought of as a variant of 'Parkinson's Law'. That is, the same level of annual fixed costs are assumed to extend outward in time to fill up the period through the delivery date. 1~ See F.M. Scherer, 'Government research and development programs,' in Robert Dorfman, ed, Measuring Benefits of Government Investments, Brookings Institution, 1965; R.L. Perry, The Mythology of Military R & D, The Rand Corporation, P-3356, May 1966; T.A. Marshak, T.K. Glennan and R. Summers, Strategy for R & D: Studies in the Microeconomics of Development, Springer-Verlag, New York, 1967; R.R. Nelson, The Economics of Parallel R & D Efforts: A Sequential Decision Analysis, The Rand Corporation RM-2482, November 1959.

    Optimal timing of the US breeder

    discounted R & D costs rise as a result of later availability, then net benefits are always maximised by the earliest possible availability. If discounted R & D costs decline with later availability, then early availability is optimal only if gross benefits fall faster than R & D costs. Otherwise, later availability is preferable. A major difference between this study and the benefit--cost analysis in the proposed final environmental statement (WASH-1535) is that the AEC in effect adopted the upper R & D cost assumption of Figure 7. In its final environmental statement, however, ERDA has switched to the assumptions of declining discounted R & D costs. 9

    In order for the discounted cost function to rise with later availability, undiscounted costs must rise even more rapidly than the discount rate. This view is common among managers of large-scale R & D programmes. They argue that once a programme is underway, later availability requires disrupting the rhythm of a previously designed programme in order to convert it to a slower timetable. They usually view timing from the perspective of large amounts of fixed costs~ and therefore phrase the issue as 'the longer the project takes, the longer we have to keep our teams and facilities together, and the more it is going to cost. '~ A key assumption in this argument is the existence of an R & D programme whose fixed costs levels are higher because they were originally influenced by a commitment to rapid commercialisation.

    If we look at the breeder development programme from the point of view of long-term strategy options, however, a longer programme need not necessarily be more costly. 'Stretch-out' costs occur whenever there are unanticipated difficulties, and a programme must be hastily revised. They do not occur if the programme timetable incorporates enough flexibility to meet a later completion date without incurring large penalties. The AEC, in considering a later completion date, viewed the extension from the perspective of 'stretch-out' costs rather than costing out a new development programme. This approach would only be justified if the momentum of the current programme meant that a large cost would have to be paid for a programme change at this date.

    Some observers view the design and ground breaking for Clinch River as the real beginning of an overall breeder programme. They regard the previous work by the national laboratories and also the FFTF (fast flux test facility) as separable components. Others believe the programme has had unity and momentum for some time, and is now suffering from efforts to guess its structure and phasing for the second time. We tend more towards the first viewpoint, for the AEC itself undertook a major restructuring of the programme in mid-1974. This leads us to believe that it is still valid to view the breeder development programme from the perspective of a long-term strategy.

    Even with 'stretch-out' costs, a longer programme may still be less costly. Shorter programme scenarios that involve a more concurrent pattern of phasing entail a higher degree of technological uncertainty and risk at each point in the programme. The cost penalties involved with more concurrent development have been examined in previous studies of large-scale military and space R & D programmes? 1 In the case of programmes involving large technological uncertainties, it is not even clear whether a concurrent development strategy will always arrive at a completed product earlier than a sequential development strategy.

    ENERGY POLICY June 1977 117

  • Optimal timing of the US breeder

    Figure 8. A l te rnat ive R s t ra teg ies .

    & D

    In this study we assume that undiscounted R & D costs are independent of LMFBR availability. That is, any 'stretch-out' costs from a longer programme are offset by the savings due to increased learning between phases. With a positive discount rate, this R & D cost-time assumption is consistent with the idea that discounted R & D costs decline along with a delay in breeder availability.

    In Figure 8 we employ the decision tree framework to describe alternative breeder R & D strategies. The decision points are denoted by squares.

    Only one path leads to the first commercial breeder reactor (CBR- 1) in 1995. This required a decision in 1977 to build the Clinch River Breeder Reactor (CRBR) and also the Prototype Large Breeder (PLBR) concurrently, and then in 1986 giving the go-ahead to CBR- 1. With this time sequence, the construction of PLBR would begin before CRBR reached criticality, and construction of CBR-1 would begin before the PLBR is completed. Hence, the upper path is labelled concurrent development. Note that this path also includes the option in 1986 of delaying CBR-1 until 2005.

    Alternatively, the middle path (sequential development) can be followed. Here, the demonstration plant is completed two years before a decision is required on the commercial prototype. Similarly, PLBR operational experience is available in time for the decision regarding CBR-I in 2005. This plan allows for maximum transfer of information between programme phases; but now CBR-I is not available until 2005.

    The third strategy involves waiting until 1986 before making a decision on CRBR and PLBR. Then, if the available information favours proceeding with the programme, the concurrent development route is followed. The fourth strategy consists of stopping now. This yields net benefits of zero, for 'nothing ventured, nothing gained'.

    Table 3 presents details on the costs for the R & D strategies of Figure 8. In this table, the costs are undiscounted, and expressed in 1975 dollars. For discounting purposes, it is essential that costs be broken down over time. ERDA has undertaken such a breakdown, but has not yet released the results of its study. Consequently, Table 3

    1977 1986

    I I I I c8 -,

    1 cRBR / I I 1984 / ~ ~, vv I PLBR ~','~ I 1988~'~.=ko 9" I

    ./:,@,"- I I ,. I .,,%o~v c##R

    T ~984 I~L r'z'g4 ~Seq ue n.tie I development ~

    \~ I Stop \ ,, s,o !

    1996

    I I CBR-I

    Wait

    I Stop~"~

    I I I CBR-I

    PLBR 1993

    I s,o~'~'- I I

    CRSR 1993 I CBR-I PLBR 1998

    I Stop~',,~ I

    118 ENERGY POLICY June 1977

  • Figure 9. R & D costs ($ bill ion

    discounted to 1 975 at 10% per year).

    lz The base programme costs in Table 3 were derived from Table 11.2-3 of the proposed final environmental statement on the LMFBR, See Reference 3. There base programme costs = total LMFBR and support - (CRBR R & D costs + cooperative projects) -= $6.8 billion (undiscounted 1975 dollars).

    The $2.4 billion base programme costs for the period 1974-1980 were calculated directly from Table 11.2-3. The remaining $4-4 billion were spread out over the period 1980-2020 in such a way as to justify the AEC's discounted total in the PFES(p 11.2-3).

    From August 1972 to September 1974, ERDA's estimate of CRBR costs

    cont inued on p 120

    Optimal timing of the US breeder

    1977 1986

    I I CBR-I ~ ^ '. 1995/b .~

    Wait

    / I s,o;-.. 4 4 PLBR / I

    / CRBR : PLBR E 1984 ~.~ ,993

    1996

    I I CBR-I

    I I I CBR-I

    I I I CBR-I

    I

    is based on considerable guesswork in order to supplement the time stream of costs implied by several ERDA documents. ~2

    The basic assumptions used in calculating the costs of alternative R & D strategies are that: undiscounted costs are independent of programme phasing. That is, at zero discount rate, the programme costs are $12.8 billion regardless of when the breeder becomes available. This assumption is consistent with a declining discounted R & D cost assumption. Base programme timing is unaffected by changes in the timing of the CRBR, PLBR, and CBR-1 projects. 13

    Figure 9 presents the costs of the alternative R & D strategies discounted at 10% per year to 1975.14 If we choose the upper path and the 1986 decision is CBR-1 in 1995, then the programme's discounted costs are $5.9 billion. However, if the concurrent development option is followed and the CBR-1 is then delayed until

    Table 3. R & D cost projections 1975--2020 (billion undiscounted 1975 dollars)

    1975-- 1980-- 1985-- 1990-- 1995- 2000-- 2005-- 2010-- 2015-- 1980 1985 1990 1995 2000 2005 2010 2015 2020

    Base programme 2-4 1.0 0.9 0.7 0.6 0.4

    Demonstration programme

    Concurrent development CRBR-1984 1-0 1.0 PLBR--1988 1.0 1.0 CBR--1 1995 1.0 1-0

    Concurrent development CR BR-1984 1.0 1.0 PLBR--1988 1.0 1.0 CBR-1 2005 1.0 1,0

    Sequential development CRBR--1984 1-0 1.0 P LBR--1993 1.0 1.0 CBR--1 2005 1.0 1.0

    Wait CRBR-1993 1.0 1.0 PLBR-1998 1.0 1.0 CBR--1 2005 1.0 1.0

    0,3 0.3 0.2

    Undiscounted total 1975-2020

    6.8

    2.0 2.0 2.0

    2.0 2.0 2.0

    2.0 2.0 2.0

    2.0 2.0 2.0

    ENERGY POLICY June 1977 119

  • Optimal timing of the US breeder

    continued from p 119 rose from $0.5 billion to $1.2 billion (1974 dollars). A recent General Accounting Office report states that the last figure was more speculative than it should have been, and hints that costs may increase even further (see Reference 1 ). To be on the safe side, CRBR costs are placed at $2.0 billion ( 1975 dollars).

    Similarly, PLBR and CBR-1 costs are also placed at $2.0 billion. Each of these reactors would be a first-of-a-kind machine. Costs should not be significantly affected by the increase in unit size - from 350 MW for CRBR to 1200 MW for CBR- 1. 13The base programme refers to those parts of the programme that are not included in the description of the demonstration programme (eg, reactor physics, advanced fuels development, etc). 14Costs for the period 1975-1980 are discounted as of 1977, 1980-1985 as of 1982, etc. is If learning costs are included, the cost savings from a 10-year delay in breeder availability will be higher. For example, suppose that there will be learning costs of $5O/kW on the first 100 GW of LMFBRs. Hence, the total undiscounted learning costs will be $5.0 billion. Discounting from the year 2000 at 10% per year yields discounted learning costs of $0.5 billion. If these costs were to occur 10 years later (2010), however, discounted learning costs would be only $0.2 billion. Hence, we have an additional cost saving of $0.3 billion.

    2005, discounted costs drop to $5.5 billion. The cost savings from later availability are the result of discounting the costs of CBR-I from a point further out in time.

    From Table 3, we see that with the sequential development strategy, the undiscounted costs of PLBR are also pushed further into the future. Consequently, if we knew that the CBR-1 would not be needed until 2005, the sequential would be clearly preferable to the concurrent strategy.

    If the 'wait' option is taken, CBR-I would be delayed until 2005 - at the earliest. This path has the lowest discounted costs of the three 2005 availability paths. Hence, although sequential development is less costly than concurrent development (in discounted dollars), the greatest cost savings would result from delaying the whole demonstration programme as long as possible. The 'wait' strategy therefore dominates sequential development. Both would deliver CBR-I at the same time.

    The R & D cost savings availability are:

    Costs of concurrent development CRBR- 1984, PLBR-1988

    from a 10-year delay in breeder

    Costs of waiting and then concurrent development CRBR-1993, PLBR-1998

    $5.9 billion $4. I billion

    = $1.8 billion

    Returning to Table 2, we see that these costs savings outweigh the loss in gross benefits in 10 out of the 12 cases with optimistic uranium supply. With pessimistic uranium supply, however, the results are reversed. 15

    The effect of a lower discount rate

    The case for concurrent development would be much stronger for a lower discount rate than 10%. The breeder programme has high front-end costs and deferred benefits. Hence, as the discount rate is lowered, the discounted loss in gross benefits from a delay in breeder availability rises at a much faster rate than the discounted R & D cost savings.

    Figure 10 presents gross benefits corresponding to a 7% discount rate for the reference case, and those scenarios that differ from the reference case, varying one assumption at a time. In every case, the loss in gross benefits greatly exceeds the undiscounted costs of the R & D programme.

    Conclusions

    When using the 10% discount rate recommended by the Office of Management and Budget for federal benefit-cost calculation, there definitely is a breeder timing issue. That is, the results do not support ERDA's contention that the breeder should necessarily be available as soon as possible. There are as many scenarios for which a delay of 10 years until 2005 would be advantageous as there are scenarios for which a breeder availability date of 1995 would be advantageous.

    120 ENERGY POLICY June 1977

  • Figure 10. Effect of t iming on gross benefits (reference case and one-a-time variations on reference case).

    :500

    t -

    o = 250 m

    $ 200

    O

    150 _m .9.0

    IO0

    ~5

    50

    O

    Optimal timing of the US breeder

    Reference case:

    No ADV ~. Pessimistic uranium supply Moderate demand $150/kW capitol cost differential

    High demand

    - Referenc~ case ~ $ '50 /kW~

    OrPet in?~ Smt ic ~ ~ ~

    I I 1995 2005

    Introduction date of CBR-I

    The analysis has shown that optimal breeder timing is very sensitive to assumptions regarding the availability of low-cost uranium ore, future energy demands, and the availability of an ADV. Optimal timing is also sensitive to the capital cost differential between the LMFBR and the LWR, but to a lesser extent.

    We must emphasise that our results would be quite different if we accepted the WASH-1535 assumption that R & D costs rise with later LMFBR availability. In fact, as shown in Figure 7, this assumption ensures that net benefits will always be higher for early availability. Without a better understanding of the cost-time function, the effect of alternative timing strategies on net LMFBR benefits cannot be resolved. Hence, this should be moved to the top of the priority list of LMFBR issues for further research.

    Finally, it is our belief that the results of this analysis should not be used to argue that the breeder R & D programme be scaled down drastically. There are many scenarios for which early breeder availability is desirable. Even if one considers those scenarios to be less likely, we feel that it is still prudent to have a substantial breeder R & D effort as an 'insurance policy' against the possibilities of higher-than-expected electricity demand growth, lower-than-expected uranium resource availability, or the failure to develop other advanced concepts on a timely basis.

    ENERGY POLICY June 1977 121