IEEE Transactions on Power Apparatus and System, VOl. PAS-96, no. 4, July/Aup+st 1977

AN ECONOMETRIC ANALYSIS OF ENERGY OVER THE NEXT 75 YEARS

R.W. Schmitt D.J. BenDaniel P.J. Stewart

Schenectady, N.Y. General Electric Company

ABSTRACT

An econometric model with a 75-year time-horizon to determine base-load power generation mix is described. A number of conventional, evolutionary and speculative genere tion systems are considered, together with constraints imposed by fuel availability and techrical development times. Preli- minary results are presented.

INTRODUCTION

This paper investigates the mix of base-load electrical power generation systems for the next 75 years. The authors are motivated to attempt this ambitious task for several reasom:

First, during the next 75 years, there will be significant changes in the energy system of the United States and of the world. The United States will be approaching exhaustion of its oil and natural gas resources, which now supply threefourths of this country's energy. World-wide production of these fuels may also be declining.

Second, the lead time for significant contributions of new technology to electrical energy demand are long, typically 30 years or more from initiating technical effort to supplying a few percent of the nation's total kilowatthours. The recent large increase in expenditures on energy R&D will not shorten this cycle significantly.* Thus, a long time-horizon is necessary if we wish to see the effect of c h w technolo- gies.

Third, short-rarp forecasts, such as those of the Federal Energy Administration that extend only to 1985 to 1990, run the risk of projecting tren& or changes that could not be slstained because of constraints which emerge only in the long run. Became of the high cost of develqing new energy technology, it is desirable to embark only on develop- ments that promise a long span of applicability.

I t is recognized that few predictions over a 75-year period are correct in detail, but we believe that with this time-horizon our view of the next 50- and, especially. 25-year period will be better than they would be if a "safer", shorter period w a s chosen.

*There are at least two reasons why we believe this to be true. First, the expenditures are spread over many alternatives, with large sums going into highly speculative technologies like fusion, solar electric, and MHD. Second, a slower - than historic - growth rate of electricity consumption will mean a proportionately slower rate of addition of new plants and thus relatively less opportunity to embody new technology than in the past.

AS . Manne Stanford University Pal0 Alto, Calif.

In making the forecasts presented in this paper, an attempt has been made to satisfy several criteria:

Internal self-consistency, i.e., that conclusions derivable from our line of argument should not contradct one another. Reasonableness and plausibility, i.e., that quali- fied experts should judge our conclusions as possible, whether or not they agree with them in detail. The answers to exogenous questions - i.e., questions posed from outside the specific f rame work of our line of reasoning - should be reasonable. The analysis is based on the best available information on cost projections, fuel availability, and other inputs. Our models and line of reasoning be consistent with history.

In this first report (which is no more than a progress report on a continuing study), these criteria have not been completely met. For example, one of our first projections yielded an unrealistically high level of annual coal production by the year 2050. To correct this, an upper bound has been imposed on coal production without, as yet, having established a price schedule for coal that would be internally consistent with this bound and also with the lower level of total energy corsumption implied by higher energy prices. However, an examination of the marginal prices of coal implied by our present formulation lea& one to believe that the results displayed in this paper are close to those of an internally self- consistent model.

The criteria are essentially a statement of policy for the conduct of this study. Because there are so few unambiguous guides to the future, it is important to establish such a policy. I t should increase the probability of being right. Nevertheless, there are inevitably a few irreducible assump- tions behind any forecast which may be crucial in finally determining whether it turns out to be right or wrong. A t least two of these should be mentioned. First, an allowance has not been made for a dramatic scientific breakthrough of importance comparable to, say, the discovery of nuclear fission. Second, a future society has been (Issumed that is largely an evolution of today's, without the social and economic upheavals that would inevitably accompany the transition to a substantially lower energy-intensive society.

For predicting the base-load power generation mix, a

Economic trade-offs (for both electric and description is utilized that takes into account:

nonelectric energy). Fuel (or energy potential) availability and cost. Advances in technology.

This approach is illustrated schematically in Figure 1.

For economic tra-ffs, the initial capital cost and subsequent operating costs for -several power generation systems as a function of time through a ?%year horizon have been estimated. based primarily on a number of ERDA studies and estimates. As oil, gas, and coal are used for both electric

1353

and nonelectric energy, nonelectric energy sptems are includ- ed in the model in orc!e? to accomt completely for resource availability. An even more compelling reason for including nonelectric systems in the model is that electric and nonelec- tric energy compete in many applications, with the substitu- tion between the two being essentially pricedetermined.

Electric and Nonelectric Energy and Other Uses of Income

Competition Between Competition Between

and Cost Development

Competition Between Various Bulk Power

Fig. 1 . Overall plan for determmation of base-load power generation mix.

MODEL FORMULATION

The formulation used in this model, which is due to Mannel, links electric and nonelectric energy and allows for price-induced conservation and for electric substitution through the following nonlinear set of equations:

where: S = net benefit less cost, which is maximized over a 75-year time-horizon to permit long- term decisions.

ql(t) = electric energy consumption in year t.

q2(t) = nonelectric energy consumption in year t.

(ao, bl, b2,y ) econometric benefit function in which Y is the time-dependent growth rate

extension has two advantages. First, the future growth of electricity use, based on the cost-dependent substitution of electric for nonelectric energy,can be analyzed. Second, this formulation is valuable in analyzing the progress of e l e c trification through the past 40 years and provides a significant insight into the growth behavior of the electric industry.

For the 40 years from 1930 to 1970, both electric and nonelectric energy growth can be characterized as exponential with time. The prices of electric and nonelectric energy can be similarly described by exponentials. When these simplified representations are used, we obtain from the condition for economic equilibrium consistent with Equation 1:

where: aE, aNE = annual rates of change of electric and nonelectric consumption, respectively.

nE, annual rates of change of electric and nonelectric prices, respectively (constant dollars).

2 data . Figures 2, 3, 4, and Table I illustrate representative

Fig. 2. Growth rate of electricity. Data from Edison - Electric Institute, Historic -Studies of .the Electric Utility Industry.

of the national GNP, bl is an econometric elasticity for electricity consumption, b2 is

10 9 8

E '

an econometric elasticity for nonelectric $ 6

consumption, mr! A - is 9 normalization fac- i s 3 1 I I I I I I I I I

' I I - I

I I [ I h 1 v - 1 I

tor based on electric and nonelectric prices and consumption, which is developed from historic data (see Appendix). L

2 4 r 0

w. 2 3 . k \

cCi(ql, q2, t) = total capital and current costs of all the energy supply systems, as determined by i linear programming.

6 = discount factor in real dollars. (10 percent is used following the practice of OMB.)

In the utility industry, it has been traditional to begin with projections of electricity consumption and then to choose cost-effective systems for supply. This approach has been taken one step further by linking electricity consumption to the cost of both electric and nonelectric energy. This

.. CUYUUTIVE PROOUCTIW IN UNITS of IO" kwh

Fig. 3. Experience curve for electricity in the United States. C w e corresponds t o a 3.3 percent average yearly decline in real ddlars for the price of electricity (1970 ddlars). Data taken from Edison Electric Institute, Historic Studies of the Electric U t i l i t y Industry.

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1% I I I

84

NONELECTRIC ENERGY

I I I YEAR

1960 1970

Fig. 4. Growth rate of nonelectric energy. Data taken from U.S. Department of Commerce, Statistical Abstract of the United States, and U.S. Federal Power Com- mission, Fuel Consrmption of Hectic Power Plants.

Table I Nonelectric Energy Price Growth Per Year

(1950 to 1970)

INDUSTRY Coal 0.68%

Oil -0.24%

Gas 0.54%

TRANSPORTATION G d i e -0.95%

DOMESTIC coal 0.56%

Oil -0.33%

Gas -0.38%

Looking at these data, we find, in real dollars

We observe that: 1) the growth of electricity consump- tion has been significantly greater than nonelectricity con- sumption, 2) this relatively rapid growth was accompanied by real price decreases of electricity during the 40-year growth penod to 1970, and 3) the past data are essentially in accord with Equation 2. This insight may be important became separate studies undertaken by the General Electric Company and others ("The Energy Conversion Alternatives Studies (ECAS)" sponsored by NASA and EPRI) did not find any type of advanced coal-fired system that would permit the production

ficantl cheaper electricity in the f u t ~ r e . ~ Projected %%%hii&iciencies combined with price rises in fuel and materials and increased construction costs appear able, at best, to keep electricity prices constant in real dollars in the foreseeable future. As a result, Equation 1 will predict future growth rates slower than historic rates for electricity con- sumption.

1

INPUTS

For our projections, the candidates for bulk power generation have been divided into conventional, evolutionary, and speculative categories. This classification is also applied to nonelectric energy. Table II lists the candidates used thus far in the s t u d y and the pertinent data for the systems and for the energy resources employed in the economic analysis.' For the speculative energy technologies, the cost parameters used have been estimated quite optimistically in line with ERDA targets. These are illustrated for solar thermal, solar photavoltaic, and Ocean thermal gradient systems (Figure 5).

Fuel availability and the rate of technology develop ment are introduced as constraints in the maximization

program. Fuel availability may be expressed as an amount of matenal available within a number of price brackets, and the runs made to date include data of this nature for uranium, derived from ERDA estimates as shown in Table III. For coal, most runs to date have included a constraint upon the maximum rate at which the coal mining industry could be

expanded (up to 50 x 1015 Btu's per year by the year 2000 and up to 100 x 1015 Btu's per year by the year 2050). In runs made to date, coal prices have been held constant at $1 per million Btu's, although price increeses are planned for subse- quent runs. The constraints on technology development are expressed in terms of a date of introduction for each new technology. plus a maximum rate of deployment thereafter. For some new technologies, such as tidal power, the total possible contribution to energy production is also comtrained. The constraints on timing and rate of introduction of the breeder reactor wed in the model are illustrated in Figure 6; similar data for the various speculative options is displayed in Figure 7.

To date, other potential constraints - such as those of the environment, materials availability, transportation, con- struction, or other elements of the infrastructure - have not been introduced exogenously, rather it has been assumed they are reflected in the costs These and other aspects of policy or strategy could, if one wished, be introduced into the model.

CAPITAL COST $ / K W

PHOTOWLTAlC

ENERGY CONVERSION

I I I

1975 2000 2025 2050 YEAR

Fig. 5 Estimated capital costs for solar thermal, solar photovdtaic and ocean thermal energy conversion systems. Data are based on an ERDA utility study soon to be w i s h e d

IC

x

Fig. 6.

YAXIYW PERCENTME OF HEN BASE- LOID 6 E T r u T 1 1 1 6 CAPKITY PERMITTED FOR LYFBR IN CWWTATIOYS

YEAR

Estimated timing for introcLcction of LMFBR. 1355

Table II Candidates for Bulk Power Generation

ELECTRIC

Cmventiaral Hydro, Geothermal (Asoumed to increase at 4% per year f r o m present levels) Steam

coal oil GWi

LWR

Evolutionary

Advanced Steam Combined Cycle PBR

SWculative Waste Tidal Wind Solar Photovoltaic Solar Thermal Ocean Thermal

NONELECTRIC

Conventional

Oil and Gas (Including I m p a t s )

Evolutionary Synthetic (Coal-based) Shale

Speculative Solar Heat iT

and MIiw Hydrogen

NOTES:

450" 300" soo(g

800(j 1500" 500(i

See Figure 7 ( h See Figure 7(h See Figure 7 ( h

73.6(b N.A. N.A. 33.7(d

71.7(b loo.o(b 21.4(d

13.1(k'1 13.1(k 92.6(i 13.1(k 13.1(k 13.1(k

--

-- --

-- --

Immediately Immediately Immediately lmmediateh

of Total Power Maximum %

Possible

100 N.A. N.A. 100

50' 50"

100

2 (g

3(g lO(P

ZS(P

25"

30"

Limit of Resources

See Table IV

3.5 x 1018Btu(r

20 x lo1' Btu/yr(g Unlimited

Based on estimates of GE NASA/EPRI "Study of Advanced Energy Conversion Systems." Based on $l.OO/MMBtu for coal in 1975 dollar constant throughout forecast period; $2.25/MMBtu for semiclean fuel. No new plants intmduced after 1975. Existing plants do not affect marginal cost, but affect oil end gas supply. Based on uranium at $30/lb, no plutonium recycle, and 0.3% tails; also included in this study are plutonium recycle and 0.2% tails. Furthermore, price of uranium varies with cumulative use up to $160/lb according to Base Case p. III-25, ERDA-38. For details see Table III. 10% capital cost premium over conventional steam. Coal-fired aspumed 50% of new additions to year 2000, despite cost premium above LWR. Estu-rjated in this study. Based on ERDA utility study, not yet published, corrected for interest and escalation. Based on GE study NAS3-19403, corrected f o r 25% availability in fuel-saver mode.

Based on a minimum 2 millkwh operation and maintenance. Based onSchultz, FmfesPional Engineeriq, November 1975.

cost is $l.OO/MMBtu and annual cost is t73.6kW-year. Credit for scrap is included. We have credited $17.50/ton for land use and no fuel cost. If $10.00/ton is credited for land use, the equivalent fuel

Based on $15.00/barrel equivalency, assuming some progress on experience curve. Price assumed to remain constant in 1975 dollars.

Based on $18.0o/barrel equivalency, assuming some progress on experience curve. Bstimate consistent with NSP/NASA report to Solar Energy Panel for the Office of Science and Tethnology. Based on ERDA targets. Based on ERDA estimates. assumes - 1.5 x 1018Btu imwrts.

~~~

growth rate of the GNP of 3.5 percent in this century, Runs made on the model to date have employed a

gradually shifting to 2.5 percent in the next century . The ratio of the econometric constants bl/b2 has been kept at 0.5,

cornistent with historic data in Equation 6 of the Appendix. Runs have been undertaken using three values of the energy price elasticity (bl + b2-l)-' of -0.1, -0.25 and, -0.4, since from historic data this parameter could be anywhere within this rarge.

5

One type of assumption is inherent in the linear programming methcd employed. Specific electric generation systems are introduced whenever they are calculated to produce the lowest cost of electricity discounted over the entire life of the plant, assumed to be 30 years. This implies that the planning of additions to generation is undertaken with complete foreknowledge of operating costs over 30 years. Since this is not achievable in practice, actual additions to Capacity will probably be more conservative and less inclined toward adoption of speculative systems than the model would indicate.

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1975 2 0 0 0 2 0 2 5 1975 2000 2025 YEAR Y E A R

1975 2 0 0 0 2 0 2 5 1975 2000 2025 YEAR Y E A R

Fig. 7. Maximum percentage of new base-load generating capacity permitted in our computations for various speculative alternatives.

I ,o, nm I).I ~m a 5 moy)

1LU

Fig. 8 Consumption of electric, nonelectric, and total en- ergy (including all uses of coal). Range bars indicate results for energy price elasticities of -0.1 (top), -0.25 (middle). and -0.4 (bottom). Consumption pattern shown illustrates relative inelastic behavior in the short term and relative elastic behavior in the long term and corresponds to rea l t s illustrated in Figures 9 and 10.

The consumption pattern shown in Figure 8 is based on the assumption of relatively inelastic behavior over the short term and relatively elastic behavior over the long term, consistent with the rising share of energy costs in the GNP.

Table I11 Still more conservative results would be obtained if a further decrease in growth of the GNP (down from 2.5 percent) were assumed for the next century. The causes for further showdown would be the combined effects of slow population growth, reduction of the available work force, and a slower growth of the GNP per work force ratio.

Cumulative Amounts of Uranium Available Vs Price Assumed in Study

Price Tons per Pound

6 ) (MM)

2.5 d 30 Base-load Power Generation Mix

4.5 75 All runs undertaken to date indicate that, for the 3.5 40

5.5 100

6.5 125 light-water reactor (LWR) systems. With the costs that we

remainder of this century, the key additions to base-load power generation mix are coal-fired steam systems and the

7.5 140 have estimated, LWR electricity is 20 to 30 percent cheaper 8.5 150 over a 30-year discounted life cycle and would be the favored

OD 160 choice. Nevertheless, the new capacity additions have been constrained to be at least 50 percent fossil fuel for the remainder of the century; thereafter the lower bound de-

RESULTS creases to zero over a 40-year period, reflecting the persis- tence of current buying practices. If this constraint were not introduced, new additions, which would be chosen solely on

Figure is a plot from a number Of made to date ful l LWR scenario would, moreover, place significant pressure economic grounds, would have been entirely LWR systems. A

indicating a range of forecasts of the consumption of electric, on uranium resowces and require the earliest possible in t r e and total energy* The gener& pattern is one of duction of the liquid metal fast breeder reactor (LMFBR). In

relatively optimistic near-term energy growth, shifting to this model, when the price of uranium rises above $40 per Significantly Slower growth aS the growth of the GNP begins to pound the LMFBR becomes economical. slow. Throughout the forecast period, we are predicting electricity growth rates above nonelectric growth rates, or a Introduction of the LMFBR has been scheduled for the continuation Of the electrification that has characterized the year 2000 and its m&mum rate of introduction constrained as past 50 years. This eleCtrifiCatiOn accelerates and the rate of shown in Figure 6. The actual rate of introduction of the growth Of nonelectric ene%Y SlOWS as one approaches t h e LMFBR will be significantly determined by the cost of

year 2030. LMFBR-based electric economy that Will be emerging by the electricity from the LWR. After the year 2000, LWR

electricity costs will begin to rise at a rate dependent on the

Although electrification is continuing, the model pre- uranium resourc-. A t introduction, the initial growth of overall electricity consumption and on the availability of

diCtS Slower growth for both electric and nOneleCtriC ene%y LMFBR capacity is not constrained by the availability of than in the past. Over the total 75-Year ftxecast Period, an plutonium, which will have been built up by previous LWR average 4 pel'Cent per year growth for electricity is predicted, operations (it has been assumed that reprocessing and and a 1-1/2 percent Per Year growth overall for nonelectric plutonium fuel fabrication facilities are available). However, energy. It is significant that the effect of varying energy by around the year 2025, the rapid growth of LMFBR capacity price Over the r a w of -0.1 to -0.4 upon these will require new additions of LWR capacity for supplementary growth rates is apparently not large, as illustrated by the plutonium production, unless a breeding gain of better than 4 range of results in Figure 8. percent can be achieved.

Energy Consumption

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Unless a very significant relative rise takes place in the costs of power generation by nuclear systems, the period 2000 to 2025 is characterized in all runs made to date by substantial additions of nuclear capacity. Coal-fired plants are projected to produce electricity at a higher cost in this period even with the relatively low constant coal price we have assumed. However, the early years of the 21st century will be characterized by a relatively slow introduction of the LMFBR. If the capacity to produce coal is also constrained. an energy "crunch" will occur which will provide an impetus for the introduction of some of the more speculative technologies. A run illustrating this possibility is illustrated in Figure 9.

GEOTHERMAL

YEAR

Fig. 9. Electric energy consumption and power generation mix.

Nonelectric Fuel Mix

A total of 3.5 x lo1* Btu in domestic and imported oil and gas available has been assumed. With this generous assumption, the nonelectric energy sector remains dependent on these resources into the early part of the 21st century, with significant reductions thereafter. Figure 10 illustrates the nonelectric fuel mix that corresponds to the electric genera- tion mix of Figure 9. Like Figure 10, it shows a period of energy "crunch" within the first three decades of the 21st century. Transportation fuels from oil and gas will be declining then and the most acceptable and economically viable alternative will be coal-based synthetic fuels. The timing of their introduction is dependent to a large extent upon government policies. However, the optimum rate of introduction is very rapid and may be constrained by capital or, as in the run illustrated in Figures 9 and 10, by coal availability. The result is that a fuel "crunch" develops with rising prices, oil from shale is introduced as rapidly as possible, and solar heating and cooling is also introduced to free up oil for transportation. This "crunch" would not occur if coal production were unconstrained and runs in which no such

becoming of overriding importance by the year 2025. and coal constraints were introduced showed coal-based synthetic fuels

production rising to as much as 36 times the present level by the year 2030. A t these production levels, we would be getting close to exhawtion of coal reserves of acceptable quality by the end of the forecast period.

Energy Prices

Table IV shows how the marginal prices of both electric and nonelectric energy vary with time under the scenarios described in Figures 9 and 10. The prices shown here are the prices that would be set, in a perfectly free market, by the cost of the next increment of energy use, in whatever form is available a t the time. For example, if the next increment of fuel for transportation has to be provided from shale oil, then the price of shale oil is the marginal price at that time. Actual energy prices will be related more closely to the average costs of all the energy sources in use and, in any case, will very likely be regulated in some way. So Table IV shows the pressures on pricerather than actual prices.

1201

1 0 0 -

40 -

20 -

'70 '80 '%I 2OOO 'IO '20

/ Y ( U E OIL --#KAR

SPKE HEATING

D YEAR

Fig. 10. Nonelectric energy commption and fuel mix.

Table IV Approximate Marginal Prices for Energy

(1970 to 2030) Year

1970 1985 2015 2030 Rate Growth

-

(at the brrsbar) Electrleity I 1 18 20 24 I8 0.5%

rniUsntWh

Nonelectrlc Energy 0.80 2.20 2.60 5.70 5.60 3 8

Electricity prices rise gradually, but they are overtaken by a very rapid price rise in nonelectric energy in fhe years 2010 to 2030. Again, this general conclusion appears to be only weakly dependent upon the exact value of energy elasticity with the costs and constraints which have been assumed here. If these prices are roughly represented by exponentials, then Equation 2 can be expressed for this 75-year period as:

0 4 percent per year growth plus 1/2 percent per

0 1-1/2 percent per year growth plus 3 percent per year price rise of electricity.

year price rise of nonelectric energy

which again confirms the rule-of-thumb provided by this equation.

Effects of Other Variables

Coal Prices: A major assumption of the projections

neighborhood of $l.OO/MMBtu (in 1975 dollars) for the foresee- made to date is that the price of coal will remain in the

able future. This assumption may not be valid, especially should demand outrun supply at any time or high grade reserves become depleted by massive coal use. A moderate

1358

rise in the price of coal will leave the electric power generation mix largely unchanged, though it will accelerate the penetration of nuclear systems. On the other hand, a large rise in the price of coal will significantly lower nonelectric energy consumption and could cause still further electrifica- tion. A hydrogen-based energy economy, with hydrogen produced from LMFBR-generated electricity, could even emerge if coal prices rise above $2/ MMBtu. Coal price inputs will be included in subsequent runs.

Limitations on Total Petroleum and Gas: In the event that total petroleum and gas, domestic and imported, is less

than the 3.5 x 1 0 l 8 Btu assumed in the results reported here, then 1) the energy "crunch" will occur correspondingly earlier, 2) greater pressure on synthetic fuels and other higher cost alternatives will result earlier, and 3) the shift to electrifi- cation will increase.

Limited Uranium Availability and Price Rises: In the event that available uranium resources prove to be less than the ERDA estimates used in these runs, the LWR electricity costs will reflect uranium price rises correspondingly earlier. This will put greater pressure on the introduction of the LMFBR, whose introduction would then definitely be limited by the rate of technical development. Once available, the LMFBR contribution to the power generation mix would need to grow rapidly, in this case accompanied by further symbiotic growth of other nuclear systems as required for supplementary plutonium production or a greater breeding gain than the 4 percent assumed here.

LMFBR Capital Cost Rises: The $800/kW capital cost of t h e m B R used to date is an estimate taken from the mainstream of present predictions6 In the event that technical factors cause significant cost escalation, t h e breeder may not be cost-effective. Then 1) the LWR will become a much more important factor in the power generation mix for a longer period, depending upon electricity consumption, urani- um availability, and price; 2) the resultant rise in the price of electricity wil l reduce electricity consumption and the pro- gress of electricity substitution will slow; and 3) one or more of the speculative alternatives will enter the power generation mix in a major way in the 2030 to 2050 period. Our estimates give a capital cost barrier of approximately $1000/kW above which the LMFBR will lose economic viability.

A similar scenario results if breeder introduction is impeded by political or environmental factors. If the whole nuclear industry is thus impeded, massive coal use could result, with resulting higher coal prices, higher electricity costs, and lower electricity consumption.

Technical "Breakthroughtt in One or More of the Speculative Alternatives: The economic effect of technical "breakthroughTt cannot be estimated. However, our cost projections for the speculative alternatives are already o p timistic and envision rapid technical progress, made possible by continued massive subsidization of research and develop ment by ERDA. The most sensitive candidate for a radical technical "breakthroughtt is solar photovoltaic. In this case, however, lowering of the effective cost of the system below $1000/kW for bulk power generation would require a wholly new concept, and the ultimate limitation would still be costs of energy storage and conversion equipment and of land.

Emergence of Other Alternatives: Thus far, this study has not included still more speculative alternatives, such as thermonuclear fusion or thermochemical hydrogen production; there exists no present credible basis for estimation of costs of such alternatives. In addition, the study does not yet include the high-temperature gas reactor (HTGR) or the CANDU reactor systems, which appear to be minor factors in the domestic power generation mix unless LMFBR development is significantly delayed.

CONCLUSIONS

It must reemphasized that we are presenting here a progress report, based upon a limited amount of experience with a very complex model. The major virtue of the model is that it can, with the assistance of historically derived data, calculate simultaneously and self-consistently an optimum long-term mix of energy systems and the pricerelated consumption of various energy forms. None of the information obtained so far should be viewed as a definitive prediction; additional or redefined inputs are needed in several cases. Nevertheless some generalizations emerge:

1. In the 40 years prior to 1970, a major reason for rapid electrical growth w a s the sustained decrease in the real price of electricity.

2. In the future, costs of all forms of energy will rise in real terms, thus growth rates for both electric and nonelectric energy will not be sustained at historic levels. (A 4 percent per year average growth rate for electricity over the next 75 years has emerged from representative runs.)

3. Nonelectric energy costs appear to rise significantly faster than electric energy costs, so that electricity substitution is expected to continue. (Electricity may be expected to reach 50 percent of all energy use by about the year 2015.)

4. During the period 2000 to 2020, there is a possibility that a "crunch" will occur in U.S. energy avail- ability. This will result from:

0 A decline in the availability of oil and gas to the United States caused by exhaustion of domestic supplies and increasing competition for world supplies.

0 A rapid rise in the price of uranium as used in light-water reactors, caused by depletion of lower cost resources.

0 Constraints on the further growth of coal pro- duction, which will already have risen to 5 or 6 times present production by the first decade of the 21st century. If coal is required to grow at a rate to offset completely the loss of oil and gas, then upward pressure on prices, and ultimately depletion, will result.

0 An LMFBR which, while developed, will not yet be in a position to become the main workhorse of U.S. energy production.

5. The "crunch", if it occurs, will result in the following changes:

0 Pressure for rapid development of a large syn- thetic fuels indlstry, limited by the availability and price of coal and by competition with the use of coal for the generation of electricity.

0 The introduction of shale oil and solar heating and cooling of buildings (although we believe that these alternatives will probably be limited by environmental and capital constraints, respec tively).

0 Increasing concern about energy for transporta- tion which, in the case of limited coal avail- ability, will likely translate into a major shift to electricity (either for direct use in electric vehicles or for producing electrolytic hydrogen fuel). Consequently, the price of nonelectric energy will rise rapidly, and consumption will decrease.

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6. If the breeder can be introduced at costs which now seem reasonable (around $800/kW in 1975 dollars), it will dominate the US. energy picture by 2030 and will result in electricity prices remaining relatively low. In this event, further growth of speculative energy techndogies may not occv, although some of them may have been rushed into use in an earlier "energy crunch" period.

APPENDIX

The economic analysis is based on obtaining the equilib- rium conditions which maximize an objective function of the form

where the various terms are defined in the text. We find a maximum at any time, t , by differentiating with respect to q1 and q2 and setting the equations to zero:

dgl ds =a(t) blqll q22 -as - 0 b - 1 b dC -

1

-- a - a(t) b2q11 b 922 b - 1 - 3 dC - - d42

We replace I p (t), - E p (t), where the functions

pl, p2 are now defined as the marginal prices. The equations

dC a1 1 d42 2

give, in terms of these prices, after some reorganization,

Differentiating the above equations with respect to time, we obtain

and these last two equations can be combined to yield

If the behavior of the quantities ql, q2, pl, and p2 can be

represented by exponentials of the form

where t* is a reference year, then we obtain the result cited in the text

9 + H~ = a2 + n 2

The equations also yield, with a = a e * y(t-t*) 0

When H ~ , H~ = 0 (constant prices), then, under the assumption that in equilibrium at constant prices a constant share of GNP is maintained, we obtain

a 1' a2 = (-)and hence, we determine

We have extended this analysis, optimizing over a 75-year time period, by using the expression

If we approximate ql, pl, q2, p2 as exponentials and approx-

after integration imate the sum as an integral over a period 0 to O, we obtain,

Differentiating under the definite integral with respect to the reference year, t , we obtain from the con&tions

*

% = O and ds

the equations

and

e ( y + blal +b2a2 -a2 - n2)t* =

ca

a0 b291 92 * *b b2-1 $ Bt ,(y + blal + b2a2)t

These may be combined to give

13 60

Under economic equilibrium as defined earlier, we have al + m 1 = a2 + n2 and hence obtain, provided the

integrals converge,

b l 92 p2

91 p1

* *

" 5 *. t

This is the condition for determining - as a function of

the reference values in year t , which can now be taken as any year O < t < m. This result is independent of the discount factor, B.

bl

* b2 I

By similar derivation, the condition Y + blal +

b2 a2 = a2 + m2 = a1 + xl, which comes from Equation 3,

permits the determination of a. from historic data by

* P"

8

P1

As described in the text, the condition a + m 1 = a2 + m 2

appears to be reasonably in accord with historic data.

Thecondition Y+b a + b 2 a 2 = a2 + m2 = a1 + m 2 1 1

is difficult to determine within the accuracy of economic statistics but is also within the statistic range provided by historic data, and we have therefore used Equation 7 to de- termine ao.

REFERENCES

(1) Manne, A.S., ETA A Model for Energy Technolcgy Assessment, Energy and Environment Policy Center, John Fitzgerald Kennedy School of Government, Harvard University, Cambridge, M e s s .

(2) Various references for historic data included in figure captions. Data for Table I from International Institute for Applied Systems Analysis, Schloss Laxenburg, Austria.

(3) General Electric Company, The Energy Conversion Alternatives Study (ECAS), sponsored by NASA and EPRI, private communication based on completion of Phase II by Corporate Research and Development, General Electric Company, Schenectady, N.Y.

(4) References to Input data are included in notes to Table II.

(5) Estimates based on work of W. Nordhals, Yale Univer- sity, private communication.

(6) Levenson, M., Murphy, P.M., and Zaleski, C.P.L., Relative Capital Cost of the LMFBR, Electric Power Research Institute, Inc. report, presented a t American Power Conference, Chicago, Ill., April 20, 1976.

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