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Forecasting technological substitution: The logistic model of energy systems revisited
TECHNOLOGICAL
FORECASTING
AND SOCIAL CHANGE
32, 273-280
(1987)
Forecasting Technological Substitution: The Logistic Model of Energy Systems Revisited P. SILVENNOINEN
. AND J. VAANANEN
ABSTRACT
A simple logistic model of market substitution has been applied to situations where price and cost parameters vary in time. In such cases the market share does not necessarily evolve as a monotonous function of time. Although this particular feature of the model has not been validated against data from past experience, it can be applied heuristically to studying future trends in market penetration. As an example, possible competition patterns of coal and nuclear power as primary fuels for electricity production have been examined under various combinations of economical parameters. The illustrative results involve both cases where the nuclear contribution would be phased out as well as those where nuclear power could still maintain a strong position a few more decades to come.
Introduction Substitution of one technology for another is a basic element in the structural evolution of any industry. Modeling this phenomenon has attracted some interest in recent years. Trend extrapolation and simple logistic functions have proved useful [ 11. Logistic models have also been applied to energy systems where the penetration processes have historically been relatively slow [4, 61. The simplicity of the existing models implies that the market share of a given technology progresses monotonously up to a maximum, and thereafter this particular technology is phased out, again monotonously. While historical data seem to provide evidence of such a behavior in many cases, there is little justification that this would hold for predictions made for the future. In particular, one may be skeptical about some of the forecasts on the future contribution of different primary energy sources. Assuming that past trends remain valid, Marchetti and Nakicenovic [4] propose continuously declining prospects for coal. However, there have been substantial investments in coal production in recent years. Fossil fuel prices have been reduced. At the same time public concern has hampered and delayed the development of nuclear energy which was thought to replace coal and oil in electricity generation. As a consequence, and especially after the accident at Chernobyl, the position of these resource bases may have changed drastically. This paper proposes a simple scheme for extending the applicability of the conven-
P. SILVENNOINEN and J. VAANANEN are research scholars at the Technical Research Centre of Finland in Helsinki. Address reprint requests to Mr. P. Silvennoinen, Technical Research Centre of Finland, P.O.B. 169, 00181 Helsinki. Finland. 0 1987 by Elsevier Science Publishing
Co., Inc.
OO40-1625/87/$03.50
,. P.SILVENNOINENANDJ.VAANANEN
214
tional substitution models. The market share of a given technology is permitted to have more than one period of dominance if its competitive market position with regard to alternative technologies can be improved. The method has been applied to the competition of coal and nuclear energy technologies. Since the last major changes in the long-term outlook for energy have occurred only around 1985-1986, the accumulated statistical data, whether for the world as a whole or for individual countries separately, are yet too sparse to validate the proposed scheme. Therefore, extrapolations into the future are to be viewed as outlining plausible bounding limits rather than a definitive forecasts. In spite of the great ambiguity, the results of the case study suggest that, for the next three to five decades, coal would retain a larger fraction of the market as a primary fuel for electricity generation than what has been predicted in corresponding earlier studies. This is not so much due to Chernobyl but derives from price-driven competition under a certain set of assumptions. In fact, it is not feasible to incorporate abrupt setbacks in the simple substitution model. Dynamic Model Using the theoretical basis suggested by Peterka 191, the logistic substitution can be displayed in the form
(YQj=
Pi (p-Cj),
model
(1)
where p denotes the price of the commodity produced, Pi is the production capacity based on the technology i, ci is the associated production cost, and oi denotes the investment cost per unit increase of capacity. Equation (1) states simply that the investments in new capacity are determined by the net income from the existing capacity based on the same technology. This fundamental principle can be modified to include more sophisticated strategies [lo]. However, these refinements are not necessary for the subsequent discussion elaborating the new scheme. The free parameters p and ci in eq. (1) are now permitted to vary in time. Iffi(t) is the market share of the technology i during the time interval t, then the price p of the commodity concerned is assumed to develop as the average
where p is a constant to be determined from case to case. A general solution of eq. (1) can readily be given by
Mf)
Pi(t) = Pi (to) exp {J Equation
(3) leads to the following Pi(t) =
&i
(3)
1.
‘0
discretized
Pi(O) exp
ci(f)ldt
-
form:
‘-’ [p(k) C k=O
-
ci(k)]Af %
(4)
TECHNOLOGICAL SUBSTITUTION: ENERGY SYSTEMS
It has been assumed each interval At and For the sake of shares fi are replaced
in eq. (4) that the cost and price parameters remain constant over therefore the integral can be expressed as a sum. convenience, the absolute values of the capacities Pi or the market by relative ones [9]. Defining JY as the relative market share _fij(f) =
for two competing
275
technologies
fi(t)lfj(t) =
(3
pi(tYpi(t)
i and j, eq. (4) leads, after some manipulation,
to
(6)
or, equivalently, fi/(t)
=
Jj(t
-
- [p(t -
1) exp ({[p(t 1) -
-
cj(t -
l)-Cj
(t -
l)]loii) At).
l)]/CYi (7)
Using eq. (7), one can proceed gradually through the time horizon and evaluate the new valuesAY after each time step At. The original market share& is obtained from the normalization condition
5 = l/(1 + X&J.
(8)
j#i
Application to Energy Conversion Technologies Marchetti has shown that the simple logistics model can be fitted rather successfully to historical data on primary energy sources [4]. It is therefore appealing to apply the dynamic model to the same energy technologies. This is in spite of the fact that the latest developments affecting primary energy substitution have emerged only recently. No firm data exist, and one has to accept that the forecasts are on a rather heuristic basis. Among the secondary energy commodities, electricity appears to exhibit most of the features embodied in the substitution model proposed in the previous section. At least limiting the discussion to base load electricity generation, the quality of the product is rather insensitive to the conversion technology used and, on the other hand, a uniform price exists. An electric utility would be expected to install new capacity based on the particular technology i for which the excess earnings p - ci are largest. Regardless of the minimum cost objective, an electricity-generating system cannot depend on one single fuel or technology. Security of supply is an important attribute in planning new investment. This requirement can be taken care of by specifying a part of the total capacity as reserve and leaving it outside the direct competition. Alternatively, the lowest permissible market shares can be assigned for some energy sources. In terms of the production cost ci, the energy conversion technologies include both high and low capital cost alternatives combined with either higher or lower operating costs. The total cost ci is split into fixed capital cost Ci and varying fuel and operating cost Fi with
216
P. SILVENNOINEN
C,(t)
=
AND J. VAANANEN
C,(t)+Fi(t).
These components obey rather different trends. Neglecting developing costs and limiting the analysis to mature energy technologies, the differences in the escalation rate of the capital costs derive mainly from nontechnical factors, i.e., political considerations or changing social and environmental standards. The societal factors naturally influence the fuel costs as well. However, in the long term, the overriding concern affecting the fuel prices is that of resource availability. The subsequent discussion focuses on this part of the problem and assumes that the capital investment costs remain constant. The substitution of energy technologies is then tantamount to resource-driven competition between primary fuels. Nuclear Versus Coal-Fired Electricity In the industrialized countries with market economies coal’s contribution to electricity generation has been around 45% around the mid- 1980s [2]. The nuclear share has increased steadily from less than 13 to almost 20% during the first half of the 1980s [7]. The case study which will be presented here aims to illustrate how further competition of these two fuels could be studied parametrically using the dynamic substitution model described above. The parameters appearing in eqs. (6) and (7) are based on energy economics data that were recently evaluated for the conditions prevailing in Finland. These basic data are reasonably close to those given for a number of other countries in a recent international study [8]. However, the interpretation of these data is not necessarily unique in the sense that they could directly yield the values of (Yand c embodied in the formal expressions of eqs. (6) and (7). The investment costs (Y,are assumed to include the direct construction costs as well as interest during construction and a provision for decommissioning in the case of nuclear power. The numbers are given in Table 1 after conversion from Finnish marks to 1985 U.S. dollars. All estimates are given in constant money. Interest is compounded at the annual rate of 5% in real terms. The total costs ci are chosen to correspond to the levelized cost of power production. Taking into account the initial construction costs and operating, fuel, and waste management costs, the levelized cost allocates the total production costs over the total amount of energy generated during the lifetime of the plant. In Table I it has been specified which part of the total cost relates to fuel. Throughout the time horizon this component may change while the fixed costs are assumed to have constant relative and absolute values. The assumptions made on the time evolution of the fuel costs are summarized in Table 2. For the sake of simplicity a single trend of development is assumed for natural uranium price. The spot market prices are much below the long-term contract prices [5]
Economical
TABLE 1 Model Parameters’
Parameter
Coal
Nuclear
All Others Lumped
a, (s&W) o(O) (millsikWh) F,(O) (mills/kWh) fi(0)
195 34 23 0.45
1335 21 1.2 0.13
NA 1.2 NA 0.42
“NA = not applicable
TECHNOLOGICAL
SUBSTITUTION:
ENERGY SYSTEMS
211
TABLE 2 Assumptions
on
Case
Relative Changes in the Fuel Costs” AFc
@O/yr)
Time Period 50 years 50 years 20 years Next 10 years Next 10 years Thereafter
2 0 2
1 2 3 -2
2 -2 “AF. = 28yr
in all cases; c = coal and z4 = uranium.
and remain, in real terms, lower than those valid ten years ago. Therefore, it appears reasonable to expect the uranium price to increase in the long term. The rate of increase AF, is assumed to be 2% per annum. In view of this development, coal prices F, are foreseen to remain at their present level or increase in the future. The various cases studied are listed in Table 2. In particular, variant 3, is devised for mainly the purpose of illustrating the capabilities of the dynamic model.
ELECTRICITY
“1
!
./
+--.-‘--’ :i__
04
---1
GENERATION
.’
\\
/’
_.-. ~_
..~.__
\\ ~_~,_-___ \
? 1
\ \
20
25
30
35
to
45
so YEhA
Fig. 1. Market shares of primary f’uels, Case 1.
I
,. P. SILVENNOINEN AND J. VAANANEN
218
Illustrative Results The results for the three illustrative cases are depicted in Figures 1-3, where the market share forecasts of coal and nuclear are drawn as a function of time. It is recalled that the sum of these two is kept rather arbitrarily constant in order to allow for decisions made on other criteria than that of economic competitiveness. In Figure 1, the relative fuel shares behave very much as in the case of simpler logistic models. The decline in coal’s contribution is actually accelerated since both fuels are assumed to become dearer at the same percentage rate. The situation is quite opposite in Figure 2, where the coal price is assumed to remain at its present value for the next 50 years. Since the uranium price is set to increase steadily, the penetration of nuclear power ends in a few years’ time and coal starts to increase its share. It is not very likely that either one of the Cases 1 and 2 would prevail on a global scale in the future. However, there might be countries for which one of these illustrative cases would correspond to reality. A steadily increasing nuclear share is foreseen in France and Japan, for example. In the aftermath of Chernobyl, it is obvious that Case 1 is feasible only in a country where the use of nuclear energy will recover from the serious lack of public confidence. On the other hand, in the countries where the setback is of a permanent nature, the phaseout of nuclear power will probably take place more rapidly than in Case 2. As was pointed out previously, the simple model may not be applicable at all to those cases. -. ELECTRICITY
GENERATION
Fig. 2. Market shares of primary fuels, Case 2.
TECHNOLOGICAL
SUBSTITUTION:
~_.-.--.-.~._.
. ..-_--.ELECTAICITY
w
I
L”
1
GENERATION
1
Lz In
219
ENERGY SYSTEMS
3 ._-.
..__._..- _.____~____~._.__ _.__._~._--_--
$01
!
2
f-----__
4___._. -=- _.._-.--.
_Y_<
“;
\\
j m; .---_-
__-_-
-...-
--__._-.--
\ ‘.
~_.
-_ ----__
--.. ._ -. - -_-..
--..-
.-.
-_
3
,,.-.-.--
4
CII !
fir-.I_-__-
A.--‘-.
‘..
COOL
nusCeor
.+L-.- _- -_-.. ~._ -..---..../
_-..._ -.- ~__.
_3+_.-,-.’
04
.----
_-_
_/’
~..
04
i
.---
.__.-
-.
._--
~_._.__.
!a
__.___ _______..__-. _-.._. ____ __..-.-.---~ --.-Fig. 3. Market shares of primary fuels, Case 3.
Figure 3 shows a synthetic case where the coal price development is discontinuous. The coal price fluctuates between a 2% increase and decrease per year. In the face of the presumed increase of the uranium price, the coal and nuclear contributions attain a balance during the planning horizon. Of course, there is no justification whatsoever for this rather peculiar assumption on the variation of the coal price, but the case is simply meant to display a nonlogistic shape of the market shape curve. From eq. (7) it is obvious that the relative market share remains unchanged between two consecutive time periods t and I+ 1 if the exponent vanishes, i.e., [p(t) -
Ci(t)]loli -
[p(t) -
Cj (t)]lUj =
0.
(10)
The fact that nuclear power is more capital intensive, i.e., onWlear> ocoalr implies that nuclear must entail a clearly lower production cost in order to remain competitive against coal. Discussion
In many cases investigated in the literature, technological change has followed a simple substitution pattern. Corresponding logistic models have also been applied to forecasting future penetration of new technologies. It is obvious, however, that the simple
280
P. SILVENNOINEN
AND J. VAANANEN
logistic curve will not describe properly the substitution process if price and market parameters change drastically. First-order modifications of the model have been proposed in this study. Forecasts based on the new model are not necessarily much more reliable than those obtained from straightforward fittings of historical data. However, the time-dependent model is a consistent generalization of the earlier work and thereby cannot perform any worse either. Historical data would be needed to validate the model in any particular case. The contribution of coal as a primary fuel is taken as an example of those situations where the forecasts made using the simple logistic model will very likely differ substantially from reality. The fact that substitution models permit little consideration of the overall potential contribution of a technology has earlier led to predictions where coal is phased out rather rapidly. The development of coal prices and other market parameters may produce a counteracting effect enhancing the market share. Coal could make a growing contribution to energy supply. Case studies displayed in this paper indicate a wide range of possibilities. In one extreme nuclear would, indeed, be phased out while at the other end it still continues to take over from coal. It has been often pointed out that the competition edge is very much country-specific [8]. The public reactions to the Chernobyl disaster also varied substantially from country to country. This may amplify the differences, and different countries may indeed adopt a wide spectrum of energy policies. Under no circumstances should the results obtained using the dynamic model be viewed as authoritative forecasts. The model rather facilitates an easy survey of the conceivable impact that changing production costs would yield in terms of market shares of competing technologies. Methods for modeling subsidized penetration [3] and market behavior [lo] have been already developed and could be used to improve the correlation with reality. As a matter of fact, these methods could be developed further to account for some rapid changes. One should, however, be very skeptical as regards the pragmatism in such modeling. References 1. Fisher, I. C.. and Pry, R. H., A Simple Substitution Model for Technological 2. 3. 4. 5. 6. 7. 8. 9. 10.
Change, Technological Forecasting and Social Change 3, 75-88 (197 I). International Energy Agency, Coal Prospects and Policies in IEA Countries, 1983 Review, Paris, 1984. Lehtinen, R., Silvennoinen, P., and Vira, J., Substitution Models for Overlapping Technologies, Angewandte SystemanalyselApplied Systems Analysis. 3(2), SO-57 (1983). Marchetti, C., and Nakicenovic, N., The Dynamics of Energy Systems and the Logistic Substitution Model, International Institute for Applied Systems Analysis, RR-79-13, Laxenburg, Austria, 1979. Nukem, Marker Reporrs on the Nuclear Fuel Cycle, Hanau, Federal Republic of Germany, 1985. OECD Nuclear Energy Agency, Nuclear Energy and Its Fuel Cycle, Prospects to 2025, Paris, 1987. OECD Nuclear Energy Agency, Nuclear Power and Fuel Cycle Data in OECD Member Countries, Paris, 1983, 1984, 1985, 1986. OECD Nuclear Energy Agency, Projected Costs of Generating Electricity from Nuclear and Coal-Fired Power Stations for Commissioning in 1995, Paris, 1986. Peterka, V., Macrodynamics of Technological Change-Market Penetration by New Technologies, International Institute for Applied Systems Analysis, RR-77-22, Laxenburg, Austria, 1977. Spinrad, B. I., Marker Substitution Models and Economic Parameters, International Institute for Applied Systems Analysis, RR-80-28, Laxenburg, Austria, 1980.
Received 8 April 1987.
FORECASTING
AND SOCIAL CHANGE
32, 273-280
(1987)
Forecasting Technological Substitution: The Logistic Model of Energy Systems Revisited P. SILVENNOINEN
. AND J. VAANANEN
ABSTRACT
A simple logistic model of market substitution has been applied to situations where price and cost parameters vary in time. In such cases the market share does not necessarily evolve as a monotonous function of time. Although this particular feature of the model has not been validated against data from past experience, it can be applied heuristically to studying future trends in market penetration. As an example, possible competition patterns of coal and nuclear power as primary fuels for electricity production have been examined under various combinations of economical parameters. The illustrative results involve both cases where the nuclear contribution would be phased out as well as those where nuclear power could still maintain a strong position a few more decades to come.
Introduction Substitution of one technology for another is a basic element in the structural evolution of any industry. Modeling this phenomenon has attracted some interest in recent years. Trend extrapolation and simple logistic functions have proved useful [ 11. Logistic models have also been applied to energy systems where the penetration processes have historically been relatively slow [4, 61. The simplicity of the existing models implies that the market share of a given technology progresses monotonously up to a maximum, and thereafter this particular technology is phased out, again monotonously. While historical data seem to provide evidence of such a behavior in many cases, there is little justification that this would hold for predictions made for the future. In particular, one may be skeptical about some of the forecasts on the future contribution of different primary energy sources. Assuming that past trends remain valid, Marchetti and Nakicenovic [4] propose continuously declining prospects for coal. However, there have been substantial investments in coal production in recent years. Fossil fuel prices have been reduced. At the same time public concern has hampered and delayed the development of nuclear energy which was thought to replace coal and oil in electricity generation. As a consequence, and especially after the accident at Chernobyl, the position of these resource bases may have changed drastically. This paper proposes a simple scheme for extending the applicability of the conven-
P. SILVENNOINEN and J. VAANANEN are research scholars at the Technical Research Centre of Finland in Helsinki. Address reprint requests to Mr. P. Silvennoinen, Technical Research Centre of Finland, P.O.B. 169, 00181 Helsinki. Finland. 0 1987 by Elsevier Science Publishing
Co., Inc.
OO40-1625/87/$03.50
,. P.SILVENNOINENANDJ.VAANANEN
214
tional substitution models. The market share of a given technology is permitted to have more than one period of dominance if its competitive market position with regard to alternative technologies can be improved. The method has been applied to the competition of coal and nuclear energy technologies. Since the last major changes in the long-term outlook for energy have occurred only around 1985-1986, the accumulated statistical data, whether for the world as a whole or for individual countries separately, are yet too sparse to validate the proposed scheme. Therefore, extrapolations into the future are to be viewed as outlining plausible bounding limits rather than a definitive forecasts. In spite of the great ambiguity, the results of the case study suggest that, for the next three to five decades, coal would retain a larger fraction of the market as a primary fuel for electricity generation than what has been predicted in corresponding earlier studies. This is not so much due to Chernobyl but derives from price-driven competition under a certain set of assumptions. In fact, it is not feasible to incorporate abrupt setbacks in the simple substitution model. Dynamic Model Using the theoretical basis suggested by Peterka 191, the logistic substitution can be displayed in the form
(YQj=
Pi (p-Cj),
model
(1)
where p denotes the price of the commodity produced, Pi is the production capacity based on the technology i, ci is the associated production cost, and oi denotes the investment cost per unit increase of capacity. Equation (1) states simply that the investments in new capacity are determined by the net income from the existing capacity based on the same technology. This fundamental principle can be modified to include more sophisticated strategies [lo]. However, these refinements are not necessary for the subsequent discussion elaborating the new scheme. The free parameters p and ci in eq. (1) are now permitted to vary in time. Iffi(t) is the market share of the technology i during the time interval t, then the price p of the commodity concerned is assumed to develop as the average
where p is a constant to be determined from case to case. A general solution of eq. (1) can readily be given by
Mf)
Pi(t) = Pi (to) exp {J Equation
(3) leads to the following Pi(t) =
&i
(3)
1.
‘0
discretized
Pi(O) exp
ci(f)ldt
-
form:
‘-’ [p(k) C k=O
-
ci(k)]Af %
(4)
TECHNOLOGICAL SUBSTITUTION: ENERGY SYSTEMS
It has been assumed each interval At and For the sake of shares fi are replaced
in eq. (4) that the cost and price parameters remain constant over therefore the integral can be expressed as a sum. convenience, the absolute values of the capacities Pi or the market by relative ones [9]. Defining JY as the relative market share _fij(f) =
for two competing
275
technologies
fi(t)lfj(t) =
(3
pi(tYpi(t)
i and j, eq. (4) leads, after some manipulation,
to
(6)
or, equivalently, fi/(t)
=
Jj(t
-
- [p(t -
1) exp ({[p(t 1) -
-
cj(t -
l)-Cj
(t -
l)]loii) At).
l)]/CYi (7)
Using eq. (7), one can proceed gradually through the time horizon and evaluate the new valuesAY after each time step At. The original market share& is obtained from the normalization condition
5 = l/(1 + X&J.
(8)
j#i
Application to Energy Conversion Technologies Marchetti has shown that the simple logistics model can be fitted rather successfully to historical data on primary energy sources [4]. It is therefore appealing to apply the dynamic model to the same energy technologies. This is in spite of the fact that the latest developments affecting primary energy substitution have emerged only recently. No firm data exist, and one has to accept that the forecasts are on a rather heuristic basis. Among the secondary energy commodities, electricity appears to exhibit most of the features embodied in the substitution model proposed in the previous section. At least limiting the discussion to base load electricity generation, the quality of the product is rather insensitive to the conversion technology used and, on the other hand, a uniform price exists. An electric utility would be expected to install new capacity based on the particular technology i for which the excess earnings p - ci are largest. Regardless of the minimum cost objective, an electricity-generating system cannot depend on one single fuel or technology. Security of supply is an important attribute in planning new investment. This requirement can be taken care of by specifying a part of the total capacity as reserve and leaving it outside the direct competition. Alternatively, the lowest permissible market shares can be assigned for some energy sources. In terms of the production cost ci, the energy conversion technologies include both high and low capital cost alternatives combined with either higher or lower operating costs. The total cost ci is split into fixed capital cost Ci and varying fuel and operating cost Fi with
216
P. SILVENNOINEN
C,(t)
=
AND J. VAANANEN
C,(t)+Fi(t).
These components obey rather different trends. Neglecting developing costs and limiting the analysis to mature energy technologies, the differences in the escalation rate of the capital costs derive mainly from nontechnical factors, i.e., political considerations or changing social and environmental standards. The societal factors naturally influence the fuel costs as well. However, in the long term, the overriding concern affecting the fuel prices is that of resource availability. The subsequent discussion focuses on this part of the problem and assumes that the capital investment costs remain constant. The substitution of energy technologies is then tantamount to resource-driven competition between primary fuels. Nuclear Versus Coal-Fired Electricity In the industrialized countries with market economies coal’s contribution to electricity generation has been around 45% around the mid- 1980s [2]. The nuclear share has increased steadily from less than 13 to almost 20% during the first half of the 1980s [7]. The case study which will be presented here aims to illustrate how further competition of these two fuels could be studied parametrically using the dynamic substitution model described above. The parameters appearing in eqs. (6) and (7) are based on energy economics data that were recently evaluated for the conditions prevailing in Finland. These basic data are reasonably close to those given for a number of other countries in a recent international study [8]. However, the interpretation of these data is not necessarily unique in the sense that they could directly yield the values of (Yand c embodied in the formal expressions of eqs. (6) and (7). The investment costs (Y,are assumed to include the direct construction costs as well as interest during construction and a provision for decommissioning in the case of nuclear power. The numbers are given in Table 1 after conversion from Finnish marks to 1985 U.S. dollars. All estimates are given in constant money. Interest is compounded at the annual rate of 5% in real terms. The total costs ci are chosen to correspond to the levelized cost of power production. Taking into account the initial construction costs and operating, fuel, and waste management costs, the levelized cost allocates the total production costs over the total amount of energy generated during the lifetime of the plant. In Table I it has been specified which part of the total cost relates to fuel. Throughout the time horizon this component may change while the fixed costs are assumed to have constant relative and absolute values. The assumptions made on the time evolution of the fuel costs are summarized in Table 2. For the sake of simplicity a single trend of development is assumed for natural uranium price. The spot market prices are much below the long-term contract prices [5]
Economical
TABLE 1 Model Parameters’
Parameter
Coal
Nuclear
All Others Lumped
a, (s&W) o(O) (millsikWh) F,(O) (mills/kWh) fi(0)
195 34 23 0.45
1335 21 1.2 0.13
NA 1.2 NA 0.42
“NA = not applicable
TECHNOLOGICAL
SUBSTITUTION:
ENERGY SYSTEMS
211
TABLE 2 Assumptions
on
Case
Relative Changes in the Fuel Costs” AFc
@O/yr)
Time Period 50 years 50 years 20 years Next 10 years Next 10 years Thereafter
2 0 2
1 2 3 -2
2 -2 “AF. = 28yr
in all cases; c = coal and z4 = uranium.
and remain, in real terms, lower than those valid ten years ago. Therefore, it appears reasonable to expect the uranium price to increase in the long term. The rate of increase AF, is assumed to be 2% per annum. In view of this development, coal prices F, are foreseen to remain at their present level or increase in the future. The various cases studied are listed in Table 2. In particular, variant 3, is devised for mainly the purpose of illustrating the capabilities of the dynamic model.
ELECTRICITY
“1
!
./
+--.-‘--’ :i__
04
---1
GENERATION
.’
\\
/’
_.-. ~_
..~.__
\\ ~_~,_-___ \
? 1
\ \
20
25
30
35
to
45
so YEhA
Fig. 1. Market shares of primary f’uels, Case 1.
I
,. P. SILVENNOINEN AND J. VAANANEN
218
Illustrative Results The results for the three illustrative cases are depicted in Figures 1-3, where the market share forecasts of coal and nuclear are drawn as a function of time. It is recalled that the sum of these two is kept rather arbitrarily constant in order to allow for decisions made on other criteria than that of economic competitiveness. In Figure 1, the relative fuel shares behave very much as in the case of simpler logistic models. The decline in coal’s contribution is actually accelerated since both fuels are assumed to become dearer at the same percentage rate. The situation is quite opposite in Figure 2, where the coal price is assumed to remain at its present value for the next 50 years. Since the uranium price is set to increase steadily, the penetration of nuclear power ends in a few years’ time and coal starts to increase its share. It is not very likely that either one of the Cases 1 and 2 would prevail on a global scale in the future. However, there might be countries for which one of these illustrative cases would correspond to reality. A steadily increasing nuclear share is foreseen in France and Japan, for example. In the aftermath of Chernobyl, it is obvious that Case 1 is feasible only in a country where the use of nuclear energy will recover from the serious lack of public confidence. On the other hand, in the countries where the setback is of a permanent nature, the phaseout of nuclear power will probably take place more rapidly than in Case 2. As was pointed out previously, the simple model may not be applicable at all to those cases. -. ELECTRICITY
GENERATION
Fig. 2. Market shares of primary fuels, Case 2.
TECHNOLOGICAL
SUBSTITUTION:
~_.-.--.-.~._.
. ..-_--.ELECTAICITY
w
I
L”
1
GENERATION
1
Lz In
219
ENERGY SYSTEMS
3 ._-.
..__._..- _.____~____~._.__ _.__._~._--_--
$01
!
2
f-----__
4___._. -=- _.._-.--.
_Y_<
“;
\\
j m; .---_-
__-_-
-...-
--__._-.--
\ ‘.
~_.
-_ ----__
--.. ._ -. - -_-..
--..-
.-.
-_
3
,,.-.-.--
4
CII !
fir-.I_-__-
A.--‘-.
‘..
COOL
nusCeor
.+L-.- _- -_-.. ~._ -..---..../
_-..._ -.- ~__.
_3+_.-,-.’
04
.----
_-_
_/’
~..
04
i
.---
.__.-
-.
._--
~_._.__.
!a
__.___ _______..__-. _-.._. ____ __..-.-.---~ --.-Fig. 3. Market shares of primary fuels, Case 3.
Figure 3 shows a synthetic case where the coal price development is discontinuous. The coal price fluctuates between a 2% increase and decrease per year. In the face of the presumed increase of the uranium price, the coal and nuclear contributions attain a balance during the planning horizon. Of course, there is no justification whatsoever for this rather peculiar assumption on the variation of the coal price, but the case is simply meant to display a nonlogistic shape of the market shape curve. From eq. (7) it is obvious that the relative market share remains unchanged between two consecutive time periods t and I+ 1 if the exponent vanishes, i.e., [p(t) -
Ci(t)]loli -
[p(t) -
Cj (t)]lUj =
0.
(10)
The fact that nuclear power is more capital intensive, i.e., onWlear> ocoalr implies that nuclear must entail a clearly lower production cost in order to remain competitive against coal. Discussion
In many cases investigated in the literature, technological change has followed a simple substitution pattern. Corresponding logistic models have also been applied to forecasting future penetration of new technologies. It is obvious, however, that the simple
280
P. SILVENNOINEN
AND J. VAANANEN
logistic curve will not describe properly the substitution process if price and market parameters change drastically. First-order modifications of the model have been proposed in this study. Forecasts based on the new model are not necessarily much more reliable than those obtained from straightforward fittings of historical data. However, the time-dependent model is a consistent generalization of the earlier work and thereby cannot perform any worse either. Historical data would be needed to validate the model in any particular case. The contribution of coal as a primary fuel is taken as an example of those situations where the forecasts made using the simple logistic model will very likely differ substantially from reality. The fact that substitution models permit little consideration of the overall potential contribution of a technology has earlier led to predictions where coal is phased out rather rapidly. The development of coal prices and other market parameters may produce a counteracting effect enhancing the market share. Coal could make a growing contribution to energy supply. Case studies displayed in this paper indicate a wide range of possibilities. In one extreme nuclear would, indeed, be phased out while at the other end it still continues to take over from coal. It has been often pointed out that the competition edge is very much country-specific [8]. The public reactions to the Chernobyl disaster also varied substantially from country to country. This may amplify the differences, and different countries may indeed adopt a wide spectrum of energy policies. Under no circumstances should the results obtained using the dynamic model be viewed as authoritative forecasts. The model rather facilitates an easy survey of the conceivable impact that changing production costs would yield in terms of market shares of competing technologies. Methods for modeling subsidized penetration [3] and market behavior [lo] have been already developed and could be used to improve the correlation with reality. As a matter of fact, these methods could be developed further to account for some rapid changes. One should, however, be very skeptical as regards the pragmatism in such modeling. References 1. Fisher, I. C.. and Pry, R. H., A Simple Substitution Model for Technological 2. 3. 4. 5. 6. 7. 8. 9. 10.
Change, Technological Forecasting and Social Change 3, 75-88 (197 I). International Energy Agency, Coal Prospects and Policies in IEA Countries, 1983 Review, Paris, 1984. Lehtinen, R., Silvennoinen, P., and Vira, J., Substitution Models for Overlapping Technologies, Angewandte SystemanalyselApplied Systems Analysis. 3(2), SO-57 (1983). Marchetti, C., and Nakicenovic, N., The Dynamics of Energy Systems and the Logistic Substitution Model, International Institute for Applied Systems Analysis, RR-79-13, Laxenburg, Austria, 1979. Nukem, Marker Reporrs on the Nuclear Fuel Cycle, Hanau, Federal Republic of Germany, 1985. OECD Nuclear Energy Agency, Nuclear Energy and Its Fuel Cycle, Prospects to 2025, Paris, 1987. OECD Nuclear Energy Agency, Nuclear Power and Fuel Cycle Data in OECD Member Countries, Paris, 1983, 1984, 1985, 1986. OECD Nuclear Energy Agency, Projected Costs of Generating Electricity from Nuclear and Coal-Fired Power Stations for Commissioning in 1995, Paris, 1986. Peterka, V., Macrodynamics of Technological Change-Market Penetration by New Technologies, International Institute for Applied Systems Analysis, RR-77-22, Laxenburg, Austria, 1977. Spinrad, B. I., Marker Substitution Models and Economic Parameters, International Institute for Applied Systems Analysis, RR-80-28, Laxenburg, Austria, 1980.
Received 8 April 1987.