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UBC Theses and Dissertations

A long term energy policy model for Canada Fuller, John David 1980

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A LONG TERM ENERGY POLICY MODEL FOR CANADA by JOHN DAVID FULLER B.Sc, Queen's University at Kingston, 1973 M.Sc., The University of British Columbia, 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Interdisciplinary.Studies --"Energy Policy"Modelling) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1980 (c) John David Fuller, 1980 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. >3>gpS>ptKrg£Ptx:scf Interdisciplinary Studies The University of British Columbia 2075 wesbrook Place Vancouver, Canada V6T 1W5 Date September 15, 1980. ABSTRACT The construction of a dynamic, long term model of the Canadian energy sector is discussed, with examples of policy analysis done with the model. A linear process model of energy supply, conversion, distribution and end-use is linked to a model of the demands for services provided by energy in combination with other inputs. Nonlinear programming is used to find the supply-demand equilibrium by maximizing the discounted sum of consumers' plus producers' surplus over all periods — three five-year periods followed by three ten-year periods, from 1975 to 2020. Long-run marginal cost curves for coal, oil and natural gas are approximated by limiting the total amounts available at different cost levels. Upper limits on exports represent current policies and bring about a two price system (domestic and inter national) in the model. Two regions are distinguished throughout the model: the west, ..west of the Ontario-Manitoba border, is the main producer of coal, oil and gas; the east, with the larger energy demands, may import coal,, oil and gas from the west, or coal and oil from other countries, if necessary. The model may be used to analyze issues of energy pricing, the timing of the introduction of frontier resources and new technologies, the competitiveness and impacts of some new technologies, the impacts of various levels of energy exports, and the impacts of various potential policy constraints. A base case is developed, with the best estimates of all parameters. In addition, low demand and high demand cases are developed to test the sensitivity of conclusions to base case assumptions about economic and population growth. Some important conclusions are as follows. Frontier natural gas will not be needed until after the year 2000. Coal liquefaction will probably not be competitive, but coal gasification may play an important role after the year 2000. Nuclear power will be important in the east. However, a "no-new-nuclear" policy after 1985 would have negligible cost, but would force a switch in the east from electricity to oil with the tar sands playing an important role after the turn of the century. District heating by cogeneration with nuclear electricity in the east may increase nuclear safety by reducing reliance on nuclear power through the partial displacement of electric resistance heating. The electric automobile will probably not be competitive unless there are technical breakthroughs which lower the initial cost difference between the conventional and electric automobiles, or the road tax burden is less for electric than for con ventional cars. iv Table of Contents Page Abstract ii List of Tables viList of Figures x Acknowledgements xiii Chapter 1. Introduction 1 Chapter 2. Review of the Literature on Energy Modelling 7 Chapter 3. An Overview of the Structure of the Model 24 Chapter 4. The Solution Method 38 Chapter 5. An Overview of the Assumptions for the Base Case 42 Chapter 6. Discussion of the Base Case Output 50 6.1 Oil 56.2 Natural Gas 63 6.3 Coal 74 6.4 Electricity 81 6.5 Transportation 92 6.6 Industry 100 6.7 DFC Heating 4 6.8 Sectoral Shares 110 6.9 Fuel Shares6.10 Total Energy 122 Chapter 7. The High Demand and Low Demand Cases 128 7.1 The Assumptions 127.2 The Results of the High Case 130 7.3 The Results of the Low Case 131 V Table of Contents (continued) Page , Chapter 8. Analysis of Some Energy Policy Questions 162 8.1 The Impacts of a No-New-Nuclear Policy , 162 8.2 Allowing Heating by Cogeneration with Nuclear Power. 175 8.3 High Oil Costs (Sensitivity Analysis) 182 8.4 The Impacts of Competitive Coal Gasification 190 8.5 The Impacts of the Electric Automobile 199 Chapter 9. Summary and Conclusions 20References 217 Appendix A. Derivation of the Demand Equations 225 Appendix B. Detailed Structure of the Model 234 B.l Coal 23B.2 Oil 7 B.3 Gas — Natural and Synthetic 240 B.4 Electricity 242 B.5 Transportation End Use Sectors 244 B.6 Industrial End Use Sector 245 B.7 Domestic, Farm and Commercial (DFC) End Use Sector . 246 B.8 Objective Function 248 B.9 Time Period Aggregation 250 B. 10 Corrections for End Effects 253 Appendix C. Data for the Base Case 257 Cl Data for the Coal Sector 25C. 2 Data for the Oil Sector 262 vi Table of Contents (continued) Page Appendix C.3 Data for the Gas Sector 269 C.4 Data for the Electricity Sector 274 C.5 Data for Transportation End Use Sectors 279 C.6 Data for Industrial End Use Sector 281 C.7 Data for Domestic, Farm and Commercial (DFC)Sector. 283 C.8 Data for the Objective Function 286 C.9 Right-Hand Side Values (Initial Conditions) 293 Appendix D. Detailed Output for the Base Case 299 Appendix E. Detailed Output for the High and Low Cases 304 Appendix F. Computer Programs and Data Listings for the Base Case 313 vii List of Tables gage 1. Units Used in the Model 36 2. Oil Production, Base Case 51 3. Crude Oil Prices, Base Case 3 4. National Oil Price, Real and Nominal Dollars, Base Case 59 5. Oil Use, Base Case 61 6. Gas Production, Base Case 65 7. Gas Use, Base Case 7 8. Gas Prices, Base Case 69 9. Gas Prices as Percentages of Oil Prices, Base Case 73 10. Coal Production, Base Case 75 11. Coal Use, Base Case 7 12. Coal Prices, Base Case 79 13. Western Electricity Production, Base Case 82 14. Eastern Electricity Production, Base Case 84 15. Electricity Use, Base Case 86 16. Western Electricity Prices, Base Case 88 17. Eastern Electricity Prices, Base Case 90 18. Transportation, Base Case 93 19. Western Output Energy Prices, Base Case 95 20. Eastern Output Energy Prices, Base Case 7 21. Road Transportation Prices, Base Case 99 22. Industrial Output Energy, by Fuel, Base Case 101 23. Shares of Fuels in Industrial Output Energy, Base Case 103 24. DFC Heating, West, Base Case 105 viii •List of Tables (continued) Page 25. DFC Heating, East, Base Case 107 26. Heat Pump Costs (in model units), Base Case 109 27. Sectoral Output Energy Shares, Base Case 111 28. Sectoral Secondary Energy Shares, Base Case 113 29. Output Energy Fuel Shares, Base Case 115 30. Secondary Energy Fuel Shares, Base Case 118 31. Primary Energy Fuel Shares, Base Case 120 32. Total Energy, Base Case 123 33. Total Energy, Percent Annual Change, Base Case 125 34. Low, Base and High Case Assumptions 129 35. Growth in Total Energy Demands Per Capita, Three Cases 133 36. Crude Oil Production, High Case 134 37. Crude Oil Production, Low Case 136 38. Crude Oil Prices, High Case 8 39. Crude Oil Prices, Low Case 140 40. Gas Production, High Case 2 41. Gas Production, Low Case 144 42. Gas Prices, High Case 6 43. Gas Prices, Low Case 148 44. Secondary Energy Fuel Shares, High Case 150 45/ Secondary Energy Fuel Shares, Low Case 152 46. Primary Energy Fuel Shares, High Case 154 47. Primary Energy Fuel Shares, Low Case 156 48. Total Energy, High Case 158 ix List of Tables (continued) Page •49. Total Energy, Low Case 160 50. Crude Oil Production, No-new-nuclear Case 167 51. Oil Use, No-new-nuclear Case 169 52. Eastern Electricity Production, No-new-nuclear Case 171 53. Primary Energy Fuel Shares, No-new-nuclear Case 173 54. DFC Heating, East, Nuclear Cogeneration Case 176 55. Eastern Electricity Production, Nuclear Cogeneration Case 178 56. Secondary Energy Fuel Shares, Nuclear Cogeneration Case 180 57. Crude Oil Production, High Oil Costs Case 184 58. Crude Oil Prices, High Oil Costs Case 186 59. Secondary Energy Fuel Shares, High Oil Costs Case 188 60. Coal Production, Coal Gas Case 191 61. Gas Production, Coal Gas Case 193 62. Secondary Energy Fuel Shares, Coal Gas Case 195 63. Primary Energy Fuel Shares, Coal Gas Case 197 64. Transportation, Electric Auto Case 201 65. Crude Oil Production, Electric Auto Case 203 66. Secondary Energy Fuel Shares, Electric Auto Case 205 67. Primary Energy Fuel Shares, Electric Auto Case 207 68. Demand Equations Used in the Model 233 69. Bounds on Industrial Fuel Shares 28X List of Figures Page 1. Schematic Diagram of Model in Each Period 25 2. Energy Flows in Western Canada 28 3. Energy Flows in Eastern Canada 9 4. Oil Production, Base Case 52 5. Crude Oil Prices, Base Case 4 6. Oil Use, Base Case 62 7. Gas Production, Base Case 66 8. Gas Use, Base Case 8 9. Gas Prices, Base Case 70 10. Coal Production, Base Case 6 11. Coal Use, Base Case 78 12. Coal Prices, Base Case 80 13. Western Electricity Production, Base Case 83 14. Eastern Electricity Production, Base Case 85 15. Electricity Use, Base Case 87 16. Western Electricity Prices, Base Case 89 17. Eastern Electricity Prices, Base Case 91 18. Transportation, Base Case 94 19. Western Output Energy Prices, Base Case 96 20. Eastern Output Energy Prices, Base Case 8 21. Industrial Output Energy, by Fuel, Base Case 102 22. DFC Heating, West, Base Case 106 23. DFC Heating, East, Base Case 8 24. Sectoral Output Energy Shares, Base Case 112 xi List of Figures (continued) Page 25. Sectoral Secondary Energy Shares, Base Case 114 26. Output Energy Fuel Shares, Base Case 116 27. Secondary Energy Fuel Shares, Base Case 119 28. Primary Energy Fuel Shares, Base Case 121 29. Total Energy, Base Case 124 30. Total Energy, Percent Annual Change, Base Case 126 31. Crude Oil Production, High Case 135 32. Crude Oil Production, Low Case 137 33. Crude Oil Prices, High Case 139 34. Crude Oil Prices, Low Case 141 35. Gas Production, High Case 3 36. Gas Production, Low Case 145 37. Gas Prices, High Case 7 38. Gas Prices, Low Case 149 39. Secondary Energy Fuel Shares, High Case 151 40. Secondary Energy Fuel Shares, Low Case 153 41. Primary Energy Fuel Shares, High Case 155 42. Primary Energy Fuel Shares, Low Case 157 43. Total Energy, High Case 159 44. Total Energy, Low Case 161 45. Crude Oil Production, No-new-nuclear Case 168 46. Oil Use, No-new-nuclear Case 170 47. Eastern Electricity Production, No-new-nuclear Case 172 48. Primary Energy Fuel Shares, No-new-nuclear Case 174 xii List of Figures (continued) Page 49. DFC Heating, East, Nuclear Cogeneration Case 177 50. Eastern Electricity Production, Nuclear Cogeneration Case 179 51. Secondary Energy Fuel Shares, Nuclear Cogeneration Case 181 52. Crude Oil Production, High Oil Costs Case 185 53. Crude Oil Prices, High Oil Costs Case 187 54. Secondary Energy Fuel Shares, High Oil Costs Case 189 55. Coal Production, Coal Gas Case 192 56. Gas Production, Coal Gas Case 194 57. Secondary Energy Fuel Shares, Coal Gas Case 196 58. Primary Energy Fuel Shares, Coal Gas Gase 198 59. Transportation, Electric Auto Case 202 60. Crude Oil Production, Electric Auto Case 204 61. Secondary Energy Fuel Shares, Electric Auto Case 206 62. Primary Energy Fuel Shares, Electric Auto Case 208 ACKNOWLEDGEMENTS My thanks go to my supervisor, William Ziemba, for several years of guidance and encouragement in the work towards this thesis. As well, I would like to thank the other members of my committee for the valuable suggestions and comments which I received at various points in the work — Ernst Berndt, Alex Meisen, Peter Larkin, Rodrigue Restrepo, James Murray, and Uri Ascher. In addition to the committee members' help, the insights and suggestions from Alan Manne, John Helliwell, Sandra Schwartz and John Rowse were very useful. I am grateful to Imperial Oil Limited, the Department of Energy, Mines and Resources, and the National Research Council of Canada for financial support at various times during the thesis work. Finally, to my wife Jennifer, my daughter Sandra, and, lately my son Daniel, I extend my deepest appreciation for their patience and support throughout the course of this work, including Jennifer's assistance with the typing and proofreading. 1 Chapter 1. Introduction Just a few short years ago, it would have been necessary to introduce a dissertation on the analysis of energy policy with an argument that it is a worthwhile topic of investigation. Today, however, it is impossible to read a newspaper without reading several articles on aspects of energy policy questions. Whether the news features a debate on oil pricing, a pipeline proposal, a report on environmental effects in Ontario from increased use of coal in the U.S.A., or the promotion of solar energy and the denigration of nuclear power, it is clear to anyone that energy policy is an important area of investigation. It is perhaps not so clear to everyone why the con struction and use of mathematical models of the energy system should form a necessary part of energy policy analysis, nor why another energy model, the one developed here, should be added to the already long list. The complex relationships among the demands for and supplies of the different energy commodities suggest that a careful and systematic analysis must be carried out before a decision is made. "Back of the envelope" cal culations cannot begin to come to grips with questions of interfuel sub stitution and changing market shares, especially over the longer term. One would expect that carefully constructed mathematical models can do better. However, as Marcuse (1980) points out "... energy models ... cannot be relied upon for prediction ... models of socioeconomic phenomena unlike those of physical phenomena cannot possibly include all of the pertinent vari ables. Even if they could, the relationships among the vari*. ables are not and perhaps cannot be known." Marcuse argues that an important role of the model in decision support is in answering "what if" questions. That is, the analyst can compare the values of key variables in the model solution under different scenarios. If certain 2 policies or technologies are preferred in a reasonable range of scenarios, they are said to be "robust", and some useful information can be given to the decision makers. Furthermore, Marcuse observes that insight is gained in the very process of modelling, by forcing the analyst to be systematic and to seek the reasons for counter-intuitive model results. As well, the need for data for the model often forces the analyst to collect previously unavailable data, which turns out to be useful information in itself. Discussed here is the construction of a model of the energy sector of the Canadian economy. The model takes into account the interaction of energy supplies and demands, but ignores effects the energy sector has on the rest of the economy. It is a long term model, covering the period 1975 to 2020, (three five-year periods, followed by three ten-year periods) a sufficiently long time for the exhaustion of the conventional reserves of crude oil and natural gas, and for the transition to alternate fuels. A linear process model of energy supply, conversion, distribution and end-use is linked to a model of the demands for services provided by energy in combination with other inputs such as capital. Nonlinear programming is used to find the supply-demand equilibrium by maximizing the discounted sum of consumers 1 plus pro ducers' surplus. Two regions - east and west, with the dividing line at the Ontario-Manitoba border — are distinguished throughout the model, since many important questions centre on the difficulties of transporting the large hydrocarbon supplies of the west to the large markets of the east. The west exports hydrocarbons to other countries and to the east. The east imports coal and oil. Electricity is exported from both regions. Upper limits are placed on all exports to other countries, to represent national decision-makers' present risk-averse behaviour. (To examine a policy of 3' unrestricted exports, the model would require some alterations from its present formulation). Linear approximations to long-run marginal cost curves for exhaustible hydrocarbon resources (coal, oil, and gas) are included in the model. Crude oil from the tar sands is considered separately. Other primary resources include hydroelectricity, nuclear electricity, solar heat and biomass. All costs of production, conversion, transportation and distribution are unit costs which include capital components (with a stipulated rate of return). The model represents a network of energy flows from primary production, through secondary conversions (e.g. coal to electricity), to end-use con versions into final demands (e.g. space heating). Linkages among the periods are found in constraints which require established new capacities of many production and conversion processes to last for stipulated lifetimes. Oil and gas production capacities decline in the latter parts of their lifetimes. Constraints limiting the total amount of production of exhaustible resources also link different periods. The model calculates equilibrium quantities and many prices throughout the network of energy sector flows. Because of the export limits, domestic resource prices are typically below the international prices — that is, the export limits imply the two-price system presently in effect in Canada.' (To examine the world pricing alternative, the model would have to be altered in the manner required for examination of unrestricted exports.) Prices for exhaustible resources rise, over time, to the costs of the "backstop" sources (i.e. sources which are, for all practical purposes, in unlimited supply, at a possibly high cost). The model fills a gap in Canadian energy modelling. It is one of only three Canadian energy models (all recently developed) which calculates both 4 equilibrium quantities and prices in an integrated supply-demand framework. The process modelling of interfuel substitution, including some functional end-use processes, make this model the only one of the three which may be used for the evaluation of both new secondary and new end-use energy tech nologies. The computational simplicity and relatively small size of the model make it possible for a single analyst to update the data and structure. It may be used to analyze issues of energy pricing (assuming continuation of the two price system), the timing of the introduction of frontier re sources and new energy technologies, the competitiveness and impacts of some new energy technologies, the impacts of various levels of energy exports, and the impacts of various potential policy constraints. For example, it is shown in this thesis that frontier natural gas is not needed until after the year 2000, according to the model. This is a robust conclusion under a reasonable range of assumptions about energy demands. Model results suggest that the "appropriate competitive relationship" of gas and oil prices (to use the phrase of the Department of Energy, Mines and Resources, 1976a) may be quite different in the west than in the east: gas should be priced lower than oil in the west, until 1990, and somewhat higher afterwards; but the eastern gas price should be about equal to that of oil until 1990, and then consider^-ably higher than the oil price. It is found that the electric automobile will not be competitive unless there is a breakthrough lowering the difference in initial cost between electric and conventional automobiles, or unless the government subsidizes the electric auto by lessening the road tax on electric auto users. Analysis of a moratorium on new nuclear power plants after 1985 suggests that the economic effects would be negligible, that total eastern electricity production and use would be much lower, and that oil from the tar sands would be the main alternative to nuclear electricity in the east after the turn of the century. 5 Chapter 2 reviews some related energy sector models and indicates the niche filled by this-model. A detailed listing of model variables, parameters and equations appears in Appendix B. An overview of the structure is contained in Chapter 3. Appendix A contains the explanation of the derivation of the demand functions. The method used to find the equilibrium quantities and prices (the maximization of consumers' plus producers' surplus) is given in Chapter 4, together with a discussion of the size of the nonlinear program and the typical computing time required to find the solution. Listings of data and program files for the base case, and an explanation of the tech nicalities of the computing procedure are presented in Appendix F. Collection of the data was a major part of the effort, as it is with most large energy modelling projects. The details of sources and calcu lations for all parameters for the base case (the most likely values) are in Appendix C, except for elasticities of demand, which are discussed in Appendix A. An overview of important (and sometimes controversial) data assumptions for the base case is presented in Chapter 5. The base case results are analyzed in Chapter 6. The sensitivity of the results to alternative assumptions about energy demands is investigated in Chapter 7, focusing on the high and low demand cases. Observations on key energy policy issues are drawn from comparisons of the high, base and low cases. Detailed listings of the calculated values of all variables of these three cases are found in Appendices D and E. Some energy policy questions are analyzed in Chapter 8 with the aid of the model. The impacts, including costs, of a moratorium on new nuclear power development are examined, followed by an estimate of the impacts and economic benefits of allowing district heating by cogeneration with nuclear generated electricity. The possibility that the real costs of producing crude oil may have recently escalated above the estimates used is examined next. Finally, the effects of the availability of coal gasification and electric automobiles at competitive costs are examined. (Under the base case cost assumptions, these two technologies do not enter the solution). Conclusions and suggestions for further research are found in Chapter •Chapter 2. A Review of the Literature on Energy Modelling Since the early 1970s, and especially since the dramatic increase in the international price of oil in 1973, hundreds of energy models have been developed in North America and Europe with the aim of aiding the analysis of energy policies. This review is a partial survey, covering those models whose elements were used in the development of the model discussed here, or may be used in future research stemming from the present modelling work. Several important Canadian models are also out lined. More thorough surveys may be found in Fuller and Ziemba (1980), and in Manne et al. (1979). Articles, on many energy models in the United States and Canada may be found in the collections edited by Ziemba, Schwartz and Koenigsberg (1980), and by Ziemba and Schwartz (1980). The models discussed in this review treat the entire energy sector of a country (or larger region) as a system, to represent the crucially important behaviour of interfuel substitution. The current state of national energy modelling in Canada is discussed, with an indication of the niche filled by the model developed here. Some comments on directions for future research follow, with reference to some models which are re viewed. (A more complete discussion of future research may be found in Chapter 9). Nordhaus (1973) introduced an important methodology and several concepts which are central to much of the later analysis. The extraction, transportation and processing of energy to meet final demands is represent ed in a linear programming (LP) framework. He considers five regions in the non-Communist world: the United States, Western Europe, Japan, the Persian Gulf and North Africa, and the rest of the world. There are five demand categories for energy products: electricity, industrial nonelectri •8 energy uses, residential nonelectric uses, substitutable transportation (i.e. electricity could conceivably supply the necessary energy), and nonsubstitutable transportation (i.e. air traffic and long-distance auto mobile traffic, neither of which can be run on electricity). Demands are specified exogenously for each category, on the grounds that price elasticities are quite low, and that the chief response to price changes is interfuel substitution, which is represented in the model. The model determines the allocation of energy resources, oyer several time periods (five ten-year periods, followed by two twenty-five-year periods and two fifty-year periods) which minimizes the discounted costs of meeting the specified final demands. Nordhaus' primary use of the model is to discuss the introduction dates of new technologies and primary resources, and to estimate the efficient price paths for the fuels. An important concept introduced by Nordhaus is the notion of the "backstop" technology. Since the planning problem is really over an indefinite length of time, it is necessary, in principle, to include at least one infinitely plentiful primary resource and technologies which can transform it into all final energy demands. Such "backstop" technologies may be much more expensive than today's tech nologies, but they must be included in order to ensure feasibility of the infinite-time-horizon problem. Nordhaus' discussion of resource prices is instructive for under standing the behaviour of other models, such as the model developed here. Exhaustible resource prices, taken from the appropriate dual variables' values at the optimal solution, have two components. The first is the exogenous cost of production. The second component of the price is the 9 -"royalty" or economic rent due to the scarcity of the resource. The price of a resource gradually rises toward the cost of the backstop technology, as the less costly but exhaustible sources are used up. As the price rises to the backstop cost, the royalty component shrinks to zero.• When the backstop technology is relied upon, there is no economic rent, because the price equals the cost of production. In earlier periods, prior to re liance on the backstop technology, the cost of the backstop is a ceiling on the price of the resource. A modelling procedure developed by Hoffman (1973) forms the basis of the Brookhaven Energy Systems Optimization Model (BESOM). The procedure begins with the "Reference Energy System", which is a network represent ation of the energy flows from primary energy commodities through con version, transportation, distribution and utilization activities. A linear programming model is developed from the Reference Energy System to minimize the cost of meeting specified end use energy demands. BESOM optimizes over a single year and one region (usually the U.S.A.). End use demands are defined by function (e.g. space heating) rather than by broad statistical categories (e.g. commercial energy demand). There is extensive detail in the energy supply, conversion, transportation, distribution and utilization technologies. Environmental emissions are also calculated. BESOM can be used either in the optimization mode with various objectives, or in a simulation procedure, as outlined-by Kydes (1980), for the assessment of energy technologies, or to study the impacts of various possible energy policies. The Hudson and Jorgenson (H-J) (1974) model ties together a macro-economic growth model, an interindustry model with energy sector detail and a model of consumer demand. There are four non-energy sectors and five energy sectors in the interindustry model, whose input-output co efficients are determined endogenously and are price responsive. Trans-log price possibility frontiers relate the prices of inputs to the prices of outputs, and provide flexibility in the representation of sub stitution responses among inputs. The H-J model finds the market equilibrium one period at a time. Its econometric estimation of behavioural responses contrasts sharply with the process-oriented models with technological detail, like BESOM. Another important distinction is the H-J model's explicit representation of the interactions between the energy sector and the whole economy. The H-J model has been used extensively to examine alternative U.S. tax policies for stimulating energy conservation and reducing dependence on energy imports. The H-J and BESOM models have been combined, using a procedure de scribed in Hoffman and Jorgenson (1977). (The integration of dynamic versions of both models is discussed in Hudson and Jorgenson, 1978.) The combined model is a single period model, like BESOM, having the ad vantages of both the H-J and BESOM models. The integration of the models is based on an interindustry accounts system which is an expansion of the H-J system. The solution procedure involves an iterative method. The combined model can provide assessments of the impacts of research, de velopment and demonstration policies on the energy sector (typical of BESOM analyses), as well as impacts of these policies on the whole economy (typical of H-J analyses). The model can be used to evaluate the impacts of energy tax policies on the economy (typical of H-J Analyses) and in particular on the detailed energy sector, including impacts on the intro duction of new technology, via the BESOM component. The PILOT modelling project at Stanford University has developed the Welfare Equilibrium Model (WEM) of energy - economic interactions in the U.S.A. (Parikh, 1980). WEM is an intertemporal linear programming model, with many linear approximations to nonlinear relations, maximizing a household welfare function that characterizes a standard-of-living measure. An input-output model of the economy is linked to a detailed energy submodel which explicitly includes resource depletion and many energy technologies. The usual unresponsiveness of input-output co*-efficients is modified in WEM by the use of multilevel hierarchy of pair-wise substitutions, represented by linear approximations to nonlinear homothetic functions. WEM is a "clairvoyant" model, solving for all time periods simultaneously as if all decision makers in the economy have per fect foresight for all future prices, in contrast to the H-J model, which is "myopic", solving for one period at a time, as if all decision makers make their decisions based strictly on present economic conditions. WEM has been used to explore the long term effects on the U.S. economy of rising energy import prices. It has also been used to aid the planning staff of the Electric Power Research Institute with pre paration of their research and development plan involving new energy technologies (Parikh et al., 1978). Long range energy projections have been developed for the U.S. Department of Energy with the aid of WEM. Generally, it can be used for detailed sectoral assessments of the impacts on the economy of various energy supply, price and tax scenarios. The Energy Technology Assessment (ETA) model (Manne, 1976) is a' 12 •nonlinear programming model which maximizes consumers' plus producers' surplus in the U.S. energy sector. The constraints are linear, as in a conventional LP process analysis. ETA has a seventy-five-year planning horizon (fifteen five-year intervals), from 1970 to 2045, but results are presented only to 2030, to avoid "horizon" effects. See Grinold (1980) for an analysis of "horizon" effects in the ETA model. Like WEM, ETA is a clair voyant model. The exogenous GNP trend is the principal driving force for ex pansion of energy demands over time. In addition, ETA demand is price-responsive, incorporating own- and cross-price elasticities of demand between electric and non-electric energy. Unitary elasticity of sub stitution between electric and non-electric energy is assumed. Prices for electric and non-electric energy are equal to their marginal costs of supply, at optimal production and distribution levels. Energy supply possibilities have their own cost parameters, and future technologies have their own introduction dates (i.e. when they are available, although they may not be part of the optimal mix). In ETA, many scenarios are possible, according to input data on costs, introduction dates, and availability of new technologies. The benefits of different technologies can be evaluated by running ETA with and without the availability of the technology in question; the difference in the optimal value of the objective function is a measure of the benefits of the technology. Manne (1977) describes a modification of the ETA energy sector model, called ETA-MACRO, which involves the replacement of the ETA objective function with an aggregated macroeconomic growth model. Electric and non electric energy are supplied by the energy sector to the rest of the economy (represented by the macro growth model). Aggregate economic output is allocated between interindustry payments for energy costs and final demands of current consumption and investment. It is assumed that gross output depends upon four inputs: capital, labor, electric energy and non electric energy. The objective function for the optimization runs is the discounted sum of the logarithms of future consumption. The macro model is driven by three exogenous parameters: the dis count rate in the objective function (the main determinant of the savings-investment accumulation process), the labor force growth index, and the elasticity of substitution between energy and non-energy (the principal factor governing the economy's ability to cope with higher energy prices) ETA-MACRO is used to examine the two-way linkage between energy and the rest of the economy. A base case is developed involving the best estimates of all parameters. The model is small enough (350 rows, 600 columns in the matrix of linear constraints, and 80 variables entering nonlinearly into the objective function) that numerous alternative cases can be run quickly, at low cost. Manne (1977) finds that a "no-nuclear" policy would have negligible macroeconomic effects, unless the elasticity of substitution is quite low and there are serious restrictions on non-nuclear energy resources. After the dramatic rise in oil prices in 1973, the U.S. federal gover: ment required not just energy trend forecasts, but a description of the interaction of the supply and demand of many energy products, over time, with a variety of geographical characteristics. Since there was little agreement in defining desirable feasible futures, a descriptive rather than a normative modelling approach was needed to calculate the .logical implications of a consistent set of assumptions or policies. The Project Independence Evaluation System (PIES) is one such forecasting tool (Eynon et al. 1975, Hogan 1975, 1977 and Greenberg 1980a). (PIES has recently been renamed as the Medium Term Energy Forecasting System). PIES is used for policy analysis for five to fifteen year planning horizons. It is a regional model, and forecasts prices and quantities of energy goods pro duced, consumed, or converted, facility construction requirements and operational modes, transportation activities and associated resource requirements. PIES is composed of a demand model, a collection of supply models, and an integrating model. There is a separate model at each supply region, for each product (coal, oil, natural gas, shale oil), to characterize the price-quantity relationship for that product. The pro ducts are moved through a transportation, conversion, and distribution system to the demand regions. A separate model, incorporating cross-price elasticities of energy demand, characterizes the price-quantity relation ship determining the demand for energy products. If the demand vector is known, the selection of supply alternatives is made by a linear programming, minimum total cost calculation. The dual variables are the supply prices, for the given demand vector. In this way, implicit supply curves are generated. The system is brought into equilibrium by the integrating mechanism when supply equals demand, and the supply prices equal the prices cal culated by the demand model for the equilibrium demand. The integrating mechanism involves iterations of a linear programming approximation to a fixed point algorithm. Eynon et al. (1975) give the following examples of exogenous inputs which have been introduced into the PIES system for policy analysis: price changes in imports; import tariffs; import quotas; domestic fuel taxes, accelerated new material supply; conservation measures; demand management; oil to coal conversion in electric utilities; various coal and nuclear construction limits; and electricity load management. Green berg (1980a) discusses the political background to use of the model for the U.S. National Energy Plan in 1977. The SRI-Gulf model was originally developed by the Stanford Re search Institute (SRI) in 19 73 to analyze a synthetic fuels strategy for Gulf Oil Corporation. Versions of the model have been used for other purposes, such as a study of the economic forces influencing the develop ment of western U.S. energy resources such as coal and oil shale (SRI, 1976). The model is regional, dynamic, and contains a great deal of detail on energy technology and market behavior (including market imperfections). In construction of the model, described by Cazalet (1977, 1978), perfect competition is not assumed/ the market adjustment process is de scribed, and process technologies are explicitly represented. The de cision problem to be analyzed is decomposed into different sub-models, which are connected by a network. At the bottom of the network are processes describing long run re source supply curves and depletion.of reserves in.the various supply regions. Later stages in the network involve transportation and con version processes. When a need can be filled from several different sources, allocation processes describe the sharing of the market among competing fuels. At the top of the network are processes describing the regional end-use demands for energy (not for fuels, but for residential/ commercail space heat, industrial steam, etc.), as functions of end use energy prices, demographic factors, economic factors, weather, etc. The model also includes simplified models of the U.S. economy and population growth, and processes describing the price changes of materials used in the construction of energy facilities due to energy industry demands. Each of these processes in the network consists of physical relations de scribing flows, efficiencies, etc., and behavioral relations describing the decision making behavior which sets prices and quantities. An iterative algorithm computes tentative prices of process outputs for all time periods, starting from the resource supply prices and moving up through the network, using the behavioural relations, with quantities estimated at the last iteration. At the second step of an iteration, the quantities of inputs to processes are computed by working downward through the network, using the physical relations. The algorithm terminates when all prices and quantities are unchanged on successive iterations. The method used in the SRI-Gulf model can account for market im perfections and human behaviour,such as price controls, rationing, learning curves for new technology, and the determination of economic rents on primary resources from estimates of future prices. Applications and ex tensions of the modelling approach are described in Cazalet (1979). Debanne" (1975, 1980) has developed a series of network based energy sector models. The version described in Debanne (1975) deals with a net work of oil, gas, nuclear, hydro, coal, geothermal and solar energy flows in ten U.S. and nine Canadian regions. The model minimizes the total cost of meeting exogenous energy demands, in interaction with submodels of in vestment in capacity expansion and of exploration and reserves accumulation. With the model, one can examine, from a continental point of view, the economic advantages of alternative pipeline projects, and the effect on fossil fuel market shares of various new energy technologies. Debanne' (1980) discusses methods for incorporating price-responsive demand and supply functions in the network minimization framework. The National Energy Board (NEB) and the federal Department of Energy, Mines and Resources (EMR) use two similar versions of a model for making energy demand projections in Canada. The EMR version is discussed in de tail in a publication by EMR (1977a). Sahi and Erdmann (1980) discuss an important development in the EMR model — an interfuel substitution component. CANDIDE, a large econometric model of the Canadian economy, discussed in McCracken (1973), supplies consistent, projected values for a majority of the independent variables of the EMR model. These are dis aggregated, by assumed ratios, over the five statistical regions of Canada — Atlantic, Quebec, Ontario, the Prairies, B.C. and Yukon. End-use energy requirements for residential, commercial and industrial sectors are projected using double-log equations involving lagged demand, weather variables, and economic and demographic projections, some of which come from CANDIDE. Elasticities of energy demand with respect to relative fuel prices, real disposable income, volume of retail trade, and real domestic product and other variables are incorporated in the projections, allowing for periods of adjustment to the relative price changes by means of the lagged demand terms. Energy prices are supplied exogenously by the model user. Input energy required for projected end-use (output) energy is estimated in the EMR model, using energy conversion efficiency data. The' model user can insert hypothetical future improvements in energy use efficiencies. The market shares of the different fuels in the input energy requirements are calculated by means of semi-log market share equations depending on relative fuel prices, described in Sahi and Erdmann (1980). The econometric model discussed in Helliwell et al. (1976), Helliwell (1979) and in Helliwell et al. (1980) will eventually be a tool for assess ing a great number of current and future energy sources and policy options, but presently, the model emphasizes questions concerning frontier and non-frontier natural gas, non-frontier crude oil, and synthetic oil from the Athabaska oil sands. The Helliwell model pays close attention to energy trade and trans portation, and to domestic oil and natural gas prices. World crude oil prices are determined outside Canada and are exogenous to the model. Domestic oil and natural gas prices are determined by a policy rule. After allowing for transport costs to Statistics Canada's five major consuming regions, the resulting prices are used in a consistent set of estimated demand equations for all end-use sectors aggregated together in each region to forecast demand for oil, gas, coal and electricity. The demand equations, which explicitly account for regional peculiarities such as unavailability of natural gas in the Atlantic provinces, are composed of fuel cost share equations and equations determining the aggregate ex penditure on total energy in each region. To account for delays in the adjustments (to changing prices) of total energy consumption and in fuel substitutions due to energy use being associated with capital stocks, the fuel prices used in the cost share equations are weighted averages of the current price and previous three years' prices. Apart from oil and gas prices, other exogenous variables are the gross national expenditure (GNE), the GNE price index, the price of electricity, the growth of hydro-electricity supply, and the growth of natural gas distribution pipelines. Production sectors for non-frontier and frontier natural gas, non-frontier conventional crude oil, and oil sands, and oil imports meet the calculated demands. Costs of discovery, development and production, production income taxes and royalties, and economic rents are computed. The model hooks up needed reserves, and additions of new reserves are fore cast exogenously (an attempt is being made to make the exploration pro cess endogenous). There is considerable detail in tax and royalty arrangements. There are two types of links between the energy model and the agg regate economy. Quarterly versions of the annual models of arctic and oil sands development, linked with RDX2, a quarterly econometric model of the Canadian economy, allow assessments of the macroeconomic impact of large energy projects. Helliwell et al. (1976) achieve consistency between the entire energy model and RDX2 by using output from the energy model as input for a new solution of RDX2, and vice versa, until a solution which satisfies both models is achieved. An example of the second type of link would be an energy trade surplus flowing into RDX2, where it influences the exchange rate (and other things), which, when fed back to the energy model, affects the Canadian dollar price of world oil and hence all Canadian energy prices. Daniel and Goldberg (1980) report on work towards integrating the EMR demand model with a model of Canadian energy supply, using the linear programming procedure developed for solving the PIES model. When this work is complete, a major theoretical deficiency in the EMR demand model will have been resolved, namely the absence of simultaneous, integrated projections of both energy demand and supply. The supply side of the Daniel and Goldberg model is to be modified from work by McConaghy and Quon (1980) on an energy supply model for Alberta. The model developed here is similar in spirit to the Daniel and Goldberg model, namely to integrate the EMR demand work with a model of energy supply, conversion and distribution in Canada. However, here, interfuel substitution is handled by a supply side linear process sub model rather than via the EMR econometric interfuel substitution com ponent. In the model developed here, interfuel substitution is handled in the manner developed by Hoffman for BESOM. Another feature of BESOM which has been used, as far as the existing data will allow, is the specification of energy demands by functional end uses. In the domestic, farm and commercial sector, heating (space and water) is distinguished from other energy demands, and the road transportation demands may be met by either gasoline or electric automobiles. However, in contrast to the static model BESOM, which is solved one period at a time (i.e. the solutions are "myopic", and represent the behaviour of decision makers whose expectations are that future prices will be the same as present prices), the model described here is solved for all time periods at once (i.e. the solutions are "clairvoyant", as if all decision makers' expect ations of future prices turn out to be exactly correct). In this respect, this model is similar to Manne's ETA model. Other points of similarity with the ETA model are: - both are small enough for a single analyst to manage (updating the data base, modifying the structure, making and interpreting runs); - both are small enough that the computing expense is small, allowing for the development of many scenarios; - both find the market equilibrium by maximizing consumers' plus producers' surplus; and - both are formulated as nonlinear programming problems with nonlinear objectives but linear constraints, using the MINOS code (described in Murtagh and Saunders, 1977) to find the solution. Some major points of dissimilarity between ETA and the model described here are: - this model carries the process analysis through to the end uses, in the cases of space heating and automobile use, while in ETA the demand is for secondary energy, which is categorized into electric and nonelectric energy; and - there are two regions, west and east in the model discussed here, but ETA is a one-region model. An examination of energy-economy interactions is one possible area of future research stemming from the work discussed here. The work could proceed by linking the present model to an existing macroeconomic model, as in the combination of the H-J and BESOM models. Alternatively, the approach of the PILOT project with the WEM model -- a single optimizing model containing an economic model and energy sector detail -- might be adopted. In the early development of the model discussed here, an attempt was made to represent energy-economy interactions by the method of ETA-MACRO. Although this approach is appealing since it keeps the model small and manageable, it had to be abandoned to keep the process detail in the end use sectors because there was no apparent way to make each end use sector's share of total output energy endogenous. Another possible direction for future work is in increasing the number of regions distinguished in the model. Computational feasibility •of such a larger model may require decomposition methods, perhaps along the lines of the solution method used by the SRI-Gulf model. A complete discussion of future research possibilities may be found in Chapter 9. The model discussed here fills a gap in the energy modelling efforts in Canada. This model, the Daniel-Goldberg model and a recent version of the Debanne' (1980) model are, to the author's knowledge, the only energy models for Canada which calculate both prices and quantities, given price-respons ive representations of supply and demand. Other models calculate demands if the prices are given (e.g. the EMR model), supplies if the demands are specified (e.g. McConaghy and Quon), or both supplies and demands if the prices are given (e.g. Helliwell). The model developed here differs from the Daniel-Goldberg model mainly in its handling of interfuel substitution by the supply side linear process submodel, which has advantages over an econo metric approach for long range projections. Another difference is in the computational methods — this model is solved by a single optimization, while the Daniel-Goldberg model is solved by the complex iterative method origin ated for the PIES work. This model is distinguished from both the Daniel-Goldberg and Debanne''models in its explicit process modelling of some end-use demands, by function. The Debanne' model also uses a complex iterative solution procedure. The advantages, then, of the model described here, com pared to other Canadian models, are the integrated supply-demand equilibrium approach, the process modelling of interfuel substitution, including some functional end-use specifications, and computational simplicity. This model will hopefully be useful in making a contribution to the debate in the areas of Canadian energy policy for which it seems well-suited, namely energy pricing, the timing of the introduction of frontier energy resources and new energy technologies, the competitiveness and impacts of some new energy technologies, the impacts of various levels of energy exports, and the impacts of various potential policy constraints (e.g. a nuclear moratorium). Examples of several such analyses are presented in Chapters 6, 7 and 8. Chapter 3. An Overview of the Structure of the Model The model is composed of a linear process submodel of energy supply, distribution and use, coupled with a model of the demands for the ser vices provided by the energy. The complete•specification of all vari ables and relations may be found in Appendix B. The model equilibrates energy supplies and demands by maximizing consumers' plus producers' surplus (the procedure is described in chapter 4). There are two regions — west and east, with the dividing line at the Ontario-Manitoba border. This division represents the most important regional aspect of Canadian energy policy questions — fossil fuel supplies are largest in the west, while the main markets are in the east. Figure 1 illustrates the general structure of the model. The west exports energy to other countries and to the east. The east is an energy importer, taking supplies of fossil fuels from the west and from other countries, but a relatively small amount of electricity is exported from the east to the U.S.A. In each region, the energy commodities undergo various conversion processes and are distributed to the four end-use sectors within the linear process model 1. the domestic, farm and commercial sector, 2. the industrial sector, 3. the road transportation sector, and 4. the "other" transportation sector. In the end-use sectors are the final conversions to output energy (which may be viewed as an index of the useful services provided by energy in com bination with other inputs such as capital - e.g. space heat, transport ation, etc.), still within the linear process model of supply. For each end-use sector of each region, output energy demand is specified as a SUPPLY remaining capacities from previous period energy exports to USA, Japan, etc. energy production, conversion, and distribution in west western primary ^ energy transported to east energy e*P°rts to USA (electricity) energy^ imports energy production, conversion , and distribution in east remaining capacities from previous periods DEMAND (for output energy ) 0 WEST other transportation road transportation industrial domestic, farm 8 commercial EAST other transportation road transportation industrial domestic ,farm S commercial FIGURE 1 SCHEMATIC DIAGRAM OF MODEL IN EACH PERIOD 26 function of several exogenous economic and demographic variables, and of the endogenous price of the output energy. Output, rather than secondary energy is used in the demand functions because the demand for secondary energy is a derived demand. The demands are for the services such as heating, transportation, etc., which may be met by various com binations of inputs such as secondary energy and capital. The use of output energy in the demand functions allows a process representation of present and possible future devices for supplying the services represented by output energy. In this way, the secondary energy fuel shares may be de termined endogenously, with explicit consideration of future technologies which will use secondary energy. The two data which represent an end-use conversion process are the conversion factor (the ratio of output energy to secondary fuel input) and the non-fuel conversion cost (representing the other inputs). It should be noted that in reality the conversion factors and non-fuel costs are price-responsive, but in the model, they are fixed exo-genously. However, this theoretical deficiency is likely minor in the case of space heating, since interfuel substitution (which is represented in the model) will probably dominate the effect of fuel price on the conversion coefficients and costs. For oil used in the two transportation sectors, the conversion coefficents are varied over time, exogenously, to indicate expected increases in fuel efficiencies. This theoretical deficiency may have a significant effect in the industrial sector. There are six time periods - three of length five years, followed by three of length ten years, for a total span of 45 years, from 1975 to 2020. A seventh "period" represents the time from 2020 to infinity, in a procedure to mitigate end effects, described later in this chapter. The later periods are longer primarily for computational efficiency, but the decreased accuracy is not very important since there is much larger uncertainty in these later periods. The production levels in a period are influenced by levels in earlier periods, as described later. In each time period, the linear process submodel is. represented as a network of flows of energy commodities. Figures 2 and 3 illustrate, in complete detail, the networks for the west and the east, respectively. Primary energy in its various forms (i.e. crude oil, natural gas, coal, hydro-electricity, nuclear electricity, biomass energy products, and solar space heat) is converted into secondary energy (oil products, gas, coal and coke, electricity, space heat from cogeneration, and solar space heat), which is converted to output energy in the four end use sectors. The aggregation chosen for the model limits the user's ability to ex amine certain questions easily with the model. For example, since coal is treated as a single commodity, separate consideration of different grades of coal is impossible. Similarly, there is no separate treatment of the different refined oil products. The upgrading of heavy oil and its separate treatment for the purposes of export may not easily be considered in the model. The modeller must make decisions on the degree of aggregation, to make the model a manageable size. The proper examination of certain questions may require a restructuring of the model. In some cases, an element may be left out of the model because the decisions associated with it are separable from the other energy policy questions. For example, nuclear power enters the model as a primary energy source, without reference to uranium, since it appears that uranium resources in Canada are so huge that their exhaustion is not a limiting factor over the time span of the model (see Energy, Mines and Resources, 1976c, 1978d). Furthermore the possibilities of the thorium near-breeder reactor and the fusion reactor replacing uranium-based plants make consideration of PRIMARY ENERGY SECONDARY ENERGY OUTPUT ENERGY [OIL] lOTHER TRANSPORTATION! conventional, low cosl conventional, high cosl frontier, low cosl frontier high cost tor sands solar heat HEATING heat by cogeneration T~| with coal or nuclear Li electricity cogeneration SYMBOL DEFINITIONS: X>~no<le^towin:vf'QW ou* node'but enerqy industry u5e i <^ node with fined input proportions ; -Q-conversion process FIGURE 2 ENERGY FLOWS IN WESTERN CANADA PRIMARY ENERGY SECONDARY ENERGY OUTPUT ENERGY OIL OTHER TRANSPORTATION |SOLAR| solor heat from west heat by cogeneration with coal or nuclear electricity ROAD TRANSPORTATION! DOMESTIC , FARM 6Y COMMERCIAL HEATING SYMBOL DEFINITIONS : )X)-node-flow in = flow out ; node, but energy industry use ; <^>- node with fixed input proportions ; -Q- conversion process FIGURE 3 ENERGY FLOWS IN EASTERN CANADA a single "nuclear" backstop electricity source quite reasonable. For most depletable primary energy resources there are simple approximations to long run marginal cost curves, represented by two cost levels (low and high), with limits on the total resources avail able at each cost level. For crude oil from the tar sands, there is only one cost level. These cost levels are intended to cover the capital costs (with a stipulated rate of return) and the operating costs of finding and extracting the resource. Economic rents (e.g. royalties) can be calculated after the solution of the model as the differences between the equilibrium prices (derived from the dual variables) and costs of production. Non-depletable primary resources (hydro, nuclear, solar and biomass), are each available at unit costs covering operating and capital expenses, with a rate of return. Apart from the costs of primary energy production, the other com ponents of the total cost of meeting a given set of output energy de mands are the costs of secondary conversion (coal gasification and lique faction, and the conversion of oil, gas and coal to electricity), of non-fuel heating in the domestic, farm and commercial sector, of transporting oil, gas and coal from west to east, of distribution of secondary energy to the end use sectors, and the extra cost of electric automobiles over conventional ones. These unit costs also incorporate both operating and capital expenses, at a stipulated rate of return. A refining cost is in cluded in the distribution cost of each oil flow to the end-use sectors. Revenues from exports of oil, gas, coal and electricity are included in the total energy cost calculation as negative amounts, since they are benefits. Many constraints in the model are physical balance constraints which account for all flows in the network, using exogenous factors to account for energy losses due to inefficiencies of conversion and the energy industries' uses of energy (e.g. transmission losses in electricity dis tribution, refinery use of still gas, energy losses in conversion of coal to electricity, etc.). Linkages between different time periods are found in the capacity expansion and retirement constraints, in the oil: and gas production de cline constraints, in the constraints limiting the total availability of depletable resources, and in the objective function (the maximization of the discounted sum of consumers' plus producers' surpluses, which is dis cussed more fully in chapter 4). The capacity expansion and retirement constraint for nuclear electricity production, for example, specifies that new capacity (productions and capacities are taken to be identical in the model) established in one period must carry on at the same level for a total of 30 years. Many primary and secondary processes also have 30 year lifetimes, but most heating processes (except cogeneration) have 15 year lifetimes, and automobiles are taken to have 10 year lifetimes. Through the oil and gas production decline constraints, typical production time-profiles are represented by insisting that new capacities established in one period last at non-zero levels for a total of 25 and 30 years for oil and gas, respectively, but at declining levels in later periods. The demand functions are derived from work done at the Department of Energy, Mines and Resources, described in Sahi and Erdmann (1980), except for the road transportation sector. In the latter case, the demand function is derived from work by Dewees, Hyndman and Waverman (1975) on •Canadian demand for gasoline. The complete derivations and descriptions of the demand functions are presented in Appendix A. From a theoretical point of view, the aggregation of output energy should be in categories distinguished by end-use functions which are performed with the aid of secondary energy inputs. For example, it would be preferable to distinguish, say, high, medium and low temperature requirements in the industrial sector, and a separate category for mechanical drive requirements, rather than the aggregate "industrial output energy" presently in the model. This would be preferable because each functional end use category could in principle be supplied by several possible fuel inputs, and if end-use conversion efficiencies and costs were known, a total cost minimization calculation would select the fuels for each functional end use. In this way, the market shares of each fuel input to the industrial sector could be determined endogenously. However, this approach cannot be fully adopted yet. In the industrial sector, demand functions would need to be estimated for each functional end use, but there are no such estimations for Canada, likely because there is not a good data base on the existing levels of the functional end uses of energy (and their fuels) in Canada, particularly in industry. The approach adopted in this model, for the industrial sector's fuel shares, has been to put upper and lower limits on the shares of the input fuels in industrial output energy. In the domestic, farm and commercial sector, the functional end use approach has been adopted in a limited way, with space/water heating distinguished as a demand which can be supplied by six possible processes (see Figures 2 and 3). However, other non-heating demand is a fixed proportion of the total sectoral output demand, and is supplied only by electricity. In the road transportation sector, output energy demand (i.e. road transportation services) can be met by either conventional, oil-fueled vehicles, or by electric vehicles. (It has been suggested that automobiles could be converted to running on natural gas. This possibility is not included in the model since the present natural gas surplus is only temporary. It is therefore unlikely that great changes will be made in the service stations and automobile engine design for a short-lived innovation.) Oil is the only fuel which can supply the other transportation sector in the model. It is assumed that the use of coal on railways and in ships will be negligible, and that there are no technical alternatives to oil fuels in aviation. In order to represent factors involving geography, climate, the in troduction dates and rates of new technologies, etc., there are upper limits on some shares - the shares- of hydro in electricity generation in each region, the share of electric automobiles in road transportation services, and the shares of solar heat, the heat pump and district heating by co-generation in the supply of heating in the domestic, farm and commercial sector. In other cases of new technologies or new primary supply sources, upper bounds have been used to model the introduction dates and rates, with a zero-bound prior to the earliest date of introduction. There is a constraint which places an upper limit on the fraction of eastern crude oil demand which can be met from western Canadian sources. This constraint represents the physical extent of the pipeline which carries western oil to eastern markets. If the upper limit on the fraction is less than one in any period, then the eastern region is forced to rely on im ported oil or eastern offshore supplies, if the latter are available in sufficient quantities. 34 The access of western coal and gas to eastern markets is modelled by upper bounds on the flows of these commodities from west to east. In the case of coal, the potential capacity limitation is taken to be in the coal-handling facilities at Thunder Bay. The bounds on the flow of gas from west to east are intended to represent the lack of a pipeline east of Montreal (or, if the modeller wishes, the elimination of the upper bound represents the existence of a pipeline to Quebec and the Maritimes). Coal, oil and gas may be exported from the west, and electricity may be exported from either region. Since the assumed export prices are usually mugh higher than domestic prices, and since export revenues are benefits in the model, upper limits are imposed on all exports, consistent with reasonable projections. Without such upper limits, the model tends to set exports at absurdly high levels. (In an early stage of model de velopment, the model was mistakenly run with no export limits, and with the highest cost source of "oil", methanol from biomass, available in unlimited quantities at a cost lower than the export price. The problem was, of course, unbounded, since even after the rapid exhaustion of con ventional oil and tar sands, the objective function could always be improved by producing and exporting more methanol from biomass). One reason for the need for export limits is that the model is deterministic, viewing all re sources and future conditions as known with certainty. If this were true, it would make sense to export cheap supplies as quickly as possible to reap the large benefits of export revenues very early. In such a situation, domestic energy prices would rise to the export prices and the "backstop" energy supplies would more quickly become the chief domestic energy sources. However, in reality, resources and all future conditions (e.g. the avail ability of the backstop supplies) are uncertain, which has led policy makers to place restrictions on exports. Therefore, upper limits on ex ports in the model are realistic representations of decision-makers' risk-averse, somewhat nationalistic, behaviour. However, an examination of the opposite policy — unrestricted exports -- would require alter ations to the model. If it is assumed that Canada is a price-taker, then energy exports would increase to the point where the marginal cost of production equals the export price, under an unrestricted export policy. To represent this behaviour, a model would need increasing marginal costs of labour, capital, and possibly other inputs to the production of the commodities for export. The present formulation of the model has simply a single unit cost of production for each resource, which is acceptable-if exports are restricted. In summary, the present formulation of the model is as a restricted-export model, which represents the present risk-averse behaviour of national policy-makers. However, this formulation has important implications for model behaviour: domestic energy prices will not rise to world prices, but will rise at the most to the backstop costs; the introduction of new, more costly technologies may be much later than in an unrestricted-export model; and of course, resources will be depleted much less quickly than in an unrestricted-export model. In short, the limitation of exports, with the implied two-price system (domestic and international), is a key assumption. Except for coal, all energy flows are in natural units in the model. Coal is in units of lO1^ BTU rather than in tons because the single commodity, coal, in the model represents all of the grades of coal, of different thermal contents. The units used in the model are listed in Table 1. Monetary values are expressed in units of IO"1"0 dollars to avoid scaling difficulties in the solution of the model. Table 1: Units Used in the Model Coal io15 BTU Oil io9 bbl Gas io12 cubic feet (Tcf) Electricity io12 kwh Solar Heat io15 BTU Heat by Cogeneration io15 BTU output energy io15 BTU monetary values io10 Canadian dollars In the reporting procedure after the model has been solved, coal quantities are expressed in short tons, using the conversion factor, 1 short ton = 21 x lO^BTU, which is midway between the factors for bituminous and sub-bituminous coal. As well, decimal points are shifted in some prices to report them in their most familiar units. , The model is a multi-stage nonlinear programming problem, with decisions in one period affecting decisions in future periods through the various constraints relating quantities in different time periods. To solve the problem, only a finite number of periods may be considered, in troducing possible end effects, or distortions in the final periods. For example, if there is no provision in the model for times beyond the end of the last period, the production capacities of some depletable resources may be increased too rapidly in the last few periods, exhausting the re sources by the last period and ignoring the usual constraints that ordinari would make new capacity last a certain length of time, beyond the last period. Grinold (1980) describes various methods for mitigating end effects. The most promising is the dual equilibrium method. This pro cedure has been adopted in the linear process model of energy supply, and extended to the demand model. The essential assumption is that undiscounted prices are constant after the last period (i.e. all dual variables are con stant, if they are converted to undiscounted, actual values in each period; and undiscounted output energy prices are constant). This is certainly justified if prices reach the backstop costs by the last period. Using this basic assumption, extra variables and constraints are derived, along with a special weight for the nonlinear expression in the objective function involving the extra variables. See Appendix B for details. Chapter 4. The Solution Method The equilibrium prices and energy quantities are calculated to maximize consumers' plus producers' surplus. In the linear process model of energy supply and distribution, the total cost in each period of supply ing and distributing a given mix of energy quantities is calculated. The sum of the areas under the eight demand curves (four end-use sectors, two regions) may be interpreted as consumers' benefits of energy use in each time period. The difference between consumers' benefits and total cost for a given mix of energy supplies is the consumers' plus producers' sur plus in a time period. Maximizing the consumers' plus producers' surplus is equivalent to finding the eight output energy demands for which the price paid by the consumer is equal to the marginal cost - i.e. finding the intersection points of the demand and supply curves. This is done in a single maximization calculation for all time periods by maximizing the discounted sum of the consumers' plus producers' surpluses in each time period. If E. = output energy in an end-use sector in period t 1, t ( i = 1,2, ...,8), P. = real price output energy in the end-use sector i,., I , t in period t, and ei = price elasticity of demand in the end-use sector i (ei > 0), then the demand curves are: Ei,t = Ai,t • Pi,t"ei'i = i'2'---'8' where Aj_ t = t*ie Pr°duct of the factors independent of P^ fc The consumers1 benefits from using E. , are 1, t rEi,t rEi,t \P. , dE. = AVf .U:1/61 dE. t \ l,t l,t l,t \ l,t l,t • v0 00 • ,, • •, s , 1/ei 1-1/ei = ei/(ei-l) A. , . E. , + constant. 1, t l, t If the lower limit of integration is zero as above, then the constant term is finite only if 1-1/ei > 0 (i.e. ei > 1). However, since the con stant term is independent of E. , the lower limit of integration may be I , t strictly positive (making the constant term finite without restricting ei) and the constant term may be dropped from the objective function. Finally, if EC^_ = total cost of the energy supply mix in period t, and d = the real social discount rate, then to maximize consumers' plus producers' surplus over time gives the objective function: 3 maximize T]l/(l+d)t . (£ei/(ei-l) . AY*1 . E1"^1 - EC ). t i=l lrt lft t The whole optimization is a nonlinear prograinming problem, with the above nonlinear objective function and the linear constraints of the linear process model of energy supply and distribution. It should be noted that it is assumed that there are no cross price elasticities among demands for output energy. Some such assumption is necessary to make the matrix of partial derivatives of demands with re spect to prices symmetric. This ensures that the demand functions are integrable (see, e.g., Intriligator, 1971, p. 165) so that a utility function (the objective function) can be constructed. Without such an assumption en-suring the existence of an appropriate objective function, nonlinear pro gramming could not be used to solve the model as it is here. It does seem reasonable, however, to assume that demands for output energy in the four sectors and two regions are independent to a great extent, that is, that the cross price elasticities are zero. Solutions to the model have been obtained using the MINOS nonlinear programming algorithm, described in Murtagh and Saunders (1977). This algorithm is well-suited to solving this model, since it is designed for large-scale problems with linear constraints and nonlinear objective functions. MINOS is a reduced gradient algorithm employing sparse LU factorization. A stable quasi-Newton method for optimizing the objective function within a given subspace is used as long as storage requirements are not excessive. Otherwise, MINOS uses a conjugate-gradient method, which requires little storage but which converges slowly. The model has 746 rows, 960 columns, 3423 non-zero matrix elements, and 56 variables entering nonlinearly into the objective function. Solution of the model requires about 700 K bytes of storage. Usually the model is solved by starting from a basis for a similar problem, in order to save computing time. In order to gain an appreciation of how efficient the model would be as a frequently-used tool in energy policy analysis, the model was solved with high-case data (see Chapter 7), from a "cold start", without specifying an initial basis near the optimal solution. (However, the INITIAL facility in MINOS was used, with which the optimal solution to a related LP problem is first found, with the nonlinear variables fixed at reasonable guesses, followed by the solution of the NLP problem starting from the basis of the LP optimal solution). The solution of this problem required 2 742 iterations, and 301 CPU seconds on the IBM 3031 at the University of Waterloo. The CPU time includes both the MINOS calculations of the optimal solution, and calculations to produce more readable printed output and plot files to be sent to the CALCOMP plotter (there are 27 plots produced). •Chapter 5. An Overview of the Assumptions for the Base Case The data for the "base case" are the best estimates of all the model parameters, and the most likely projections of all exogenous variables and limits. The details of all derivations and sources may be found in appendix C, "Data for the Base Case". The key assumptions and approaches to estimating parameters are discussed here. There are many unit costs which are derived from data on capital and operating costs. In all such cases, a real social rate of return on capital of 8% per annum was used to amortize the capital costs over assumed fixed lifetimes of the processes' equipment. The choice of 8% was based on work by Jenkins (1977), who estimated real social rates of return on all physical capital in Canada for the period 1965-1974. Jenkins ad justed reported rates of return by revising depreciation estimates to correspond to actual service lives, and by removing the spurious effects of inflation on capital stock valuation (he estimates the current replacement value of the capital stock) and on income (he makes an inventory valuation adjustment). The return on capital includes all taxes attributable to the capital investment, in order to derive a social rate of return. The real social rate of return averaged over all industries(including housing and agriculture), weighting each industry's rate by the fraction of total 1970 capital stock found in that industry, and averaged over 1965-1974, was approximately 8%. The real social discount rate, used in the objective function, is taken to be 10%, based on a result of the study by Jenkins (1977). Jenkins calculated the social opportunity cost of government expenditures. He assumed that if government funds for expenditures are borrowed, then these funds are not available for the private sector to make the usual rate of 43-return. Furthermore, Jenkins assumes that even if the funds were raised through taxes, they could alternatively be used to lessen government debt, making more funds available to the private sector. In either case, the private sector's usual rate of return enters into the calculation of the social opportunity cost of government expenditures. Other factors are the after-tax (Canadian taxes) rate of return earned by foreign investors in Canadian assets, the decrease in consumption due to increases in personal savings when interest rates rise because of government borrowing, a "foregone foreign exchange premium", and the difference between the social opportunity cost of labour and the wage rate which would be paid if the investment funds were available to the private sector. Jenkins finds that "the social opportunity cost of government funds is at least 10 percent per year on the total amount invested in public projects."- In the energy sector model dis cussed here, one of the key intertemporal elements is the calculation of the prices of exhaustible resources. Since these prices include large royalty components, and since the royalties, or economic rents, accrue largely to governments, it is sensible to use the social opportunity cost of government . funds, 10 percent per year, as the discount rate. The National Energy Board (1979) has also used a 10% real social discount rate in a cost-benefit analysis of new natural gas exports. All costs and prices in the input data and in the output are expressed in real terms, in 1975 dollars. The Consumer Price Index has been used for all conversions to 1975 dollars, including conversions in energy production sectors. The "low cost" levels, in the approximations to the long-run supply curves for coal, crude oil and natural gas production from sources important before 1975, are taken to be the average prices, at the point of extraction (after natural gas plant processing, in the case of gas), just prior to the rapid rise in prices in the early 1970s. This procedure avoids the inclusion of "windfall profits" and vastly increased royalties which are characteristic of the mid and late 1970s. These estimates of production costs are on the high side, since royalties are included in the prices which are used, although the royalties are at the relatively low levels of the early 1970s. These low costs for existing sources are $0.20 per million BTUs for western coal, $0.80 per million BTUs for eastern coal, $4 per barrel for western conventional oil, and $0.30 per thousand cubic feet for western natural gas. The "high cost" levels for existing production, and the cost of levels for oil and gas production not yet important in the early 1970s, are based on estimates by other researchers, as explained in appendix C. In particular, synthetic crude oil from the tar sands is assumed to be avail able at a cost of $12 per barrel, using estimates of capital and operating costs by Energy, Mines and Resources (1977c), and a real rate of return of 8% per annum, over 30 years. The non-fuel costs of fossil-fuel electricity generation are based on figures presented by Hedlin, Menzies and Associates (1976), using an 8% real rate of return, over 30 years. The generation cost of hydroelectricity is assumed to be 7.7 mills per kilowatt-hour, based on the capital cost of a recent, large project in Manitoba (see Protti, 1978), using an 8% rate of return over 30 years, and assuming that non-fuel operating costs are the : same as for coal-fired electricity. This is in line with costs of projected new hydro sites for several provincial utilities (also in Protti, 1978). Nuclear electricity is assumed to have a generation cost of 10 mills per kilowatt-hour, using capital and non-fuel operating costs in Hedlin, Menzies and Associates (1976), and fuelling costs in Kee and Woodhead (1977). The capital and non-fuel operating cost estimates are higher than for exist ing .reactors, since they are based on Bruce units 5-8 which will be oper ational in 1983. The older Pickering reactor recorded a generation cost of less than 8 mills per kilowatt-hour in 1976, according to Dalrymple and Anderson (1978). Except for district heating by cogeneration, the non-fuel costs of heating in the DFC sector are based on estimates presented by the Stanford Research Institute (1976) for "high load" (cold) regions of the U.S.A., using an 8% rate of return, over 15 years. The non-fuel cost of heating by cogeneration is based on work by Berthin (1980), using an 8% rate of return, over 30 years. The cogeneration cost is mainly the distribution cost — i.e. the cost of the network of pipes to the customers. The margins for distribution, refining (in the case of oil), and taxes, for coal, oil, gas and electricity,, have been estimated by subtracting pro duction costs from prices paid in 1970 or 1971 (before the sharp increase in energy prices) by customers in the end use sectors. These margins are assumed to be constant in all time periods. The extra cost of the electric automobile is based on the estimate by Wayne (1979) of a $1500 price difference between the electric and con ventional automobiles, in Canadian, 1975 dollars. It is further assumed that cars last 10 years and travel 10,000 miles per year, on the average. The costs of transporting energy commodities from the west to the east are based on various sources. They are $1.03 per million BTUs for coal, $0.50 per barrel for oil (from Edmonton to Port Credit), and $0.44 per thousand cubic feet for gas. The price elasticities of demand for output energy in each end use sector are based mainly on work by Energy, Mines and Resources, and in the case of road transportation, on Dewees, Hyndman and Waverman (1975) . The elasticities are 0.81 for the DFC sector (this would be 0.39 if the output energy price did not include the non-fuel costs of heating), 0.48 for the industrial sector, and 0.36 for both transportation sectors (see appendix A for details). The demand functions have been calibrated using price and quantity data from 1970 and 1971, and 1970 values of the indices for pop ulation and for the exogenous economic parameters. The projections of the indices of the exogenous variables (eastern and western population, eastern and western real domestic product, income per capita, and industrial capital-output ratio) up to 2000 are based on the base case values of the most recent National Energy Board projections, ex cept for the capital-output ratio projection which is based on the projection by Energy, Mines and Resources (1977a), until 1990. The growth rate of the capital output ratio is assumed to decrease to zero by the period after 2010. Population after 2000 is assumed to grow at the rate of the mean of the Statistics Canada (cat. no. 91-520) projections. Other economic variables after 2000 are tied to population growth, assuming approximately a 2% per annum rate of increase of output per worker, due to technological change. Conversion efficiencies for coal gasification and liquefaction, and for heating in the DFC sectors are based on estimates by the Stanford Re search Institute (1976). End use conversion efficiencies in industry, road transportation and other transportation are based on estimates presented by Energy, Mines and Resources (1977a), with improvements in the transportation sectors in later periods. Conversion efficiencies for electricity from fossil fuels have been calculated from data for 1971-1975 compiled by Statistics Canada (cat. no. 57-207), with improvements assumed in later time periods. The parameters representing energy industry use of the energy commodities are also based on Statistics Canada data for 1971-1975, with improvements assumed in the case of electricity. The remaining reserves of oil and natural gas are based on the 40% probability levels of the resource estimates by Energy, Mines and Resources (1977b)(because the distributions are skewed, the 40% level is closer to the mean value of the estimates than the 50% level). It is assumed that 9 there are 200 x 10 barrels of recoverable synthetic crude oil from the tar i-5 sands. Coal reserves are assumed to be very large in the west — 1,587 x 10 BTUs at the low cost level — but very limited in the east — 22 x 10 "*"5 BTUs at the low cost level. The prices of coal imports and exports are assumed to increase at the real rate of 2.5% per year until 2000, from their levels in 1975. The real prices of natural gas and crude oil exports are assumed to increase at the rate of 4% per year until 2000. The oil import price is assumed to be lower than the export (international) price, in the first three periods, because of the import subsidy. The subsidy is reduced gradually to zero by the fourth period, 1991-2000. The upper limits on oil and gas exports have been set at the currently approved export levels. Western coal exports are allowed to reach a maximum which increases at the rate of 5% per year. The maximum levels of electricity exports increase at the rate of 1% per year in the two regions. Production from the tar sands is fixed at the "base case" level of the National Energy Board (1978) for the first four periods. This is necessary because the cost of syncrude from the tar sands is higher than most other sources of oil, which would ordinarily cause the tar sands to be left out of the model's solution until well after the turn of the century. In reality, though, tar sands production is an attractive, immediate alternative, since it is certain and accessible, while frontier sources are not. Fixing pro duction at the most likely level is therefore a realistic approach. To ensure a reasonable transition to the use of eastern offshore oil and gas, there are bounds on several variables in the first few periods. Production of oil from southeast offshore sources is assumed to be available in large quantities for the first time in the 1986-1990 period, at a maximum level of 50 million barrels per year, with a buildup in the previous period. There are no upper limits in later periods. Oil production from northeast offshore sources is allowed in the model for the first time in the period 1991-2000, at a maximum rate of 50 million barrels per year, with a buildup in the previous period, and no limits in later periods. Southeast offshore 12 gas is available in the model starting in 1988, at a maximum of 0.8 x 10 cubic feet per year, and- no upper limit after 1990. Reasonable transition behaviour of energy flows from west to east are brought about by a constraint on oil and upper bounds on coal and gas in the first few periods. Western oil is allowed full accessibility to eastern markets for the first time in the period 1986-1990. Upper limits on the transportation of western gas to the east, in the first three periods, are intended to represent the possible installation of a Quebec and Maritimes pipeline in 1985, and a five-year buildup to the full potential of gas in the energy markets east of Montreal. The transportation of coal from west to east is bounded above in the first three periods, to represent likely limits on the coal-handling facilities at Thunder Bay. The maximum production rate allowed from eastern coal reserves is increased at the rate of 15% per year for the first three periods. Without such limits, the model tends to expand production unrealistically quickly, 'because the cost of eastern coal is so low, compared to the alternative coal sources available to the eastern region. Chapter 6. Discussion of the Base Case Output. Throughout this chapter and the two following chapters, there are many figures which present plotted output of the model. Since the plotted points (which are connected by straight lines) are the average values for the periods in which they occur, the points have been plotted at the mid  points of the periods. Thus, the last plotted point in each graph is for the year 2015, representing the average annual value in the period 2011-2020. 6.1. Oil Production from conventional areas in the west (Figure 4, 'western'), including Lloydminster heavy oils, continues at an almost steady level until 1990, then declines rapidly. Northern frontier oil, both western Arctic and offshore Labrador, is not used until after 2000, even though there are no exogenous assumptions which directly force such a late entry. Southeastern offshore oil becomes important after 1985, when exogenous upper limits in the model first allow high production levels. This source is depleted by 2020. Oil production from the-tar sands is fixed at the National Energy Board (1978) base case level until 2000. After 2000, tar sands production drops slightly since there is no new capacity added during 2001-2010, but old capacity is retired. It then increases, to become the predominant oil source (49% of total supply) in the last period (2011-2020). Imports cease after 1985, when it is assumed that the entire eastern oil market first becomes fully accessible to western oil. There is no oil pro duced from coal and none from biomass. The total of oil production plus imports drops from the first period to the second, and then levels off. Crude oil prices (Figure 5) in the east are $0.50 per barrel higher than in the west, after 1985, when there are no more imports. The $0.50 difference is the transportation cost from west to east. Apart from this 51 Table 2. Oil Production, Base Case. BASE CASE; OIL PRODUCTION: IN DNITS OF 10**9 BBL PEE YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; FROM BIOMASS; FROM COAL; EASTERN; TAR SANDS; WEST ARCTIC; WESTERN; 0.2786 0.0000 0.0000 0.0008 0.0362 0.0000 0.5567 0.1109 0.0000 0.0000 0.0100 0.0744 0.0000 0.4956 0.0000 0.0000 0.0000 0.0500 0. 1534 0.0000 0.5010 0.0000 0.0000 0.0000 0.1772 0.2756 0.0000 0.2512 0.0000 0.0000 0.0000 0.2058 0.2516 0.0635 0.1319 0.0000 0.0000 0.0000 0.0740 0.3442 0.2554 0.0332 {N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 4. Thus, the differences between the plotted lines are the entries in Table 2.) 52 1.60 I-.UO H BASE CRSE OIL PRODUCTION: IMPORTS X FROM BIOMflSS • FROM COAL <!> EASTERN X TAR SANDS + WEST ARCTIC * WESTERN © 1.20 H cr l.oo H LU LU Q_ 0.80 CO CD CD X X o 0.60 H 0.40 H 0.20 0.0 1975 1985 1995 2005 2015 2025 Figure 4. Oil Production, Base Case. 53 Table 3- Crude Oil Prices, Base Case. BASE CASE; CEODE OIL PBICES: IN UNITS OF 1975$ PEE BBL AVEBAGE VALUES FOB THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPOBTS; 14.6000 17.8000 IMPOSTS; 10.8000 14.8000 EAST; 8.0200 10. 1021 WEST; 5.1521 8.1992 21.6000 32.0000 32.0000 32.0000 19.3000 32.0000 32.0000 32.0000 9.1277 8.9758 11.0672 12.5000 8.6276 8.4755 10.5673 11.9998 54 U0.00 -i 35.00 H BASE CRSE CRUDE OIL PRICES: EXPORTS X IMPORTS + ERST A WEST © 30.00 H 25.00 H _J CD CD CC DJ °- 20.00 LO r~ CD 15.00 H IO.OO H 5.00 H 0.0 1975 1985 35 lSi 20LT5 2015 2025 Figure 5. Crude Oil Prices, Base Case. 55 difference, prices (in 1975 $) in both regions move gradually upward to the cost of synthetic crude oil from the tar sands ($12 per barrel) as the less costly oil is depleted. This $12 ceiling is to be expected, since the tar sands production is effectively a "backstop" source of oil over the timespan considered in the model. (An examination of the value of the tar sands reserves limit constraint shows that the tar sands are far from depletion, even including the production for the extra "end effects" period which is an approximation of the remainder of the infinite problem beyond 2020. See Appendix B, section 10 for details of the approximation.) However, prices are below the $12 ceiling until after 2010, even though tar sands production is used, because this oil source is forced into the solution exogenously in the first four periods. The model brings new tar sands capacity into the solution without exogenously forcing it only in the sixth period, when the oil price therefore reaches the tar sands cost. The difference between the cost of oil from the tar sands ($12/bbl) and the western oil price in the solution of the model may be interpreted as an upper limit on the subsidy to be paid to tar sands producers for the "insurance" of production from the certain tar sands resource, in the face of uncertainties about the existence and costs of the other oil resources. The oil prices should therefore be viewed as lower limits (under the re stricted trade, two-price assumption), except for the last period. A de tailed, stochastic model of the oil sector may be needed to examine more carefully the problem of the subsidy for tar sands "insurance". In the first two periods,the eastern oil price is more than $0.50 above the western price because the east is forced to rely to some extent on costly imported oil. The eastern price is the average of the western price (plus the transportation cost) and the price of imported oil, weighted by the two corresponding quantities. The exogenous prices of oil imports and exports are included in Figure 5 for comparison with the endogenous domestic prices. The export price is assumed to increase at the rate of 4 percent per year until the year 2000, and the import subsidy is assumed to shrink to zero after the period ending in 1990. The reader familiar with the dictum that price must be equal to marginal cost may be puzzled by the fact that in the first two periods the eastern price is not as high as the price of imported oil, which is the highest cost source of supply in those periods. The reason is related to the form of the constraint limiting the accessibility of western oil to the eastern region: NOMEM: WOE < opipe-E0G, where opipe = 0.54 and 0.77 in the first and second periods, respectively. In words, the constraint says that the amount of western oil flowing east (WOE) must be less than or equal to a fraction (opipe) of eastern oil de mand (EOG). In the third and later periods, opipe = 1.0, giving western oil full access to eastern markets. Because of exogenous limits on eastern production in the first two periods, the constraint is ..binding then, be cause western oil is much cheaper than imported oil. However, the marginal cost of oil to the east is not the price of imported oil in the model. A fraction (opipe) of the last barrel of oil demanded comes from the west, and the remaining fraction (1-opipe) comes from imports. Therefore, the cost of the "last barrel" demanded is the average of the prices of the two sources, weighted by their fractional contributions to the "last barrel." If the constraint limiting the flow of oil from west to east had been a binding, absolute upper limit rather than a "relative" upper limit, then the marginal cost of eastern oil would have been the price of imported oil, since the "last barrel" of oil would have come entirely from imports. Of the two types of upper limit - relative or absolute - which is the more realistic? An absolute upper limit would correctly represent a sharply defined physical limit on pipeline capacity, but it may be argued that no such limit exists. The velocity of the fluid in the pipe, and therefore the flow rate, can usually be increased, perhaps with additional pumping capacity, up to a point. After that point, capacity can be increased quickly (compared to the five-year length of the first two periods), by looping. Quick increases in capacity may also be achieved by oil "swap" agreements with the United States, whereby oil is shipped from western Canada to the United States and an equal amount is shipped from the eastern United States to eastern Canada. However, if there are in fact constraints on western oil production in addition to those in the model, then real be haviour may be more like a model with an absolute upper limit on oil ship ments from west to east. (The only limitations on western oil production in this version of the model are the reserves limits, and the oil production decline constraints by which new capacity is forced to continue for ten years, then decline at 10% per year for 15 years, and then cease.) The present formulation, with the "relative" upper limit,-may therefore be viewed at least as a very plausible representation. The gradual transition to full access to eastern markets for western oil could be made first by supplying all Montreal refiners1 needs from the Sarnia to Montreal pipeline and secondly by either constructing an extension of the pipeline to the east coast or constructing facilities at Montreal for loading oil onto tankers which would unload at points east of Montreal. The solution of the model, with the "relative" limit on oil shipments from west to east, in effect indicates a subsidization of the 58 portion of the east not served by western oil, during the first two periods. Since the import price in the model is subsidized exogenously in the first two periods (to represent behaviour if the subsidy cost is not borne by the energy sector, which appears to be the case), the results indicate an ex tension of the present policy of subsidization out of concern by national policy makers for economic conditions in the Atlantic region and part of Quebec, which must rely on imported oil. In the model, the further subsidy comes from an extra charge for oil in the portion of the east served by western oil, making the calculated eastern price an average price. The other major oil subsidy indicated by the model — that on tar sands pro duction — is not included in any sort of average. As discussed above, it may be calculated after solution of the model as the difference between the cost of oil from the tar sands, and the western price calculated by the model. The difference in price, above the transportation cost, between east and west in the first two periods is unrealistic (although not large -$2.37/bbl and $1.40/bbl in the first two periods), given the federal govern ment's determination to pursue a policy of a single, national price. Since it would be difficult to put a constraint into this model, representing a single, national price, it is probably best to assume that the calculated eastern price for crude oil, adjusted for the west-to-east transportation cost, should be interpreted as the national oil price, since eastern oil demand is much larger than western demand. Under this interpretation, the calculated national oil price is shown below in Table 4. Also included in Table 4 is the national oil price in nominal dollars, adjusted by the in crease in the Consumer Price Index from 1975 to 1978 (26%, according to the Economic Council of Canada, 1979), at 8% per annum to the mid-year of the next period, 1983, and at 6% per annum to the mid years of the re maining periods. For reference, the ceiling price of $12/bbl — the cost of oil from the tar sands — is converted to nominal dollars in the third line of Table 4. . _ Table 4. National Oil Price, Real and Nominal Dollars, Base Case,. Period Ending 1980 1985 1990 2000 2010 2020 Price (1975 $/bbl) 7.52 9.60 8.63 8.48 10.57 12.00 Nominal Price 9.48 17.77 21.38 .32.52 72.60 .,147.61 Nominal Tar Sands Cost 15.12 22.22 29.73 46.03 82.42 147.61 How does the first period's price compare with the actual price levels? According to Helliwell (1979), the actual wellhead prices in 1978, the re presentative year of the first period, were $11.75/bbl after January 1, and $12.75 after July 1. The nominal price calculated by the model, $9.48/bbl, is lower than the actual price. This may indicate that the oil production costs perceived by the oil industry have been higher than has been assumed in this study. The possibility that oil costs are higher than those assumed for the base case is examined in Chapter 8. 1 Such uncertainties in key data indicate the need for continually updating a model such as this one. An earlier discussion indicated that the assumption of oil export limits implies a two-price system for oil — the domestic price is lower than the international price, and it has a ceiling equal to the domestic backstop cost (as long as the oil export limits are not so great that the tar sands are exhausted in the model). A related observation may be made: if the price paid to oil producers is raised much higher than the domestic equilibrium price (allowing for royalties to the owners, provincial govern ments), there would be very strong pressure to raise export limits, as pro ducers would bring in higher cost supplies too quickly to be absorbed in the domestic market. This has happened recently in the Canadian natural gas industry. The price paid to producers (the "netback", not including royalties) was increased dramatically after 1974, leading to vast new additions to reserves and tremendous industry pressure to export more natural gas. The same phenomenon could be observed in the case of oil if the domestic price is raised much above the domestic equilibrium price and if the producing companies receive some of this extra economic rent. It is now clear why there is no oil produced from coal, and none from biomass. With the price of coal in the model output, the distribution margin applied to coal for oil production, the assumed factor for conversion of coal to oil, and the assumed conversion cost, the cost of oil from coal is $17.23/bbl in all periods (1975 $). Therefore, as long as the tar sands can produce, with no binding upper limits, at $12.00/bbl, coal from oil will be uneconomic. It should be noted that one key assumption in this matter is that the same distribution margin for coal to western industry applies to coal for liquefaction. This margin amounts to $7.46 of the $17.23/bbl. It is conceivable that this distribution margin could be lower, since coal liquefaction plants could be located close to the mine. Even with no dis tribution margin, coal liquefaction would not be economic until after 2000, given the prices in the base case solution. Oil products from biomass, assumed to cost $25/bbl, are also uneconomic as long as oil is available from the tar sands or from coal liquefaction. Of course, if it turns out that there are unavoidable environmental or other limits on tar sands production, or if the oil price is set above the optimal price, we could see oil from biomass or coal. An examination of the detailed output of the base case reveals that the rate of transport of western oil to the east decreases as eastern offshore oil 61 Table 5. Oil Use, Base Case. BASE CASE; ; OIL USE: IN UNITS OF 10**9 BBL PEE YEAR AVEBAGE VALUES FOB THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPOBTS; OTHEB TRANSPORT; ROAD TRANSPORT; INDUSTRY; DFC; ELECTRICITY; 0.1194 0.0304 0.0623 0.0692 0.2128 0.2046 0.1508 0.1214 0.2545 0.2007 0.0172 0.0160 0.0146 0.0067 0.0815 0.1029 0.2115 0.2351 0.1753 0.2984 0.1565 0.0000 0.0142 0.0095 0.0000 0.0000 0.1283 0-1646 0.2672 0.3311 0.2093 0.1591 0.0000 0.0000 0.0000 0.0000 {N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 6. Thus, the differences between the plotted lines are the entries in Table 5.) 62 BASE CASE 1.60 -OIL USE: EXPORTS + OTHER TRANSPORT O ROAD TRANSPORT X INDUSTRY + 1.U.0 - DFC A ELECTRICITY © 1.20 H Figure 6. Oil Use, Base Case. 'is exploited, beginning mainly after 1990, but it rises again after 2010 when the main oil source for the east is from the west (mainly from the tar sands, but also from the western arctic). Oil is used in the DFC sector for heating (Figure 6) in the early periods, but is phased out rapidly to zero in the west after 1985, and in the east after 1990. Oil ceases to be used for electricity in the west and east after 2000. The use of oil in industry peaks in the period ending in the year 2000. (For a complete discussion of fuel use in industry, see section 6.6 below, in this chapter.) Oil remains the sole fuel used in road transportation (the electric automobile is not in the optimal solution). Because of assumptions about early, rapid improvements in the efficiency of automobiles, the use of oil in road transportation stays nearly constant until after 2000, then begins to rise, since efficiency improvements are not assumed to be as rapid then. The use of oil in "other" transportation increases gradually, and exports of crude oil and oil products are at the exogenously assumed upper limits. Total oil use drops by a large amount between the first and second periods, for several reasons — the oil export limit is lower, the eastern oil price rises to a temporary peak in the east in the second period (it falls in the third), and oil is phased rapidly out of use in several areas, as discussed above. 6.2. Natural Gas Natural gas production (Figure 7) -is almost entirely from the con ventional western areas until after 1985, when significant quantities of southeast offshore gas are allowed to enter the model solution. Western conventional gas production peaks in the period 1981-1985. This is roughly in agreement with the National Energy Board (1979), which projects a peak in 1985. Overall production, including eastern production peaks in the period 1986-1990. Eastern production by itself peaks in the period 1991-2000. Natural gas from northeast offshore sources is not needed until after 2000, and gas from the northwest arctic is not used until after 2010. This conclusion clearly contradicts the conclusions reached by the National Energy Board (NEB) and the Department of Energy, Mines and Resources in the mid-1970s, reported in Helliwell (1979, Table 7). The "date of estimated need for frontier gas" made by the NEB in 1969, according to Helliwell (1979, Table 7) was after 2000, as this present model predicts. As Helliwell (1979) discusses, the reasons for the mid-1970s pessimism about conventional natural gas supplies, at least in the case of the NEB, included the NEB's acceptance of the arguments by the Mackenzie'Valley pipeline groups, the major pro ducing companies, and some Canadian nationalist groups and individuals. According to Helliwell (1979), the pipeliners were trying to justify their northern gas pipeline applications, the producers were attempting to show the need for higher prices and lower taxes, using the argument that the ex pensive northern gas must soon be tapped, and the nationalists argued that the need for expensive northern gas proved that oil and gas exports should be reduced immediately. There is a tiny amount of gas produced from biomass after 2000 in the east, at the upper limits allowed in the base case. There is no gas produced from coal. The use of natural gas (Figure 8) for electricity declines to zero after the turn of the century. However, the use of gas in both the DFC and in dustrial sectors grows until 2000. Gas use in western industry falls to its lower limit (in share terms) in the next period, producing a dip in the total of industrial gas use in both regions. (See section 6.6 below for a discussion 65 Table 6. Gas Production, Base Case. BASE CASE; ; GAS PRODUCTION: IN UNITS OF TCF PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 FEOH BIOMASS; FROM COAL; EASTERN; WEST ARCTIC; WESTERN; 0.0000 0.0000 0.0002 0.0000 2.9561 0.0000 0.0000 0.0002 0.0000 4.0261 0.0000 0.0000 0.4800 0.0000 3.7211 0.0000 0.0000 0.7703 0.0000 3.0271 0.0004 0.0000 0.7054 0.0000 1.2000 0.0004 0.0000 0.6165 0.3428 0.2212 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 7. Thus, the differences between the plotted lines are the entries in Table 6.) 66 8.00 -i 7.00 H 6.00 H 5.00 H az CE LU Lu u.oo H Q_ 3.00 H 2.00 H l.oo H 0.0 1975 BASE CASE GPS PRODUCTION: FROM BIOMflSS FROM CORL ERSTERN WEST ARCTIC WESTERN 19^5 <!> X + © 1995 SiJ 2005 2015^ 20^5 Figure 7. Gas Production, Base Case. 67 Table 7. Gas Use, Base Case. BASE CASE; GAS USE: IN UNITS OF TCF PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPORTS; INDUSTRY; DFC; ELECTRICITY; 1.0800 0.5497 0.7996 0.1474 1.6800 0.6120 1.0851 0.1382 0.7400 0.7909 2.0334 0.1232 0.0300 0.7988 2.4460 0.0805 0.0000 0.5928 1.1395 0.0000 0.0000 0.7733 0.3158 0.0000 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 8. Thus, the differences between the plotted lines are the entries in Table 7.) 68 BASE CASE 8.00 —i 7.00 H GRS USE: EXPORTS X INDUSTRY + DFC ^ ELECTRICITY © 6.00 H Figure 8. Gas Use, Base Case. 69 Table 8. Gas Prices, Base Case. BASE CASE; ; GAS PRICES: IN UNITS OF 1975$ PER HCF AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EAST,AT TORONTO; 2.1488 2.5052 1.9103 2.1086 3.0005 3.0005 WEST, WELLHEAD; 0.9194 0.9653 1.0227 1.4741 2.2610 2.5003 Corrected, Toronto; 1.48 1.53 1.60 2-11 3.00 3.00 BASE CASE U.00 -i GflS PRICES: ERST.PT TORONTO A WEST. WELLHEAD © CORRECTED,TORO/\»TO + 3.50 -0.50 H °"° 1975 19^5 lS 2005 2015 20^5 Figure 9. Gas Prices, Base Case. 71 "of fuel shares in industry.) Exports continue to be very large in the first two periods, but decline to zero by the turn of the century. Exports are at the exogenous upper limits, which represent existing approved exports, as reported by the NEB (1979). Wellhead prices for gas in the west (Figure 9) rise quite smoothly from $.92/mcf in the first period to $2.50/mcf after 2010. The latter price is the cost of "low cost" gas from the western arctic, which comes into use after 2010 for the first time. Toronto city-gate prices are more volatile than western prices, with quite high prices in the first two periods, followed by a drop,- then a rise to $3.00/mcf after 2000, when northeastern offshore gas (costing $3.00/mcf) first comes into use. A large component of the eastern price in the first three periods is due to the binding upper limit on WGE, gas transported from west to east, in these periods. This limit, which is increased at the rate of 3.5% per year in the first two periods (from its level in 1971-1975) and by a larger amount in the third period, is intended to represent the initial inaccessibility of gas to points east of Montreal, followed by an extension of the pipeline to Quebec and the Maritimes during the third period, from 1986-1990. There is no upper limit on WGE after the third period. This method of representing the inaccessibility of gas to part of the east has the drawbacks that the model behaves as if consumers in all of the eastern region have access to gas distribution lines and as if equipment that uses gas is spread evenly over the entire region. The imposed supply shortage forces the price up and drives some gas "users" to alternate fuels. Of course, there will be no gas distribution lines in the region in question for several years, at least, and there will be no gas-using equipment there until then. A more theoretically pleasing procedure to represent the situation would involve the distinction of a third region which has no gas-using equipment in the end-use sectors and secondary electricity, and which shrinks in some way to represent the extension of the gas pipeline and gradual market penetration of gas. However, such a procedure would introdue great complexities. A simpler procedure is the present model formulation, together with the recognition that the com ponent of the eastern price which is due to the upper limit on WGE is artificial and should be removed. This price component reflects an artificial, unsatisfied demand for gas in the model from points east of Montreal. The corrected Toronto city-gate gas price is given in Table 8, according to this approximation to the more theoretically exact type of model discussed above. The corrected price for gas at Toronto in the first period (whose re presentative year is 1978) agrees well with the Toronto city-gate prices in 1978 reported by Helliwell (1979). If the corrected price is inflated by the increase in the Consumer Price Index between 1975 and 1978 (26%), reported by the Economic Council of Canada (1979), the price in 1978, in 1978$, is $1.87/mcf. The actual Toronto city-gate prices in 1978, reported by Helliwell (1979) were $1.68/mcf during January, $1.85/mcf beginning on February 1, and $2.00/mcf beginning on August 1. The Department of Energy, Mines and Resources (1976a) has stated a policy of moving domestic natural gas prices to an "appropriate competitive relationship with oil". What is this relationship, according to the base case results of this model? The following table shows the prices of natural gas in the west and east (corrected as above), as percentages of the prices of crude oil, where prices are initially expressed in dollars per million BTUs, using the conversion factors: 1 oncf gas = 1.04 MMBTU, and 1 bbl oil = 5.8 MMBTU. The crude oil prices were taken to be the national 73 •wellhead prices calculated in section 6.1 of this chapter, for the west, and the same prices for the east, adjusted upward by the cost of trans porting oil from west to east ($.50/bbl). Table 9. Gas Prices as Percentages of Oil Prices Period Ending 1980 1985 1990 2000 2010 2020 East 103% 84% 98% 131% 151% 134% West 68% 56% 66% 97% 119% 116% Apparently the "appropriate competitive relationship" should be different in the two regions. According to this analysis, gas in the east should be priced about equivalently with oil until 1990 but significantly higher than oil after 1990. However, in the west, gas should be priced considerably below the equivalent oil price until 1990 (perhaps 2/3 of the oil price, roughly), but the price should move to somewhat higher than the oil price after the year 2000. The higher price ratio in the east may be largely explained by the fact that the west-to-east transport cost is a much greater fraction of the eastern gas price than of the eastern oil price (the transport costs are $.44/mcf and $.50/bbl). Thus, the conclusion that the "appropriate competitive relationship" should be different in the two regions is simple to understand, but it may not have been obvious without the "prompting" of the model results. It is now apparent why there is no gas from coal in the base case solution. Using the price of coal in the solution, the assumed distribution margin for coal used in gasification, and the assumed conversion efficiency and cost, the cost of gas from coal would be $3.00/mcf. Since the price of gas in the west (the only region in which gasification is allowed) only reaches $2.50/mcf over the time span of the model, coal gasification is uneconomic. Coal gasification could therefore be introduced some time after 2020, when the western arctic gas costing $2.50/mcf nears depletion. Note that $1.41/mcf of the $3.00/mcf cost is due to the.assumed margin for the distribution of coal to industry, which is also applied to coal for gasification. However, even if this margin were zero (for a mine-mouth plant, say), coal gasification would not be economic until after 2000, given the western gas prices from the base case solution. In the long run, though, coal gasification could play the role of a backstop technology for gas, be cause of the huge size of the coal reserves. 6.3. Coal Coal production (Figure 10) rises quite significantly over the time span of the model. Eastern coal imports decline to zero after 1985, when a combination of eastern coal production and shipments from the west be comes sufficient to meet eastern demand. There is a strong and growing demand in the east for western coal, through all time periods. Eastern "low-cost" coal is depleted by 2020, but western "low-cost" coal is far from depletion. Eastern use of coal (Figure 11) for electricity drops to zero after 2000, but in the west, coal used for electricity production grows gradually until 2010, and sharply after that. The combined effect on total use of coal for electricity in both regions is a temporary drop in the period ending in 2010, followed by an increase. After 2000, there is cogeneration of heat for space heating from coal-fired electricity production in the west. The sharp increase, after 2010, in coal used for electricity in the west is related to the substitution of cogeneration for gas heating in the DFC sector (Figure 23)There is no coal used for liquefaction or gasifaction. In later periods, after 1990, industry is the biggest coal user, in both regions. Exports increase at the rate of 5% per year, which is the exogenous 75 Table 10. Coal Production, Base Case. BASE CASE; ; COAL PRODUCTION: IN UNITS OP 10**8 TONS PEE YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; 0.1581 0.1473 0.0000 0.0000 0.0000 0.0000 EASTERN; 0.0482 0.0964 0.1928 0.3453 0.3267 0.2070 WESTERN; 0.2646 0.3748 0.5026 0.9075 1.3324 2-3532 {N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 10. Thus, the differences between the plotted lines are the entries in Table 10.) 76 U..00 -i 3.50 H 3.00 H BASE CASE COAL PRODUCTION: IMPORTS + EASTERN A WESTERN © az S 2.50 H az LU Q_ g 2.00 CO O 1.50 H l.oo H 0.50 H 0.0 1975 1985 ii 1995 2005 2015 2025 Figure 10. Coal Production, Base Case. 77 Table 11. Coal Use, Base Case. BASE CASE; ; COAL USE: IN UNITS OF 10**8 TONS PER YEAR * AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPORTS; SYNFUELS; INDUSTRY; ELECTRICITY; 0.1619 0.0000 0.1325 0.1763 0.2095 0.0000 0.2321 0.1765 0.2667 0.0000 0.2545 0. 1739 0.4381 0.0000 0.6514 0.1626 0.7048 0.0000 0.8273 0.1260 1.1524 0.0000 1.0793 0.3270 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 11. Thus, the differences between the plotted lines are the entries in Table 11.) 78 BASE CASE 4.00 -i 3.50 H CQRL USE: EXPORTS X SYNFUELS + INDUSTRY A ELECTRICITY © 3.00 H Figure 11. Coal Use, Base Case. 79 Table 12. Coal Prices, Base Case. BASE CASE; ; C0A1 PRICES: IN UNITS OF 1975$ PER TON AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EAST,AT TORONTO; 32.5514 36.7489 35.6156 25.8355 25.8355 25.8355 WEST, AT MINE; 4.1983 4.1983 4.1983 4.1983 4.1983 4.1983 80 56.00 -i 49.00 H 42.00 H BASE CASE CORL PRICES-. ERST.PT TORONTO A. WEST. RT MINE © 35.00 cc LU °- 28.00 H LO CD 21.00 H 14.00 H 7.00 H © © © ©- -©- -© 0.0 1975 1985 35 19^5 2005 . 2015 "2025 Figure 12. Coal Prices, Base Case. -upper limit. Coal prices (Figure 12) in the west are at the "low-cost" in all time periods, because the "low-cost" coal is not depleted, even including pro duction in the extra period which mitigates end effects. After 1990, eastern coal prices are equal to the "low-cost" of western coal, plus the cost of transporting coal from west to east. Before 1990, there is a bulge in eastern coal prices due to the (binding) upper limit placed on WCE, the quantity of coal shipped from west to east, in the first three periods. These upper limits are intended to represent the capacity of the coal-handling facilities at Thunder Bay on Lake Superior. 6.4. Electricity Production of electricity (Figures 13,14) from oil and gas is phased out by the turn of the century in both regions. The bulk of electricity in the west is produced from hydro power, with the remainder (except'for electricity from oil and gas in the first four periods) produced from coal. The production of hydroelectricity never reaches its exogenous maximum be fore 2020 in the west, but the eastern maximum is reached after 1990, forcing an increasingly heavy reliance on nuclear power after the turn of the century. This may be interpreted to mean that after the turn of the century, Quebec and Newfoundland, with their James Bay and Labrador sites fully developed, will be forced to adopt a nuclear future, as Ontario has done. The rapid rise in generation in the west during the period after 2010 — at the rate of 9.8% per year — corresponds to a substitution of electricity for oil in western industry. The large increase in the east after 2000 — at the rate of 8% per year in the period 2001-2010 — corresponds to a switch from oil to electricity in eastern industry, and to a switch from gas heat to electric resistance in the eastern DFC sector. (See section 6.6 below for 82 Table 13. Western Electricity Production, Base Case. BASE CASE; ELECTRICITY, WEST: IN UNITS OF 10**12 KWH PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 FROM BIOMASS; NUCLEAR; OIL AND GAS; COAL; HYDRO; 0.0008 0.0000 0.0086 0.0126 0.0506 0.0008 0.0000 0.0085 0.0147 0.0522 0.0008 0.0000 0.0075 0.0170 0.0548 0.0004 0.0000 0.0051 0.0235 0.0677 0.0000 0.0000 0.0000 0.0295 0.0877 0.0000 0.0000 0.0000 0.0764 0.2224 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 13 . Thus, the differences between the plotted lines are the entries in Table 13.) 83 0.80 -i 0.70 H BASE CASE ELECTRICITY, WEST* FROM BI0MRS3 O NUCLEAR X OIL RND GRS + CORL A HYDRO © O.BO H £ 0.50 -| CC LU Q_ g 0.140 OJ .—I X D 0.30 H 0.20 H o.io H ©—©—© 0.0 1975 1985 35 19&5 2005 20*15 2025 Figure 13. Western Electricity Production, Base Case. 84 Table 14. Eastern Electricity Production, Base Case. BASE CASE; ELECTRICITY, EAST: IH UNITS OF 10**12 KWH PERYEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 FROM BIOMASS; NUCLEAR; OIL AND GAS; COAL; HYDRO; 0.0000 0.0201 0^0124 0.0228 0.1666 0.0000 0.0509 0.0128 0.0223 0.2620 0.0000 0.0726 0.0117 0.0205 0.3220 0.0000 0.1216 0.0076 0.0145 0.4420 0.0000 0.8277 0.0000 0.0000 0.4420 0.0000 1.0650 0.0000 0.0000 0.4420 {N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 14. Thus, the differences between the plotted lines are the entries in Table 14.) 85 3.20 -i 2.80 H BHSE CASE ELECTRICITY. ERST: FROM BIOMASS O NUCLEAR X OIL AND GAS + COAL ^ HYDRO © 2.40 H CE 2.00 H OC LU Cu 1.60 C\J X o 1.20 H 0.80 H 0.40 H 0.0 1975 1985 1995 2005 Ei 2015 2025 Figure 14. Eastern Electricity Production, Base Case. 86 Table 15. Electricity Use, Base Case. BASE CASE; ; ELECTRICITY USE: IN DNITS OF 10**12 KWH PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPORTS; ELECTRIC AUTO; INDUSTRY; DFC; 0.0099 0.0104 0.0000 0.0000 0.1164 0.1927 0.1411 0.1828 0.0110 0.0120 0.0000 0.0000 0.2849 0.2537 0.1662 0.3563 0.0133 0.0147, 0.0000 0.0000 0.6327 0.9632 0.6267 0.6778 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 15. Thus, the differences between the plotted lines are the entries in Table 15.) 87 BASE CASE ELECTRICITY USE: EXPORTS ELECTRIC AUTO INDUSTRY OFC 2.40 H Figure 15. Electricity Use, Base Case. 88 Table 16. Western Electricity Prices, Base Case. BASE CASE; ; WEST ELECTRIC PRICES IH UNITS OF 1975 CENTS PER KWH AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 DFC; 2.4623 2.4575 ROAD TRANSPORT; 1.9423 1.9375 INDUSTRY; 1.0923 1.0875 2.4560 2.4680 2.4255 2.4072 1.9360 1.9480 1.9055 1.8872 1.0860 1.0980 1.0555 1.0372 89 11.00 -i 3.50 H 3.00 H BASE CASE WEST ELECTRIC PRICES OFC + RQflO TRANSPORT A INDUSTRY O 3 2.50 H az LU Q_ CO LU L_) LO CD 2.00 H H —I-Al A Ar-1.50 © © -© ©-l.oo H -© © 0.50 H 0.0 1975 1985 35 19^5 2005 2015 20^5 Figure 16. Western Electricity Prices, Base Case. 90 Table 17. Eastern Electricity Prices, Base Case. BASE CASE; ; EAST ELECTRIC PRICES IN DNITS OP 1975 CENTS PER KHH AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 DFC; ROAD TRANSPORT; INDUSTRY; 2.4514 2.5024 1.9314 1.9824 0.8014 0.8524 2.4724 2.4588 1.9524 1.9388 0.8224 0.8088 2.6318 2.6318 2.1118 2-1118 0.9818 0.9818 91 BRSE CASE 4.00 -i EAST ELECTRIC PRICES DFC + ROAD TRANSPORT A INDUSTRY © 3.50 H 3.00 H Figure 17. Eastern Electricity Prices, Base Case. a discussion of industrial fuel use in the model.) The use of electricity (Figure 15), except for exports, grows at an average rate of 5.2% per year between 1978 and 1995 (the representative years of the first and fourth periods, respectively), and at 5.1% per year between 1995 and 2015. Electricity exports from the two regions are at the exogenously specified levels, increasing at the rate of 1% per year. There is a quickly growing demand for electricity in industry. The growth in electricity demand from the DFC sector is quite strong after 2000, when there is a switch from gas heat to electric resistance and solar in the east. The growth in DFC demand slackens somewhat after 2010, when solar heating becomes quite important in the east. It might be noted that self-generation of electricity by industry is not explicitly allowed in the structure of the model. However, the margins allowed in the model for the distribution of electricity to the industrial sectors are very small (1.8 mills/kwh in the west, and -1.0 mills/kwh in the east) compared to the generation costs and to the margins for distribution to the other sectors. Therefore, to minimize the size of the model, the possibilities of industrial self-generation of, say,hydroelectricity or electricity from wood waste, were included in the appropriate electricity variables as_ if_ such electricity originated from the utilities. Electricity prices (Figures 16,17) are stable in both regions. The cost of nuclear power (1 cent per kwh) becomes the determining element of eastern electricity prices after 2000, when hydroelectric production is at its maximum. 6.5. Transportation In the road transportation sector (Figure 18), the use of output energy 93 Table 18. Transportation, Base Case. BASE CASE; ; TRANSPORTATION; IN UNITS OF 10**15 BTU PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 OTHER TRANSPORT; 0.0908 0.1046 0.1272 0.1708 0.2196 0.2813 ROAD,ELECTRIC; 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ROAD, GASOLINE; 0.2879 0.3399 0.4165 0.5425 0.7069 0.9880 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 18. Thus, the differences between the plotted lines are the entries in Table 18.) 94 BRSE CASE 2.U0 -i TRANSPORTATION: OTHER TRANSPORT + ROAD.ELECTRIC A ROAD. GASOLINE © 2.10 H 1.80 H CC 0.0 1975 19^5 1955 2005 20T~5 2025 Figure 18. Transportation, Base Case. 95 Table 19. Western Output Energy Prices, Base Case. BASE CASE; . ; OUTPUT PRICES, WEST: IH UNITS OF INDEX (1970=1) AVERAGE VALUES FOR THE PEHIOD ENDING IN 1980 1985 1990 2000 2010 2020 OTHER TRANSPORT; ROAD TRANSPORT; INDUSTRY; DFC; 1.0991 1.3262 0.8134 0.7503 1.2587 1.3703 1.0307 1.0418 1.31.95 1.2281 0.6433 0.5458 1.3654 1.4491 1.0576 1.1730 1.3519 1.4613 0.5140 0.5399 1.6918 1.7706 1.3776 1.4077 96 U.00 -1 3.50 H 3.00 H 2.50 H BASE CASE OUTPUT PRICES. WEST: OTHER TRANSPORT X ROAD TRANSPORT + INDUSTRY A DFC © II O 2.00 H X UJ o 1.50 H l.oo H 0.50 H o.o 1975 1985 35 19&5 2005 2015 20^5 Figure 19. Western Output Energy .Prices, Base Case. 97 Table 20. Eastern output Energy Prices, Base Case. BASE CASE; ; OUTPUT PRICES, EAST: IN UNITS OP INDEX (1970=1) AVERAGE VALUES POR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 OTHER TRANSPORT; 1.3245 1.4658 1.3348 1.2421 1.3700 1.4825 ROAD TRANSPORT; 0.9152 0.8028 0.6544 0.5554 0.5207 0.5456 INDUSTRY; 1.5848 1.8146 1.6484 1.5390 1.8249 1.8502 DPC; 1.2706 1.3602 1.1936 1.2779 1.3743 1.3710 98 11.00 —i 3.50 H 3.QM 2.50 H BRSE CASE OUTPUT PRICES. ERST: OTHER TRANSPORT X ROAD TRANSPORT + INDUSTRY A DFC © II O CT) 2.00 H X LU Q 1.50 l.oo H 0.50 H •—f-0.0 1975 1985 35 19^5 2005 io^ 2025 Figure 20. Eastern Output Energy Prices, Base Case. ('which may be interpreted as a measure of road transportation services performed) grows 3.8% per year between 1978 and 1995, and 3.0% per year between 1995 and 2015. This strong growth even in the face of rising oil prices can be explained by a look at the prices of energy in the road transportation sectors (Figures 19,20). Apparently the assumed rate of increase of automobile efficiency is more than enough to offset the effect of rising oil prices on the price of output energy (except for the last period). Although motorists will be paying more and more per gallon for fuel, they will be spending less and less per mile for fuel, according to the base case solution. Thus, even though population growth slows, the declining cost of road transportation encourages rapid growth in the total amount of driving which people do. The electric automobile is not introduced in either region. The following chart shows the prices of output energy, in model units, in road transportation, using the conventional and the electric automobile. (The price for conventional is from the gradient of the objective function, with the discounting removed, while the electric price is derived from the electricity generation price, plus the distribution margin, converted to an output price, and added to the differential cost of the electric car.) Table 21. Road Transportation Prices, Base Case. Period Ending 1980 1985 1990 2000 2010 2020 West, conventional 1.8302 1.6882 1.4474 1.2282 1.157 1.2149 West, electric n.a. n.a. 2.1307 2.1357 2.1179 2.1103 East, conventional 2.1557 1.8908 1.5413 1.3083 1.2265 1.2850 East, electric n.a. n.a. 2.1376 2.1319 2.2043 2.2043 Two major elements in the price of road transportation by electric 100 "car are the road tax assumed to be placed on electricity for electric autos (equal to 0.4313 in the units of the above chart), and the extra initial cost of the electric automobile versus a conventional one (equal to 1.32 in the above units). According to the base case results, then, a substantial narrowing of the difference in the prices ($1,500 for sub-compacts is assumed here) of the electric and conventional autos will be necessary, perhaps in combination with a lessening of the road tax for the electric alternative, if the electric auto is to be competitive. It is worth noting, too that the increasing efficiency of the conventional auto makes the electric auto (assumed to have a constant efficiency) less com petitive. In the "other" transportation sector (Figure 18) output energy grows at the rate of 3.8% per year between 1978 and 1995, and at 2.5% per year between 1995 and 2015. The slower growth in other transportation compared to road transportation is likely due to an assumed slower growth in efficiency, which offsets rising oil prices less than in road transportation. This is apparent from a glance at the price indices for other transportation (in Figures 19, 20). 6.6. Industry The use of oil and gas in industry (Figure 21) peaks in the period 1991-2000. After 1990, coal becomes a very important source for industry, and after 2000, electricity plays the largest role of all the four fuels. Total output energy used in industry grows at the rate of 5.0% per year from 1978 to 1995, and at 2.6% per year from 1995 to 2015. Output energy prices for industry (Figures 19,20) are somewhat erratic, particularly in the east, in part because any efficiency changes are due 101 Table 22. Industrial Output Energy, by Fuel, Base Case. BASE CASE; ; INDUSTRY: IN UNITS OF 10**15 OUTPUT BTO/YR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 ELECTRICITY; COAL; GAS; OIL; 0.3972 0.2420 0.4672 0.6228 0.6575 0.4240 0.5202 0.5014 0.9721 0.4649 0.6723 0.7240 0.8656 1.1901 0.6790 1.2324 2.1588 1.5115 0.5039 0.8644 3.2864 1.9719 0.6573 0.6571 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 21. Thus, the differences between the plotted lines are the entries in Table 22.) 102 12.00 ~i 10.50 H 9.00 H BASE CASE INDUSTRY: ELECTRICITY COAL GAS OIL X + © y-\ 7.50 H ZD I— CO ZD Q_ O LO 6.00 5 4.50 3.00 1.50 H 0.0 1975 1985 35 lS 2005 2015 20^5 Figure 21. Industrial Output Energy, by Fuel, Base Case. solely to the changing fuel mix, and because of the bulges in oil and gas prices in the first two periods in the east. The somewhat erratic behaviour (ups and downs) of electricity, gas and oil use in industry is due to the model structure. There are upper and lower bounds on the shares of industrial output energy in the model. A lower bound indicates non-substitutable uses of the fuel. Above the lower bound, there is perfect inter-fuel substitutability, up to a point (the upper bound). These share bounds spread apart until 2000 and are constant after that. At the optimal solution, the industrial fuel mix in a period is the least cost mix, given all the optimal fuel prices. It is therefore not surprising to see the erratic behaviour of some fuels. Table 23 gives the calculated shares of the four fuels in industrial output energy, at the optimal solution of the base case. Table 23. Shares of Fuels in Industrial Output Energy, Base Case. (Note: The symbols " which are at (L)" and "(u)" indicate the their lower or upper bounds, shares respectively .) Period Ending Fuel Region 1980 1985 1990 2000 2010 2020 Electricity West East .23(L) .23(L) .22(L) .34(U) .21(L) .39 • 2(L) .22 • 2(L) • 5(U) -5(U) .2 (L) Coal West East .08(U) .16(L) .14(U) .22(U) .19(U) .16 • 3(U) • 3(U) • 3(U) .3(U) .3(U) • 3(U) Gas West East .44 .21(L) .43 •19(L) .42 .18 .4 • KL) • KL) • KL) -KL) • KL) Oil West East .24(L) .40(U) .21(L) .25(L) •17(L) .28 . 1 (L) .38 .4 • KL) • KL) • KL) The upper and lower bounds were taken from estimates by Hedlin, Menzies and Associates (1976) of future technical possibilities in the industrial sector. An alternative method of modelling fuel shares might involve-econometric estimation of substitution parameters in a function giving in dustrial output energy for different fuel inputs. Although such an approach would likely produce smoother projections of fuel shares, it would be based on past technical possibilities, a serious drawback when making projections into the distant future. The best approach theoretically, would be to dis tinguish industrial output energy demand by major functional end uses, and to construct a process model of energy supply and use for these functional end use demands. This deficiency in the model's structure can likely be corrected only by a large effort in the categorization of industrial uses of energy, together with estimates of demand curves for these categories. Since there is apparently no reliable data in this area, the present form ulation of the industrial sector of the model is the best possible now. 6.7. DFC Heating Oil heating (Figures 22,23) is phased out as rapidly as possible in the west (zero after 1985). However in the east, there is new oil heating capacity installed in the first period, and oil heating is consequently phased out later in the east than in the west (zero after 1990). Gas heating plays a big role in the west until 2010, and in the east until 2000. Depletion of the low cost reserves, and the rising gas prices make alternative fuels more economical after these dates. Electric resistance heating is phased out quickly in the west (zero after 1985), in favour of gas, and later cogeneration and solar, but it plays an increasingly important role in the east, becoming the single most important heating source in the east after 2000, when gas becomes too expensive. Heating by cogeneration with coal-fired electricity production is used in the west after 2000 (the model allows it after 1980), but not at all in the east because cogeneration with nuclear electricity production is not allowed in the base case, and because there is no new coal-fired electricity capacity 105 Table 24. DFC Heating, West, Base Case. BASE CASE; ; DFC HEATING, WEST: IN UNITS OF 10**15 OUTPUT BTU/YR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; HEAT PUMP; ELECTRIC RESIS.; GAS; OIL; 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0478 0.0293 0.3082 0.4207 0.0782 0.0384 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5525 0.6198 0.0000 0.0000 0.0000 0.3461 0.0497 0.2379 0.0000 0.0000 0.0000 0.0000 0.6291 0.2400 0.0000 0.0000 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 22. Thus, the differences between the plotted lines are the entries in Table 24.) 106 8.00 -i 1.75 H BASE CRSE DFC HEATING. WEST: SOLAR COGENERATION O HEAT PUMP X ELECTRIC RESIS. + GAS A OIL © 1.50 CC >-\ 1.25 H I— CD i— l.oo H ZD CD LO *—i X O 0.75 H 0.50 H 0.25 0.0 1975 1985 1^5 20TJ5 20^5 202 2025 Figure 22. DFC Heating, West, Base Case. 107 Table 25. DFG Heating, East, Base Case. BASE CASE; ; DFC HEATING, EAST: IN UNITS OF 10**15 OUTPUT BTU/YR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; HEAT PUHP; ELECTRIC RESIS.; GAS; OIL; 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1570 0.2975 0.2995 0.4039 0.8978 0.7313 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2040 0.8042 0.9929 1.2392 0.6002 0.0000 0.5048 1.2496 0.0000 0.0000 0.0000 0.0000 1.6616 1.7254 0.2369 0.0000 0.0000 0.0000 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 23. Thus, the differences between the plotted lines are the entries in Table 25.) 108 BASE CASE H.00 -i DFC HERTING. ERST: SflLRR COGENERRTIGN HERT PUMP ELECTRIC RESIS. GRS OIL O X + © 1975 2025 Figure 23. DFC Heating, East, Base Case. established in the east. The heat pump is not in the solution in either region. Solar heating is used in the west to its maximum allowed share after 2010, but is at the zero level before 2010. Solar is at its maximum share after 2000 in the east (when electricity prices increase significantly), and zero before then. In both the west and east, solar heating is allowed by the model constraints after 1980. How close does the heat pump come to being competitive? Table 26 shows what the output energy heating costs would be for the heat pump in the west and east, given the electricity prices calculated in the base case, and all of the assumed conversion efficiencies and costs. Table 26. Heat Pump Costs (in model units), Base Case Period ending 1985 1990 2000 2010 2020 West .8261 .8259 .8277 .8214 .8188 East .8327 .8283 .8263 .8517 .8517 Since the cost of solar heating is 0.706, in model units, it is clear from the above figures why solar heating is the preferred new technology. It was assumed for both regions that the non-fuel cost of the heat pump for heating purposes was 5/6 of the total cost, since 1/2 of the users would have air conditioning with or without a heat pump, and that the air con ditioning function of a heat pump would be used in 1/3 of the year, for a total, average credit of 1/6 of the non-fuel cost. It may be argued that for the half of the users who would have air conditioning in any case, there should be a credit of the full 1/3 of the non-fuel cost of the heat pump. However, this further reduction in the cost would only be 0.0932, in model units, still leaving solar heating less costly, according to the above 110 'figures. If the "thermal efficiency" of the heat pump (assumed to be 2.0) can be improved, perhaps by a hybrid heat pump/solar device (which would have the outside coils of the heat pump in a device which is warmed by trapping solar radiation), then the heat pump could be competitive. 6.8. Sectoral Shares The shares of total output energy (Figure 24) allocated to the two transportation sectors stay approximately constant over all periods, in dicating that the growth rates of transportation services are about the same as the growth rate of total output energy. However, since the in dustrial share increases and the DFC share decreases, we may conclude that the energy services provided in the former sector increase faster than total output energy, and in the latter, slower than total output energy. The rates of growth of output energy are determined by the exogenous assumptions about rates of growth of population and some economic variables, by price and other elasticities, and by prices determined in the solution of the model. The shares of total secondary energy, the energy inputs to the end use sectors, are shown in Figure 25 . The share consumed in road transportation decreases in the first three periods, reflecting the large efficiency im provements assumed in conventional automobiles. The increasing share of industry and the decreasing share of the DFC sector in total secondary energy consumption follow the pattern observed in the sectoral shares of output energy. 6.9. Fuel Shares The shares of total output energy (Figure 26) provided by electricity and coal both increase fairly steadily, except for a lull in the third period corresponding to temporary drops in eastern industrial coal use 111 Table 27. Sectoral Output Energy Shares, Base Case. BASE CASE; OUTPUT SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 DFC; INDUSTRY; ROAD TRANSPORT; OTHER TRANSPORT; 0.4948 0.4654 0.4145 0.4413 0.0690 0.0713 0.0218 0.0219 0.4455 0.3965 0.4652 0.5115 0.0684 0.0700 0.0209 0.0220 0.3737 0.3620 0.5291 0.5425 0.0742 0.0723 0.0231 0.0232 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 24. Thus, the differences between the plotted lines are the entries in Table 27.) 112 1.60 -I 1.U0 1.20 H BASE CASE OUTPUT SHARES-. DFC X INDUSTRY + ROAD TRANSPORT A OTHER TRANSPORT © 1.00 H X x- X x-o I—I U 0.80 H CE cc 0.60 H o.uo H 0.20 H -A -A-0.0 © © © © © -© 1975 1985 35 19^5 2005 2015 20^5 Figure 24. Sectoral Output Energy Shares, Base Case. 113 Table 28. Sectoral Secondary Energy Shares, Base Case. BASE CASE; SECONDARY SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 DFC; 0.4287 0.4172 0.4157 0.3575 0.3259 0.3059 INDUSTRY; 0.3261 0.3556 0.3875 0.4560 0.4813 0.4976 ROAD TRANSPORT; 0.1897 0.1698 0.1421 0.1297 0.1302 0.1313 OTHER TRANSPORT; 0.0554 0.0575 0.0548 0.0568 0.0626 0.0652 {N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 25. Thus, the differences between the plotted lines are the entries in Table 28.) 114 1.60 -i 1.40 H 1.20 H BRSE CASE SECONDARY SHARES: DFC X INDUSTRY + ROAD TRANSPORT A OTHER TRANSPORT © 1.00 H X X X X X X i—i CJ 0.80 CE CC 0.60 0.40 H 0.20 H © © © ©-0.0 1975 1985 -© © 35 I9S5 2005 " 20*15 2025 Figure 25. Sectoral Secondary Energy Shares, Base Case. 115 Table 29. Output Energy Fuel Shares, Base Case. BASE CASE; OUTPUT SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.0000 0.0000 0.0530 0.1305 0.0000 0.2105 0.2576 0.4739 0.0580 0.0000 0.2688 0.2822 0.3600 0.0890 0.0000 0.2528 0.3642 0.3067 0.0763 0.0000 0.2684 0.3272 0.2509 0.1535 0.0052 0.4512 0.1438 0.1880 0.1587 0.0195 0.4579 0.0734 0.1575 0.1613 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 26. Thus, the differences between the plotted lines are the entries in Table 29.) 116 Figure 26. Output Energy Fuel Shares, Base Case. 117 and in eastern electric resistance heating. The large increase in electricity's share after 2000 corresponds to a switch from oil to electricity in eastern industry, and from gas to electric resistance heating in the east. The share of gas peaks in the period 1986-1990, while oil's share of output energy steadily decreases. The share of electricity in secondary energy inputs to the end-use sectors (Figure 27) increases steadily, except for a lull in the third period, to 38% in the last period, 2011-2020. Coal's share increases to 15% by the last period. The share of gas peaks at 34% in the period 1986-1990, and oil's share declines steadily from 61% in the first period to 26% in the last period. The shares of cogeneration and solar in second ary energy are less than their shares in output energy because the quantities of output energy are taken to be the same as the quantities of secondary, input energy for these two energy sources, while other fuels generally lose energy in conversion from secondary to output energy. Primary fuel shares (Figure 28) change in a way similar to the changes observed in secondary and output energy fuel shares in the cases of coal, gas and oil. Hydro's share of primary energy increases to about 15% by 2000, and nuclear's share takes a sharp jump after 2000, when eastern hydro has been expanded to its maximum. The tiny share of "biomass" (this category in cludes energy production from garbage, wind, tidal power) comes mainly from western electricity production. Solar's share of primary energy is even smaller than its share of secondary energy because the quantities of primary and secondary solar energy (and output, too) are taken to be the same. In summary, oil becomes less important but remains significant as an energy source; coal increases in importance; there is a major shift to greater reliance on electricity, with nuclear power playing an important part, 118 Table 30. Secondary Energy Fuel Shares, Base Case. BASE CASE; SECONDARY SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.0000 0.0000 0.0424 0.0000 0.1350 0.2157 0.6065 0.0428 0.0000 0.1833 0.2525 0.4945 0.0697 0.0000 0. 1783 0.3402 0.4197 0.0619 0.0000 0.1979 0.3209 0.3510 0.1301 0.0042 0.3611 0.1514 0.2948 0.1460 0.1091 0.0163 0.3827 0.0774 0.2596 0.1549 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 27. Thus, the differences between the plotted lines are the entries in Table 30.) Figure 27. Secondary Energy Fuel Shares, Base Case. 120 Table 31. Primary Energy Fuel Shares, Base Case. BASE CASE; PRIMARY FOEL SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; BIOHASS; HYDRO; NUCLEAR; GAS; oil; COAL; .0000 ,0004 ,0953 ,0088 .2508 0.5613 0.0834 0. 0« 0. 0. 0. 0000 0003 1280 0207 2912 0.4572 0.1025 0.0000 0.0003 0. 1281 0247 3586 ,3986 ,0897 0. 0. 0. 0. 0.0000 0.0001 0.1470 0.0351 0.3312 0.3419 0.1446 0.0391 0.0000 0.14 00 0.2188 0.1535 0.2933 0.1553 0.1011 0.0000 0.1437 0.2303 0.0778 0.2598 0.1873 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 28. Thus, the differences between the plotted lines are the entries in Table 31.) 121 1.60 -i 1.40 H BRSE CASE PRIMRRY FUEL SHARES'. SOLRR X BIOMASS + HYDRO O NUCLEAR X GAS + OIL A COAL © 1.20 H 1.00 D i—i O 0.80 CC CO 0.60 H o.uo H 0.20 H 0.0 1975 1985 ^5 iS 2005 2015 20^5 Figure 28. Primary Energy Fuel Shares, Base Case. 122 especially after the turn of the century; gas peaks in importance in the period 1986-1990 and declines rapidly after 2000; and solar energy becomes significant only after the turn of the century. 6.10. Total Energy Total output energy (Figure 29) increases at the rate of 3.7% per year between 1978 and 1995, and at 2.3% per year between 1995 and 2015. Total secondary energy increases at an average 2.9% per year between 1978 and 1995, and at 1.7% per year between 1995 and 2015. Total primary energy grows at the rate of 2.5% per year between 1978 and 1995, and at 1.5% per year between 1995 and 2015. The primary energy contributions of hydro and nuclear electricity are evaluated at 3,412 BTUs per kilowatt-hour, which is the amount of usable energy in one kilowatt-hour. Other authors (e.g. Energy, Mines and Resources, 1977a) have used a different accounting convention — 10,000 BTUs per kilowatt-hour -- for the reason that approximately 10,000 BTUs of fossil fuel input is necessary to produce one kilowatt-hour of electricity. Thus, the generation of one kilowatt-hour of electricity by hydro or nuclear would have required 10,000 BTUs of fossil fuels if-fossil fuels had been used. The "10,000" con vention facilitates international comparisons of primary energy use, when the focus is on exhaustible, fossil fuels. However, the "10,000" convention masks changes in the overall efficiency of primary energy use by obscuring the effects of fossil fuel use to generate electricity. It should be noted that the adoption of one convention or another has no effect on the solution of the model — the only effect is on the calculation of total primary energy for the report on the results of the model. The rates of change of primary, secondary and output energy, (Figure 30) are the average annual rates obtained by comparing total energy in each period 123 Table 32. Total Energy, Base Case. BASE CASE; ; TOTAL ENERGY: IN DNITS OF 10**15 BTD PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 PRIMARY; SECONDARY; OUTPUT; 7.7796 6.5064 4.1730 8.3782 10.0368 11.8286 12.9086 15.7803 6.9898 8.6347 10.5149 11.8984 14.6298 4.7656 6.0896 7.7554 9.5239 12.2283 BASE CASE 32.00 TOTAL ENERGY: PRIMARY SECONDARY OUTPUT + © 28.00 H 2U.00 H 0.0 1975 19£ 19^5 2005 2015 20^5 Figure 29. Total Energy, Base Case. 125 Table 33. Total Energy, Percent Annual Change, Base Case. BASE CASE; ; TOTAL ENERGY: IN UNITS OF % CHANGE PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 PRIMARY; SECONDARY; OUTPUT; 4.1609 1.4936 3.6784 2.2138 0.8776 2.0289 5.1685 1.4437 4.3172 2.6608 1.2437 2-0880 5.8897 2.6914 5.0252 3.2757 2.0754 2-5309 126 8.00 -i 7.00 -\ BASE CASE T0TBL ENERGY: PRIMARY SECONDARY OUTPUT + © 6.00 H °f 5.00 -j LU OC LU Q_ LU CD 4.00 H CE IC CD ^ 3.00 H 2.00 H l.oo H 0.0 1975 1985 35 2005 2LY15 20^5 Figure 30. Total Energy, Percent Annual Change, Base Case. 127 to the previous period. The drop in rates of change in the second period coincides with higher coal, oil and gas prices in the east, as well as the slower economic growth which is assumed for this period. The rise in rates of change in the third period coincides with a drop in coal, oil and gas prices in the east, and higher assumed economic growth rates. The temporary drop in rates of increase in the period ending in 2010 is apparently due to a large jump in oil and gas prices (especially gas) and in the eastern electricity price. The eastern gas and electricity prices reach a plateau and do not change in the final period, which means that only the economic and demographic factors in the demand function can have an effect on the rate of increase of demand for output energy between the last two periods. The rate of growth of secondary energy is less, in all periods, than the rate of growth of output energy, and the rate of growth of primary energy is even less than that of secondary energy in most periods. These observations indicate an increasing, overall energy system efficiency in the base case, both in the end-use sectors and at the intermediate level of secondary energy. The increasing efficiency reflects such things as the rapid growth in hydro-electricity and nuclear power (rather than total reliance on fossil fuels for electricity), the introduction of cogeneration in the west, the switch to efficient electric resistance heating in the east (away from oil and gas heat), the use of solar heat (whose energy content is evaluated at the same amount at the primary, secondary and output stages), and the assumed improving efficiencies in transportation. 128 Chapter 7. The High Demand and Low Demand Cases 7.1. The Assumptions The base case assumptions are the best estimates of all parameters. One key element of uncertainty is the exogenous projection of the economic and demographic variables which, along with prices, determine demands for output energy. In order to test the sensitivity of some conclusions to the assumptions about these exogenous demand-related variables, the model has been solved for high and low estimates of the future levels of the economic and demographic variables. The assumptions on the supply side are the same as in the base case (since the sensitivity analysis here is for demand-related variables), except for some different exogenous projections of production from the tar sands. (The linear process model of supply adjusts to the altered demand conditions, except for the exogenously-projected tar sands production. Thus, to be consistent, the tar sands projections must be altered in a reason able way.) The assumptions for the low, base and high'cases are presented in Table 34, below. The high case estimates of population and economic growth are based on the high case assumptions of the National Energy Board, described in Douglas and Nichols (1979), which is also the source of the base case estimates. The National Energy Board's estimates, derived using the CANDIDE model of the Canadian economy, should be internally consistent (coming from CANDIDE), and they represent a plausible,"respectable" range of projections of the future of the Canadian economy. The low case estimates are based on this author's judgement, since there were no low projections of these variables prepared for the National Energy Board. (Their approach to their low demand case was to take the base case estimates of demographic and economic variables, 129 and project high energy prices, which are exogenous in their model.) The National Energy Board (1978) base case projection of tar sands production to 1995 is used as the base case exogenous projection here, and as the lower limit from 1980 to 2000 for projection in the high case. The low case projection of the National Energy Board (1978) is the basis for the values assumed for tar sands production in this low case. Table 34. Low,Base and High Case Assumptions. (for end Period Ending 1980 1985 1990 2000 2010 2020 effectsi Population High 1.5 1.3 1.2 1.2 0.8 0.8 0.6 Growth, West, Base 1.5 1.2 1.1 0.9 0.6 0.5 0.3 % per year Low 1.5 1.1 1.0 0.6 0.4 0.2 0.0 Population High 1.2 1.0 0.9 0.9 0.8 0.8 0.6 Growth, East, Base 1.2 0.9 0.8 0.7 0.6 0.5 0.3 % per year Low 1.2 0.8 0.7 0.5 0.4 0.2 0.0 Income per High 3.7 2.3 2.9 3.0 3.1 2.7 2.5 Capita Growth, Base 3.7 1.9 2.3 2.5 2.3 2.3 2.3 % per year Low 3.7 1.5 1.7 2.0 2.0 2.0 2.0 Real Domestic High 3.5 4.9 4.3 4.2 4.2 3.8 3.6 Product Growth, Base 3.5 4.0 3.7 3.8 ' 2.9 2.8 2.6 West, %/yr. Low 3.5 3.5 3.2 2.8 2.4 2.2 2.0 Real Domestic High 3.2 4.5 4.0 4.0 4.2 3.8 3.6 Product Growth, Base 3.2 3.7 3.4 3.6 2.9 2.8 2.6 East, %/yr. Low 3.2 3.2 2.9 2.6 2.4 2.2 2.0 Capital/Output High 2.0 2.1 2.8 2.0 1.0 0.5 0.0 Ratio Growth, Base 2.0 2.1 2.8 1.0 0.5 0.0 0.0 % per year Low 2.0 2.1 2.0 1.0 0.5 0.0 0.0 Tar Sands High =.0362 >.0744 >.1534 >.2756 Production Base =.0362 =.0744 =.1534 =.2756 109 bbl/yr Low =.0362 >.0706 >.1380 y.2205 130 7.2. The Results of the High Case Generally speaking, production and use levels are higher in the high case than in the base case, but the overall patterns (peaks, introduction of new sources, etc.) are the same as in the base case. Some noteworthy exceptions to these general observations are: - some oil and coal sources are exhausted sooner in the high case; - gas production and use are at roughly the same levels in the high case as in the base case, except for the last period; - solar heat is introduced one period earlier in each region (after 1990 in the east, and after 2000 in the west, in the high case); and - oil and gas prices rise slightly faster in the medium term (1985 to 2000) than in the base case. Some conclusions drawn from an examination of the base case solution are strengthened by the results of the high case. As in the base case, northwestern arctic oil is not used until after 2000 in the high case in spite of the higher demand (but northeastern offshore oil is used one period sooner, 1991-2000, in the high case). Imports of oil and coal cease after 1985 in the high case, as in the base case. The crude oil price still does not reach its upper limit of $12 per barrel until the last period, 2011-2020, in spite of the higher demand. As in the base case," natural gas from the northeast offshore is not needed until after 2000, and gas from the northwest arctic is not used until after 2010. The two primary fuels which appear to make up the extra supply required to meet the higher demands are nuclear electricity and coal. A related ob servation is that electricity prices are not affected very much by the in creased demands in the high case (compared to the base case), because of the virtually limitless supplies of nuclear power in the east and coal for electricity in the west. Thus, the base case conclusion that electricity prices are stable, is strengthened. Plots and tables from the high and low cases relating to this dis cussion may be found on pages 134 to 161. 7.3. The Results of the Low Case Compared to the base case,- there are, of course, generally lower levels of production and use of energy, and the overall pattern is similar. Some exceptions are: - oil from the northwest arctic is introduced one period later (after 2010) than in the base case; and - western conventional oil supplies are used less in the first four periods and more in the last two periods, "stretching out" the cheaper oil supplies. Solar heating is introduced in the same periods as in the base case in both regions - 2011-2020 in the west, and 2001-2010 in the east. This reinforces the conclusion that solar heat will be a competitive energy source, even if energy demands grow slowly, although it will not be com petitive in the near future. Since nuclear's share of primary energy is less than for base case demand, it may be concluded that nuclear power will play a key role in matching energy supplies and demands. This reinforces the observation made on the high case results, that nuclear made up a good part of the extra energy supply required over the base case requirements. It is noteworthy that the periods of introduction of natural gas from the northwest arctic and the northeast offshore areas are the same in the low case as in the high case — the periods ending in 2020 and 2010, respectively. This puts upper bounds on the introduction dates - before '2020 for northwest arctic gas, and before 2010 for northeast offshore gas. The conclusion that these frontier gas sources need not be tapped until after the turn of the century, first discussed with reference to the base case, is therefore a robust conclusion. An examination of the high, base and low results reveals that eastern gas production (the sum of southeast and northeast offshore production) is the same in the first four periods in all three cases. There are two reasons for this behaviour. First, southeast offshore gas is used at the maximum allowable rates in the first three periods because it is inexpensive, and in the fourth period, the reserve limit and the production decline constraint combine to make another upper limit on production. Secondly, the other component of eastern gas production, the northeast offshore gas, is not brought into the solution until the fifth period in all three cases. There fore, differences among the cases in eastern gas production do not appear until the fifth period. There is very little difference in the price series of the low and base cases. Plots and tables from the high and low cases relating to the above discussion appear on pages 134 to 161. Table 35, below shows the growth rates of total energy demand per capita for the three cases, at the primary, secondary and output energy levels, using each case's population projection. Table 35. Growth in Total Energy Demands Per Capita, Three Cases (average growth, percent per year, between midpoints of periods) Period Ending 1980 1985 1990 2000 2010 2020 Primary -- High 2.9 0.7 3.3 1.5 1.7 2.4 - Base 2.9 0.5 2.7 1.4 0.3 1.5 - Low 2.9 0.2 2.1 1.1 0.0 1.1 Secondary- High 3.9 0.6 3.9 1.9 2.1 2.4 - Base 3.9 0.4 3.4 1.8 0.6 1.6 - Low 3.9 0.1 2.7 1.5 0.4 1.2 Output High 4.6 1.8 4.6 2.6 3.0 2.8 - Base 4.6 1.7 4.1 2.5 1.5 2.0 Low 4.6 1.4 3.4 1.9 1.2 1.8 The demand for output energy grows, even on a per capita basis, because the demand is also related to several economic variables, which grow faster than population, partly because of technological change. 134 Table 36. Crude Oil Production, High Case. HIGH CASE; OIL PRODUCTION: IN UNITS OF 10**9 BBL PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; FROM BIOMASS; FROM COAL; EASTERN; TAR SANDS; WEST ARCTIC; WESTERN; 0.2796 0.1138 0.0000 0.0000 0.0000 0.0000 0.0008 0.0362 0.0000 0-5572 0.0000 0.0000 0.0100 0.0744 0.0000 0.5081 0.0000 0.0000 0.050O 0. 1534 0.0000 0.5641 0.0000 0.0000 0.2023 0.2756 0.0000 0.3045 0.0000 0.0000 0.0000 0.1925 0.2516 0.2803 0.0801 0.0000 0.0000 0.0000 0.0647 0.8018 0.1317 0.0007 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 31. Thus, the differences between the plotted lines are the entries in Table 36.) 135 HIGH CASE 1.60 OIL PRODUCTION: IMPORTS X FROM BIOMRSS + FROM CORL O EASTERN X 1.140 H TRR SANDS + WEST ARCTIC A WESTERN © 1.20 H 0.20 H 0.0 1975 2025 Figure 31. Crude Oil Production, High Case. 136 Table 37. Crude Oil Production, Low Case. LOR CASE; ; OIL PRODUCTION: IN UNITS OF 10**9 BBL PEE YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; FROM BIOMASS; FROM COAL; EASTERN; TAR SANDS; WEST ARCTIC; WESTERN; 0.2728 0.1065 0.0000 0.0000 0.0000 0.0000 0.0008 0.0362 0.0000 0.5499 0.0000 0.0000 0.0100 0.0706 0.0000 0.4821 0.0000 0.0000 0.0500 0.1380 0.0000 0.44 30 0.0000 0.0000 0.1772 0.2205 0.0000 0.2086 0.0000 0.0000 0.0000 0.2058 0.1965 0.0000 0.1790 0.0000 0.0000 0.0000 0.0740 0.1419 0.2917 0.0618 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 32. Thus, the differences between the plotted lines are the entries in Table 37.) 1.60 nio H LOW CASE OIL PRODUCTION: IMPORTS FROM BIOMASS FROM CORL EASTERN TAR SANDS WEST ARCTIC WESTERN + X + © 1.20 H CC CC 1.00 H CC LU CL. _j 0.80 H CO CO CD X X 2 0.60 H 0.40 H 0.20 H 0.0 1975 1985 1995 2005 2015 2025 Figure 32. Crude Oil Production, Low Case. 138 Table 38. Crude Oil Prices, High Case. HIGH CASE; CBUDE OIL PRICES; IN UNITS OF 1975$ PER BBL AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPORTS; IMPORTS; EAST; WEST; 14.6000 10.8000 8.1506 5.3935 17.8000 14.8000 10.3586 8.5321 21.6000 19.3000 9.2055 8.7055 32.0000 32.0000 10.5151 10.0156 32.0000 32.0000 11.7794 1 1.2794 32.0000 32.0000 12.5000 11.9998 139 140.00 -i 35.00 H HIGH CASE CRUDE OIL PRICES: EXPORTS X IMPORTS + ERST A WEST © 30.00 H 25.00 H _J 03 CO QZ UJ °- 20.00 LO r~ 15.00 -A lo.oo H 5.00 H 0.0 1975 1985 35 19^5 2005 2LT15 20^5 Figure 33. Crude Oil Prices, High Case. 140 Table 39. Crude Oil Prices, Low Case. LOW CASE; ; CfiUDS OIL PRICES: IH UNITS OF 1975$ PER BB1 AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPORTS; I(SPORTS; EAST; WEST; 14.6000 10.8000 8.0181 5.1497 17.8000 14.8000 10.0808 8.1714 21.6000 19.3000 9.1703 8.6702 32.0000 32.0000 8.8665 8.3671 32 32 10 10 ,0000 .0000 ,9143 ,4143 32.0000 32.0000 12.5000 11.9998 141 I4Q.00 -i 35.00 H LOW CASE CRUDE OIL PRICES: EXPORTS X IMPORTS + EAST A WEST O 30.00 H 25.00 _J CO CO cc LU °- 20.00 -| if* LO r-CD 15.00 H IO.OO H 5.00 H 0.0 1975 1985 19^ 2005 2S5 2025 Figure 34. Crude Oil Prices, Low Case. 142 Table 40. Gas Production, High Case. HIGH CASE; ; GAS PRODUCTION: IN UNITS OF TCP PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 FROM BIOMASS; FROM COAL; EASTERN; BEST ARCTIC; WESTERN; 0.0000 0.0000 0.0000 0.0000 0.0002 0.0002 0.0000 0.0000 2.9493 4.0447 0.0000 0.0000 0.0000 0.0000 0.4800 0.7703 0.0000 0.0000 3.7841 3.0256 0.0004 0.0004 0.0000 0.0000 0.8816 0.9498 0.0000 0.4734 1.1770 0.2083 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 35. Thus, the differences between the plotted lines are the entries in Table 40.) 8.00 —i 7.00 HIGH CASE GflS PRODUCTION: FROM BIOMASS O FROM CORL .X EASTERN + WEST ARCTIC A WESTERN © 6.00 H 5.00 H CC CC UJ CC UJ 1.00 0_ CJ 3.00 2.00 1.00 H 0.0 1975 Ei 1985 ii 1995 2005 2015 2025 Figure 35. Gas Production, High Case. 144 Table 41. Gas Production, Low Case. LOW CASE; ; GAS PRODUCTION: IN UNITS OF TCF PEE YEAS AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 FROM BIOMASS; FROM COAL; EASTERN; WEST ARCTIC; WESTERN; 0.0000 0.0000 0.0002 0.0000 2.9565 0.0000 0.0000 0.0002 0.0000 4.0057 0.0000 0.0000 0.4800 0.0000 3^6569 0.0000 0.0000 0.7703 0.0000 3.0310 0.0004 0.0000 0.5997 0.00 00 1.2249 0.0004 0.0000 0.4779 0.2369 0.2345 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 36. Thus, the differences between the plotted lines are the entries in Table 41.) 8.00 -i 7.00 -\ LOW CASE GflS PRODUCTION: FROM BIOMASS FROM CORL EASTERN WEST ARCTIC WESTERN <!> X + © 6.00 H 5.00 H CC CE LU Lu 4.00 H (_> 3.00 H 2.00 H 1.00 0.0 1975 Ei 1985 Ei 1995 2005 Ei 2015 2025 Figure 36. Gas Production, Low Case. 146 Table 42. Gas Prices, High Case. HIGH CASE; GAS PRICES: IN UNITS OF 1975$ PER MCF AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EAST,AT TORONTO; 2.1009 2.5780 2.0856 2.4036 3.0397 3.1039 WEST, WELLHEAD; 0.9547 1.0024 1.0360 1.7346 2.3785 2.5003 Corrected, Toronto; 1.52 1.58 1.61 2.40 3.04 3.10 147 HIGH CASE •4.00 -GflS PRICES: EAST,RT TORONTO A WEST. WELLHEAD CD CORRECTEPjTORONTO + 3.50 -0.50 H °'° 1975 lijjs 19E 2005 20i5 20^5 Figure 37. Gas Prices, High Case. 148 Table 43. Gas Prices, Low Case. LOW CASE; GAS PRICES: IN UNITS OF 1975$ PER MCF AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EAST,AT TORONTO; 2.1612 2.4803 1.9189 2.0884 3.0005 3.0005 WEST, WELLHEAD; 0.9176 0.9627 1.0227 1.4555 2.2610 2.5003 Corrected, Toronto; 1.48 1.53 1.60 2.09 3-00 3.00 149 LOW CASE GflS PRICES: ERST.RT TORONTO A WEST. WELLHEAD O CORRECTEPjTORONTO + 0.50 H 0.0 1975 19£ I9B5 2005 2015 20^5 Figure 38. Gas Prices, Low Case. 150 Table 44., Secondary Energy Fuel Shares, High Case. HIGH CASE; SECONDARY SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.0000 0.0143 0.0437 0.0000 0.1350 0.2147 0.6076 0.0427 0.0000 0.1810 0.2508 0.4981 0.0700 0.0000 0.1715 0.3307 0.4376 0.0602 0.0000 0.1872 0.2999 0.3652 0.1335 0.0056 0.3728 0.1313 0.2896 0.1569 0.0914 0.0227 0.3788 0.0765 0.2612 0.1694 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 39. Thus, the differences between the plotted lines are the entries in Table 44.) o 151.: 1.60 —i 1.140 H HIGH CASE SECONDARY SHARES: SOLAR • COGENERATION O ELECTRICITY X GAS + OIL A CORL © 1.20 li>GO X X «-0.60 ~\ 0.40 H 0.20 H 0.0 1975 1985 35 19b 2005 2015 2025 Figure 39. Secondary Energy Fuel Shares, High Case. 152 Table 45. Secondary Energy Fuel Shares, low Case. LOW CASE; SECONDARY SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.1420 0.2166 0.5985 0.0000 0.0000 0.1867 0.2553 0w4883 0.0000 0.0000 0.1837 0.3543 0.3976 0.0000 0.0000 0.1816 0.3574 0.3355 0.0436 0.0043 0.3373 0.1680 0.3064 0.1137 0.0160 0.3822 0.0775 0.2607 0.0429 0.0696 0.0644 0.1256 0.1404 0.1498 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 40. Thus, the differences between the plotted lines are the entries in Table 45.) 1.60 -i 1.140 H LON CASE SECONDARY SHARES: SOLAR + COGENERATION O ELECTRICITY X GAS + OIL A COAL © 1.20 H 1.00 H m s *-o i—i CJ 0.80 CE OZ 0.60 H 0.»40 H 0.20 H 0.0 1975 1985 -©-35 2005 2015 20^5 Figure 40. Secondary Energy Fuel Shares, Low Case. 154 Table46. Primary Energy Fuel Shares, High Case. HIGH CASE; PRIMARY FUEL SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; BIOMASS; HYDRO; NUCLEAR; GAS; OIL; COAL; 0.0000 0.0004 0.0953 0.0089 0.2499 0.5624 0.0832 0.0000 0.0003 0. 1265 0.0204 0.2892 0.4609 0.1026 0.0000 0.0003 0. 1236 0.0236 0.3490 0.4158 0.0878 0.0128 0.0001 0.1395 0.0329 0.3104 0.3565 0.1478 0.04 05 0.0000 0.1194 0.2503 0.1326 0.2891 0. 1681 0.0847 0.0000 0.1071 0.2560 0.0765 0.2612 0.2145 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 41. Thus, the differences between the plotted lines are the entries in Table 46.) 155 HIGH CPSE 1.60 -PRIMARY FUEL SHARES'. SOLAR X BIOMASS • HYDRO <!> NUCLEAR X 1.140 - GAS + OIL A CORL © 1.20 H "° 1975 iSs 2005 2~3l5 2025 Figure 41. Primary Energy Fuel Shares, High Case. 156 Table 47. Primary Energy Fuel Shares, Low Case. LOW CASE; PRIMARY FUEL SHARES: IH UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; BIOMASS; HYDRO; NUCLEAR; GAS; OIL; COAL; 0.0000 0.0004 0.1002 0.0102 0.2518 0.5539 0.0000 0.0003 0. 1301 0.0211 0.2945 0.4511 0.0000 0.0003 0.1315 0.0253 0.3729 0.3773 0.0000 0.0001 0.1337 0.0313 0.3678 0.3261 0.0401 0.0000 0.1589 0.1763 0.1712 0.3041 0.1053 0.0000 0.1660 0.2083 0*0779 0.2606 0.0837 0.1028 0.0927 0.1409 0.1494 0.1819 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 42. Thus, the differences between the plotted lines are the entries in Table 47.) 157 1.60 -i 1.140 -A LON CASE PRIMARY FUEL SHARES-. SOLAR X BIOMASS + HYDRO O NUCLEAR X GAS + OIL A COAL © 1.20 H 1.00 H O i—i O 0.80 cr az u_ 0.60 H 0.(10 0.20 H o.o 1975 1985 E 19^5 2005 2015 20^5 Figure 42. Primary Energy Fuel Shares, Low Case. 158 Table 48. Total Energy, High Case. HIGH CASE; ; TOTAL ENERGY: IN UNITS OF 10**15 BTU PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 PRIMARY; SECONDARY; OUTPUT; 7.7803 6.5072 4.1747 8.5048 10.5024 12.6197 16.1401 22.1788 7.1052 9.0571 11.2611 14.9247 20.5556 4.8368 6.3592 8.3191 12.0677 17.2103 159 32.00 -i HIGH CASE TOTAL ENERGY: PRIMARY SECONDARY OUTPUT + A CD 28.00 H 24.00 -A °'° 1975 19^5 I9E5 2005 2CV15 2025 Figure 43. Total Energy, High Case. 160 Table 49. Total Energy, Low Case. LOH CASE; ; TOTAL ENERGY: IN ONITS OF 10**15 BTO PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 PRIMARY; SECONDARY; OUTPUT; 7.7524 6.4808 4.1699 8.2129 6.8390 4.6710 9.4743 10.6642 11.0860 12.6733 8.1230 9.4369 10.1908 11.7338 5.7482 6.9101 8.0804 9.8033 32.00 -i 28.00 H 24.00 A CC £j 20.00 LOW CASE TOTAL ENERGY: PRIMARY SECONDARY OUTPUT + © CC LU Q_ =2 16.00 CO LO *—i X X O 12.00 8.00 H 4.00 H 0.0 1975 1985 35 I965 2005 2015 2025 Figure 44. Total Energy, Low Case. 162 Chapter 8. Analysis of Some Energy Policy Questions 8.1. The Impacts of a No-New-Nuclear Policy To examine the effects of a moratorium on the construction of new nuclear power facilities, the model was solved with additional limits fixing new nuclear electricity capacity at zero after 1985. Upper bounds were placed on new nuclear capacity in the east in the first two periods, at the base case solution's level in 1976-1980, and slightly below the base case level in 1981-1985. For reasons that will become apparent shortly, the fixing of tar sands production until 2000 was changed to lower bounding, but at the same level. All other assumptions were those of the base case. There were unexpected results. The east, which in the base case relies heavily on nuclear power especially after 2000, does not switch mainly to coal-fired electricity production. Instead, the main change is a massive switch away from electricity production and use after 1985 in the east. Oil, notably from the tar sands, largely takes the place of electricity in the industrial sector and in the domestic, farm and commercial sector. There is increased use of western conventional oil in the early periods, followed by increased use of oil from the western arctic and especially from the tar sands after the year 2000. Since western coal, with its high trans portation cost, is the alternative source for new electric capacity after eastern hydro is used to its maximum, electricity is more expensive than oil in end uses. Oil heating regains its importance in the east after 2000, re placing heavy reliance on electric resistance heating. There is some heating by cogeneration with the small amount of new coal-fired electricity production, and solar heating is introduced after 1990 in the east, one period earlier than in the base case. At the primary energy level, there is a big switch from nuclear energy to oil and somewhat to coal. Oil prices rise more quickly to the backstop price, $12/bbl, because of the more rapid exhaustion of the cheaper sources than in the base case. Tables 50 to 53 and Figures 45 to 48 illustrate these trends. There are no significant changes in the west, compared to the base case, apart from changes in oil production discussed above. The economic benefits of allowing nuclear power can be estimated by comparing the values of the objective function in the solutions of the base case and the no-new-nuclear case. The objective function is the discounted sum of consumers' plus producers' surplus. (The dual equilibrium method to mitigate end effects is an approximation to the infinite horizon problem.) The difference in the two values of the objective function is approximately 9 $1.7 x 10 (1975$, discounted to 1975 using a 10% per annum discount rate). This is a surprisingly small value when one considers the importance of nuclear power in the base case solution. In per capita terms, the cost of following the no-new-nuclear route is only $77 per person (assuming a popu lation of 22 million), discounted to 1975, and in 1975$. Discounting to 1980, and converting to 1980$, this cost is only about $300 per person, or $30 per person per year, using 10% discount rate. Manne (1977, 1979) used the ETA-MACRO model to calculate the economic effects of banning additional civilian nuclear power plants in the United States after 1975. The present value of the losses in aggregate consumption (not of energy, but of all non-investment goods and services) from 1975 through 2050, also discounted at 9 10% per year, is $77 x 10 , in 1975$. The macroeconomic losses are low in the early years, but rise rapidly after the year 2000, when there are binding constraints on coal supplies. Manne concludes that "although a 'no-nuclear' policy would have negligible macroeconomic effects, there would be impacts throughout the energy sector." These general results are the same as the "no-nuclear" results for Canada, discussed above. The estimated value of 9 the losses in the United States, $77 x 10 , is higher than the value for 9 Canada, $1.7 x 10 , even if the usual factor of 10 is applied for rough economic comparisons between the two countries. Reasons for the higher figure include Manne's earlier cutoff of nuclear (after 1975, versus after 1985 in the model discussed here), and the existence in Canada of a relatively inexpensive alternate fuel — oil from the tar sands. The cost of the no-new-nuclear route to nuclear safety may be com pared to the cost of the permanent containment of nuclear wastes, since this appears to be the most important consideration in nuclear safety. Aikin, Harrison and Hare (1977), made a very rough estimate of the cost of an under ground nuclear waste repository. The capital cost is irrelevent here, since even in the no-new-nuclear alternative, the repository would have to be built, and operated until the old nuclear stations are shut down. The operating cost estimated by Aikin, Harrison and Hare (1977), $100 million per year, is based on a projection of nuclear power development in the year 2000. The operating cost in the no-new nuclear alternative, until the plants are shut down, would presumably be much less than $100 million per year, since the maximum nuclear level, in 1981-1985, is considerably less than in 2000. The extra cost of the containment of nuclear wastes in the nuclear alter native is therefore approximately ( ($100xl06)/0.10) x (1.10)~15^= $0.24 x 109, discounted to 1975 at the rate of 10% per year, under the assumption that the repository would not begin operation until 1991. This cost is small 9 compared to the cost of the no-new-nuclear path, $1.7x10 , calculated above. These cost calculations do not necessarily suggest that the nuclear path should be favoured as the cheaper alternative. Since the estimated costs of safety are quite low in either case, it may be concluded that the issue should not be decided on economic grounds. Rather, the closest attention should be paid to the technical feasibility of the nuclear safety proposals by the nuclear advocates, and to the health effects of nuclear power production. Some key plots are shown in Figures 45 to 48, with the corresponding Tables 50 to 53. The above analysis of the no-new-nuclear path depends on assumptions about the cost and availability of oil from the tar sands. If there are in fact upper limits on tar sands production (due to physical and environ mental limits such as water shortages, or inability to treat the waste water) , or if synthetic crude oil is much more expensive than was assumed (due perhaps to cost escalations in periods of rapid increases in capacity) , the cost of the no-new-nuclear path would be greater. Inclusion of upper limits on tar sands production, or an increasing marginal cost for expansion of tar sands capacity would likely bring about a smaller shift to tar sands, and a greater shift to other fuels, such as natural gas (in the medium term, at least, before supplies are nearly exhausted) and coal. As a step in this direction, the no-new-nuclear case was solved again, but with oil from the tar sands at a cost of $13.50/bbl, rather than $12/bbl. Still the tar sands play a big role in replacing electricity in general, and nuclear power in particular, but frontier natural gas adopts much of the replacement role initially, before the last period, 2011-2020. Another assumption which influences the no-new-nuclear case, but in a way which does not affect the main conclusions above, is the constraint limiting the share of new eastern electricity generation which may be met by hydro. In the first period, this constraint has no effect different from the base case, since there is no severe restriction on nuclear in this 166 period. In the second period, the upper limit on new nuclear capacity, smaller than the level calculated in the base case, brings about a forced decrease in hydro, through the hydro share constraint. This is unrealistic since in reality, restrictions on nuclear would likely increase hydro's share, perhaps by Quebec exporting hydroelectricity to Ontario. Similarly, in the third period, there is no new nuclear capacity allowed, and no coal-fired electricity is added, which together force zero new hydro capacity, through the share constraint. After the third period, there is some coal-fired electricity capacity added, which allows new hydro to be added, until the upper limit on hydro generation is reached after the year 2000, one period later than in the base case. This deficiency does not affect the conclusions of the switch from nuclear to tar sands and from electricity in general to oil, since the main switch is after 2000, when hydro is at its upper limit in the no-new-nuclear case. Furthermore, the calculation of the economic benefits of allowing nuclear power would lead to even lower benefits if the restrictions on hydro were relaxed, since the no-new-nuclear route would be less costly. Thus, the overly-restrictive assumptions about hydro reinforce the conclusion that the economic benefits of allowing nuclear power are negligible. 167 ( Table 50. Crude Oil Production, No-new-nuclear Case. BASE CASE; NO NEW NUCLEAR; OIL PRODUCTION:. IN UNITS OF 10**9 BBL PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; FROM BIOMASS; FROM COAL; EASTERN; TAR SANDS; WEST ARCTIC; WESTERN; 0.2791 0.0000 0.0000 0.0008 0.0362 0.0000 0.5566 0.1141 0.0000 0.0000 0.0100 0.0744 0.0000 0.5056 0.0000 0.0000 0.0000 0.0500 0.1534 0.0000 0.5714 0.0000 0.0000 0.0000 0.1772 0.2756 0.0000 0.3039 0.0000 0.0000 0.0000 0.2058 0.4122 0.2803 0.0793 0.0000 0.0000 0.0000 0.0740 1.1234 0.1317 0.0000 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 45. Thus, the differences between the plotted lines are the entries in Table 50.) 168 BASE CASE NEW NUCLEAR OIL PRODUCTION: IMPORTS FROM BIOMASS FROM CORL EASTERN X TAR SANDS + WEST ARCTIC WESTERN m CD 1.20 H az cr 1.00 LU az LU Q_ 0.80 H CD CD CD X X o 0.60 0.40 H 0.20 H 0.0 1975 2025 Figure 45. Crude Oil Production, No-new-nuclear Case. 169 Table 51. Oil Use, No-new-nuclear Case. BASE CASE; NO NEW NUCLEAR; OIL USE: IN UNITS OF 10**9 BBL PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPORTS; OTHER TRANSPORT; ROAD TRANSPORT; INDUSTRY; DFC; ELECTRICITY; 0.1194 0.0304 0.0620 0.0688 0.2123 0.2039 0.1501 0.1331 0.2562 0.2024 0.0172 0.0160 0.0146 0.0067 0.0804 0.0997 0.2098 0.2308 0.2416 0.2980 0.1582 0.0569 0.0142 0.0095 ,0.0000 0.0000 0.1247 0.1646 0.2627 0.3311 0.3833 0.5052 0.1347 0.2303 0.0000 0.0000 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 46. Thus, the differences between the plotted lines are the entries in Table 51.) 170 1.60 -i BASE CASE NO NEW NUCLEAR l.urj H OIL U5E: EXPORTS • OTHER TRANSPORT • ROflO TRANSPORT X INDUSTRY + DFC A ELECTRICITY CD 1.20 OC CE 1.00 H UJ OC UJ Q_ CO CO CD X X o 0.80 H 0.60 H o.uo H 0.20 H 0.0 O . CD 1975 19^5 19 CD ©-995 2005 201! 20^5 Figure 46. Oil Use, No-new-nuclear Case. 171 Table 52. Eastern Electricity Production, No-new-nuclear Case. BASE CASE; NO NEW NUCLEAR; ELECTRICITY, EAST: IN UNITS OF 10**12 KHH PERYEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 FROM BIOMASS; NUCLEAR; OIL AND GAS; COAL; HYDRO; 0.0000 0.0000 0.0201 0.0427 0.0124 0.0128 0.0228 0.0223 0.1666 0.2331 0.0000 0.0000 0.0427 0.0421 0.0117 0.0076 0.0205 0.0368 0.2165 0.2406 0.0000 0.0000 0.0275 0.0000 0.0000 0.0000 0.0979 0.1254 0.4420 0.4420 (N.B., The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 47. Thus, the differences between the plotted lines are the entries in Table 52.) 172 3.20 -i 2.80 H 2.U0 H CC cr 2.00 H LU >-az LU Q_ 1.60 H CM X X o 1.20 H 0.80 H 0.40 H 0.0 1975 1985 BASE CASE NO NEW NUCLERR ELECTRICITY. ERST: FROM BIOMASS NUCLEAR OIL AND GAS COAL HYDRO X + CD Ei liSi 2005 20*15 2025 Figure 47. Eastern Electricity Production, No-new-nuclear Case. 173 Table 53. Primary Energy Fuel Shares, No-new-nuclear Case. BASE CASE; NO NEH NUCLEAR; PRIMARY FUEL SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; BIOHASS; HYDRO; NUCLEAR; GAS; OIL; COAL; 0.0000 0.0000 0.0000 0.0177 0.0361 0.0925 0.0004 0.0952 0.0088 0.2500 0.5624 0.0003 0.1170 0.0175 0.2926 0.4705 0.0003 0.0927 0.0146 0.3605 0.4419 0.0002 0.0905 0.0125 0.3416 0.3787 0.0000 0.1578 0.0071 0.1419 0.4264 0.0000 0. 1333 0.0000 0.0680 0.4606 0.0832 0.1020 0.0900 0-1589 0.2307 0.2457 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 48. Thus, the differences between the plotted lines are the entries in Table 53.) 174 1.60 -i 1.40 H BASE CASE NO NEW NUCLEAR PRIMARY FUEL SHARES: SOLAR X BIOMASS • HYDRONUCLEAR X GAS + OIL A COAL CD 1.20 H 1.00 H O i—i O 0.80 H CE cn 0.60 H 0.40 H 0.20 H 0.0 1975 1985 c^T 19b5 2005 2L?15 20^5 Figure 48. Primary Energy Fuel Shares, No-new-nuclear Case. 8.2. Allowing Heating by Cogeneration with Nuclear Power It was assumed in the base case that heating by cogeneration with nuclear electricity is not allowed, because the public might not accept it. To investigate this, the base case was run again, but allowing co-generation with nuclear power. It was assumed that the maximum ratio of heat to electrical output in nuclear cogeneration is half the maximum ratio in coal-fired cogeneration - i.e. for every kilowatt-hour of nuclear electricity, up to 2,132.5 BTU of heat can be supplied to the domestic, farm and commercial sector. This lower figure for nuclear cogeneration was chosen because, according to Berthin (1980), there is less heat available in a CANDU generation system for this purpose than in a coal-fired electricity generation station. The cost of using nuclear cogenerated heat was assumed to be the same as for cogeneration using coal. As with coal cogeneration,it was assumed that new capacity of heat by cogeneration with nuclear can only be established with new nuclear electricity capacity. Judging by Berthin's study, it is likely that nuclear facilities would have to be closer to population centres than at present, for the district heating scheme to work with the costs Berthin estimates. Under these assumptions, nuclear cogeneration begins in the east as soon as it is allowed (after 1980), and reliance on this heating method becomes quite heavy after 2000, indicating that nuclear cogeneration is competitive in the east. The main heating method displaced is electric resistance heating, although it is still very important. Solar heating enters the solution one period later (2011-2020) than in the base case. One curious consequence of the displacement of electric resistance heating- is that the generation of electricity by nuclear power is considerably lower than in the base case. 176 Table 54. DFC Heating, East, Nuclear Cogeneration Case. BASE CASE; NUCLEAR COGEN.; DFC HEATING, EAST: IN UNITS OF 10**15 OUTPUT BTU/YR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; HEAT PUMP; ELECTRIC RESIS.; GAS; OIL; 0.0000 0.0000 0.0000 0.0594 0.0000 0.0000 0.1989 0.2938 0.3000 0.4026 0.8498 0.6834 0.0000 0.0000 0.0594 0.1535 0.0000 0.0000 0.2003 0.6660 0.987 9 1.2308 0.5522 0.0000 0.0000 0.1439 1.2633 1.8313 0.0000 0.0000 0.9618 1.0768 0.2350 0.0000 0.0000 0.0000 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 49. Thus, the differences between the plotted lines are the entries in Table 54.) 177 U.00 -i BASE CASE NUCLEAR COGEN. DFC HEATING. EAST: SOLAR COGENERATION HEAT PUMP ELECTRIC RESIS. GAS OIL X + © 2025 Figure 49. DFC Heating, East, Nuclear Cogeneration Case. 178 Table 55. Eastern Electricity production, Nuclear Cogeneration Case. BASE CASE; NUCLEAR COGEN. ELECTRICITY, EAST: IN UNITS OF 10**12 KWH PERYEAR AVERAGE VALOES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 FROM BIOMASS; NUCLEAR; OIL AND GAS; COAL; HYDRO; 0.0000 0.0230 0.0124 0.0228 0.1769 0.0000 0.0509 0.0128 0.0223 0.2620 0.0000 0.0726 0.0117 0.0205 0.3220 0.0000 0. 1162 0.0076 0.0145 0.4228 0.0000 0.6206 0.0000 0.0000 0.4420 0.0000 0.8696 0.0000 0.0000 0.4420 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 50. Thus, the differences between the plotted lines are the entries in Table 55.) 179 BASE CASE 3-20 i NUCLERR COGEN. ELECTRICITY, ERST: FROM BIOMRSS • NUCLEAR X OIL AND GR5 + COAL A 2.80 H HYDRO O 2.40 H Figure 50. Eastern Electricity Production, Nuclear Cogeneration Case. 180 Table 56. Secondary Energy Fuel Shares, Nuclear Cogeneration Case. . BASE CASE; NUCLEAR COGEN.; SECONDARY SHARES; IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.1420 0.2169 0.5982 0.0429 0.0000 0.0085 0.1835 0.2528 0.4851 0.0701 0.0000 0.0069 0.1791 0.3418 0.4100 0.0622 0.0000 0.0146 0.1905 0.3204 0.3440 0.1305 0.0000 0.1089 0.3025 0.1502 0.2920 0.1464 0.0332 0.1402 0.3375 0.0770 0.2576 0.1545 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 51. Thus, the differences between the plotted lines are the entries in Table 56.) 181 1.60 -I BASE CASE NUCLEAR COGEN. SECONDARY SHARES: SOLAR COGENERATION ELECTRICITY GAS OIL COAL O X + © Figure 51. Secondary Energy Fuel Shares, Nuclear Cogeneration Case. 182 This suggests an unexpected route to lessen future growth in the number of nuclear power stations. If district heating using waste heat from nuclear power stations can be proven to be 100% safe, then the environ mental hazards of nuclear power may be reduced in magnitude by adopting this type of heating on a large scale in the east, although the likelihood that nuclear stations would have to be closer to population centres may in fluence this result. The difference in the value of the objective function between the base case and the nuclear cogeneration case - i.e. the economic benefit 9 of nuclear cogeneration - is $0,562 x 10 , in 1978$, discounted to 1975 at the rate of 10% per year, or about $26 per person in 1975. Even when this is converted to 1980$, and discounting is done to 1980, the benefit is only approximately $100 per person, or $10 per person per year. Thus, as with the question of whether to forbid new nuclear power stations, the issue of nuclear cogeneration should not be decided on economic grounds. The important questions are the technical feasibility and safety of the system. Some key plots for this case are shown in Figures 49, 50 and 51, with the corresponding Tables 54, 55 and 56. 8.3. High Oil Costs (Sensitivity Analysis) There have recently been suggestions that the costs of syncrude from the tar sands and of conventional oil have been escalating more rapidly than the general rise in prices. Quon (1980) suggests that the real costs of oil production have been increasing as both capital and labour have demanded a higher portion of the perceived economic rent (in the ex pectation of much higher oil prices). Furthermore, they have actually received higher payments for drilling rig rentals, wages, etc. because 183 of the strong demand for these services (again due to the expectation of much higher oil prices). To investigate this possibility the model was solved with all the base case assumptions except the following higher oil costs: Oil Source Base Case Cost Higher Cost western conventional, "low cost" $ -4/bbl western conventional, "high cost" $ -8/bbl northwest frontier, "low cost" $10/bbl northwest frontier, "high cost" $14/bbl tar sands $12/bbsoutheast offshore $ 7/bbl northeast offshore $10/bb$ -4/bbl $10/bbl $12/bbl $16/bbl $15/bbl $ 9/bbl $12/bbl (unchanged) The tar sands cost has been increased to approximately the 1980 inter national price of oil (in 1975$) since the participants in proposed new tar sands projects claim that the world price is needed to make the projects economically viable. Other costs have been increased by $2 per barrel, except the established, low cost western oil. The results of this sensitivity analysis were not surprising, with one exception - solar heating is introduced in the east after 1980, although it remains at a very low level until after 2000, when it is first introduced in the base case. Apparently the higher oil costs cause increases in the price of heating in the east just enough to make solar competitive earlier. Except for the last period, there is lower oil production and use. Tar sands production in the first five periods is at the same level as in the base case because production in the first four periods is fixed exogenously, and drops in the fifth to the same level in both cases because there is no capacity added, but old capacity is removed. Production of "low cost" western oil, the cheapest source, at an unchanged cost, is delayed, 184 Table 57. Crude Oil Production, High Oil Costs Case. BASE CASE; HIGH OIL COSTS; OIL PRODUCTION: IN UNITS OF 10**9 BBL PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; FROM BIOMASS; FROM COAL; EASTERN; TAR SANDS; WEST ARCTIC; WESTERN; 0.2553 0.0000 0.0000 0.0008 0.0362 0.0000 0.5283 0.0976 0.0000 0.0000 0.0100 0.0744 0.0000 0.4477 0.0000 0.0000 0.0000 0.0500 0.1534 0.0000 0.3885 0.0000 0.0000 0.0000 0.1772 0.2756 0.0000 0.1735 0.0000 0.0000 0.0000 0.0784 0.2516 0.0000 0.2330 0.0000 0.0000 0.0000 0.1467 0.1646 0.2917 0.0917 (M.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 52. Thus, the differences between the plotted lines are the entries in Table 57.) 1.60 -i BASE CASE HIGH OIL COSTS 1.140 -\ OIL PRODUCTION: IMPORTS FROM BIOMRSS FROM COAL EASTERN TAR SANDS WEST ARCTIC WESTERN X X + A © 1.20 H DZ CE 1.00 H LU DZ LU Q_ 0.80 H CO CD CD X X o 0.60 H o.uo H 0.20 H 0.0 1975 1985 Si 1995 2005 Ei 2015 2025 Figure 52. Crude Oil Production, High Oil Costs Case. 186 Table 58. Crude Oil Prices, High Oil Costs Case. BASE CASE; HIGH Oil COSTS; CBUDE OIL PRICES: IN UNITS OF 1975$ PER BBL AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 EXPORTS; IMPORTS; EAST; BEST; 14.6000 10.8000 8.2645 5.6049 17.8000 14.8000 11,5173 10.0369 21.6000 19.3000 11.2635 10.7639 32.0000 32.0000 10.3818 9.8821 32.0000 32.0000 11.97 48 11.4750 32.0000 32.0000 14.0171 13.5176 187 UO. 00 35.00 H BASE CASE HIGH OIL COSTS CRUDE OIL PRICES: EXPORTS X IMPORTS + ERST A WEST © 30.00 H 25.00 H _i CO CO cc LU °- 20.00 -I LO r-co 15.00 H IO.OO H 5.00 H o.o 1975 1985 1995 Si 2005 Ei 2015 2025 fe Figure. 53. Crude Oil Prices, High Oil Costs Case. 188 Table 59. Secondary Energy Fuel Shares, High Oil Costs Case. BASE CASE; HIGH Oil COSTS; SECONDARY SHARES; IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.1602 0.2198 0.5769 0.0054 0.0000 0.1920 0.2634 0.4699 0.0044 0.0000 0.1877 0.3580 0.3689 0.0018 0.0000 0.2062 0.3362 0.3260 0.0432 0.0121 0.3916 0.1462 0.2592 0.1100 0.0191 0.3844 0.0740 0.2573 0.0432 0.0693 0.0811 0.1298 0.1477 0.1552 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 54. Thus, the differences between the plotted lines are the entries in Table 59.) 1.60 -i l.uo H BRSE CASE HIGH OIL COSTS SECONDARY SHARES: SOLAR • COGENERATION & ELECTRICITY X GAS + OIL A CORL © 1.20 H 1.00 D i—i c3 eso H CE DZ 0.60 H 0.40 0.20 H 0.0 1975 19B5 -©- -© IB5 ttbs 2005 20*15 2025 Figure 54. Secondary Energy Fuel Shares, High Oil Costs Case. compared to the base case — in effect "saved" for the future, to put off the use of the more expensive sources at the increased costs. The intro duction dates of northwestern arctic and northeastern offshore oil are de layed one period due to the assumed higher costs and consequent lower de mand and production . The prices of oil are higher, but the increase over the base case is less than the cost increase ($2/bbl for all except tar sands) except in the period 1986-1990. The oil price does not reach the backstop cost (tar sands) within the model's time horizon. Gas prices are higher in the east, until the last two periods. There is a small switch from oil use to greater reliance on gas in the medium term and on electricity from coal and nuclear sources, compared to the base case. In the two transportation sectors, which depend on oil alone, there is only a slightly reduced demand for oil, due to the quite inelastic de mand specified in those sectors. See Figures 52, 53 and 54 for plots of this case. 8.4. The Impacts of Competitive Coal Gasification As discussed in chapter 6, coal gasification is not in the base case solution, but is almost competitive in the later periods. To examine the impacts of the introduction of coal gasification, the model was solved with the base case assumptions except that the distribution margin for coal to gasification plants was reduced by one half, to $0.40/10^ BTU. This is equivalent to reducing the price of gas from coal to $2.30/mcf, from the price of $3.00/mcf in the base case, making this gas source cheaper than gas from the northwest arctic. Another change in the assumptions for this 191 Table 60. , Coal Production, Coal Gas Case. BASE CASE; CHEAP COAL GAS; COAL PRODUCTION: IH UHITS OF 10**8 TONS PEE YEAR AVEBAGE VALUES FOR THE PEEIOD ENDING IN 1980 1985 1990 2000 2010 2020 IHPOBTS; 0.1580 0.1465 0.0000 0.0000 0.0000 0.0000 EASTERN; 0.0482 0.0964 0.1928 0.3453 0.3267 0.2070 WESTERN; 0.2642 0.3743 0.5037 0.8817 1.6627 4.0277 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 55. Thus, the differences between the plotted lines are the entries in Table 60.) 192 BASE CASE Figure 55. Coal Production, Coal Gas Case. 193 fable 61. Gas Production, Coal Gas Case. BASE CASE; CHEAP COAL GAS; GAS PRODUCTION; IN UNITS OF TCF PEE YEAS AVERAGE VALUES FOE THE PEBIOD ENDING IN 1980 1985 1990 2000 2010 2020 FBOM BIOMASS; FBOM COAL; EASTEBN; WEST ARCTIC; WESTERN; 0.0000 0.0000 0.0000 0.0000 0.0002 0.0002 0.0000 0.0000 2.9523 4.0228 0.0000 0.0000 0.0000 0.0000 0.4800 0.7703 0.0000 0.0000 3.7306 3.0290 0.0004 0.0004 0.3861 2.1806 0.4578 0.1317 0.0000 0.0000 1.1982 0.2199 (N-B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 56. Thus, the differences between the plotted lines are the entries in Table 61.) 8.00 -i 7.00 H BASE CASE CHEAP COAL GAS GAS PRODUCTION: FROM BIOMRSS FROM COAL EASTERN WEST ARCTIC WESTERN X + o 6.00 H 5.00 H DC CE LU UJ 4.00 H CL. C_) 3.00 H 2.00 H l.oo H 0.0 1975 Ei 1985 Ei 1995 2005 Ei 2015 2025 Figure 56. Gas Production, Coal Gas Case. 195 Table 62. Secondary Energy Fuel Shares, Coal Gas Case. BASE CASE; CHEAP COAL GAS; SECONDARY SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.0000 0.0000 0.0421 0.0829 0.0000 0.1351 0.2156 0.6066 0.0428 0.0000 0.1836 0.2527 0.4941 0.0696 0.0000 0.1782 0.3406 0.4193 0.0619 ,0000 .2038 .3318 .3346 . 1298 0.0000 0.3575 0.1619 0.2929 0.1456 0.0000 0.3422 0.1711 0.2523 0.1515 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 57. Thus, the differences between the plotted lines are the entries in Table 62.) 1.60 -i 1.40 -\ BASE CASE CHEAP COAL GAS SECONDARY SHARES: SOLAR • COGENERATION <!> ELECTRICITY X GAS + OIL A COAL CO 1.20 H 1.00 H O i—i O 0.80 H CE DC 0.60 H 0.40 H 0.20 H 0.0 1975 1985 -©-E 19^5 2005 2315 20^5 Figure 57. Secondary Energy Fuel Shares, Coal Gas Case. 197 Table 63. Primary Energy Fuel Shares, Coal Gas Case. BASE CASE; CHEAP COAL GAS; PRIMARY FUEL SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; BIOMASS; HYDRO; NUCLEAR; GAS; OIL; COAL; 0.0000 0.0004 0.0953 0.0088 0.2508 0.5614 0.0834 0.0000 0.0003 0.1281 0.0208 0.2915 0.4569 0.1024 0.0000 0.0003 0.1280 0.0246 0.3591 0.3982 0*0898 0.0000 0.0001 0.1512 0.0362 0.3422 0.3257 0.1446 0.0378 0.0000 0.1358 0.2106 0.1291 0.2843 0.2023 0.0704 0.0000 0.1069 0.2057 0.0206 0.2315 0.3648 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 58. Thus, the differences between the plotted lines are the entries in Table 63.) 198 1.60 -i I.UO H BASE-CASE CHEAP CORL GRS . PRIMARY FUEL SHARES: SOLAR X BIOMASS HYDRO O NUCLEAR X GAS '•' + OIL A CORL O 1.20 H 1.00 H D i—i O 0.80 cr cc 0.60 H 0.140 H 0.20 H 0.0 1975 1985 35 1955 2005 20*15 2025 Figure 58. Primary Energy Fuel Shares, Coal Gas Case. •case was to make the 1991-2000 tar sands projection into an upper limit on production in that period, in order to allow for some switching to gas from oil. Under these assumptions, coal gasification is introduced after 2000, bringing about much higher coal production then. Since this is a backstop source of gas at $2.30/mcf (as long as the huge coal supplies last), the more expensive northern frontier sources (in the west and the east) are left out of the solution. Total gas production and use are larger in the period 2011-2020, with the industrial and domestic, farm and commercial sectors taking the extra gas. There is much less electricity produced in 2011-2020 in the west, with industrial electricity use largely switched to gas. Heating by cogeneration and by solar in the west are left out of the solution, in favour of gas heating, unlike the base case solution. At the secondary energy level, after 2000, there is a switch away from heat by cogeneration, solar heat and electricity, towards the use of gas, compared to the base case. At the primary energy level, the switch is away from solar, hydro, crude oil and natural gas, especially in the last period, to coal. The share of coal in total primary energy rises to 36% in the last period, compared to 19% in the base case. Tables 60 to 63 and Figures 55 to 58 give the relevant detailed output for this case. 8.5. The Impacts of the Electric Automobile. The electric auto does not enter the base case solution. To study the impacts of the electric auto on the energy system, the base case was solved with a lower cost associated with the electric auto. The amount of the cost reduction was chosen to be just large enough to make the electric auto 200 competitive, after examination of the base case output. This lowering of the cost is equivalent to (a) lowering the initial cost difference between the electric and conventional autos from $1500 to $364, but keeping the road tax on electricity used by electric cars; (b) lowering the initial cost differences from $1500 to $1,127 and eliminating the electricity road tax; or (c) combinations of (a) and (b). In addition, the projected value of tar sands production in the period 1991-2000 was changed to an upper limit, to allow for the likelihood of lower oil consumption. There are no surprises in the solution. Oil production is lower than in the base case, especially from the tar sands, after 1990. Coal pro duction is higher in the last two periods (after 2000) in the west, fuelling higher electricity production for the electric auto. Electricity production is higher in the east, as well, after 2000. The share of electricity in secondary energy reaches 45% by the last period, 2011-2020, compared to 38% in the base case. At the primary energy level, crude oil's share reaches 18% by the last period, compared to 26% in the base case, with coal, nuclear and hydro energy taking oil's place. One small side effect of the higher electricity production is the partial displacement of solar heating in the west by an increased quantity of heat by co-generation with coal-fired electricity production, in the last period. Refer to Tables 64 to 67, and Figures 59 to 62 for specific details of this case. 201 Table 64. Transportation, Electric Auto Case., BASE CASE; CHEAP ELEC. AUTO TRANSPORTATION: IN UNITS OF 10**15 BTU PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 OTHER TRANSPORT; 0.0909 0.1044 0.1279 0.1697 0.2196 0.2813 ROAD,ELECTRIC; 0.0000 0.0000 0.0213 0.1860 0.4263 0.5588 ROAD, GASOLINE; 0.2888 0.3379 0.4000 0.3630 0.2841 0.3724 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 59. Thus, the differences between the plotted lines are the entries in Table 64.) 202 BASE CASE CHEAP ELEC. AUTO TRANSPORTATION: OTHER TRANSPORT + ROAD,ELECTRIC A ROAD. GASOLINE © 1.80 H Figure 59. Transportation, Electric Auto Case. 203 Table 65. Crude Oil Production, Electric Auto Case. BASE CASE; CHEAP ELEC. AUTO OIL PRODUCTION: IN UNITS OF 10**9 BBL PER YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; FROM BIOMASS; FROM COAL; EASTERN; TAR SANDS; WEST ARCTIC; WESTERN; 0.2788 0.1107 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008 0.0362 0.0000 0.5572 0.0000 0.0100 0.074U 0.0000 0.4942 0.0000 0.0500 0.1534 0.0000 0.5098 0.0000 0.1772 0.1505 0.0000 0.3136 0.0000 0.2058 0.1265 0.0559 0.0965 0.0000 0.0000 0.0000 0.0740 0.1445 0.2597 0.0086 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 60. Thus, the differences between the plotted lines are the entries in Table 65.) 204 1.60 -i BASE CASE CHEAP ELEC. AUTO OIL PRODUCTION: IMPORTS FROM BIOMRSS FROM COAL EASTERN TAR SANDS WEST ARCTIC WESTERN X X + © Figure 60. Crude Oil Production, Electric'Auto Case. 205 Table 66. Secondary Energy Fuel Shares, Electric Auto Case-BASE CASE; CHEAP E1EC. AUTO SECONDARY SHARES: IN UNITS OF FRACTION AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; COGENERATION; ELECTRICITY; GAS; OIL; COAL; 0.0000 0.0000 0.1349 0.2154 0.6070 0-0000 0.0000 0.1836 0.2526 0-4941 0.0000 0.0000 0.1782 0.3379 0.4224 0.0000 0.0000 0.2112 0.3296 0.3277 0.0436 0.0072 0.4222 0.1519 0.2250 0. 1041 0.0262 0.4485 0.0782 0.1841 0.0427 0.0698 0.0615 0.1315 0.1501 0.1589 (N.B. The series in this table are summed, one line at a time, starting with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 61. Thus, the differences between the plotted lines are the entries in Table 66.) 1.60 1.40 H BASE CASE CHEAP ELEC. AUTO SECONDARY SHRRES: SOLRR + COGENERATION <> ELECTRICITY X GAS + OIL A COAL © 1.20 -\ 1.00 H D i—i . CJ 0.80 CE CC 0.60 H 0.140 0.20 H 0.0 1975 1985 Ei 19^5 2005 20*15 2025 Figure 61. Secondary Energy Fuel Shares, Electric Auto Case. 207 Table 67. Primary Energy Fuel Shares, Electric Auto Case. BASE CASE; PRIMARY FUEL SHARES: IN UNITS OF FRACTION CHEAP ELEC. AUTO AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 SOLAR; BIOMASS; HYDRO; NUCLEAR; GAS; OIL; COAL; 0.0000 0.0004 0.0952 0.0088 0.2505 0.5618 0.0834 0.0000 0.0003 0. 1281 0.0208 0.2914 0.4569 0. 1026 0.0000 0.0003 0. 1281 0.024 5 0.3563 0.4010 0.0899 0.0000 0.0001 0.1561 0.0359 0.3387 0.3181 0.1511 0.0400 0.0000 0.1562 0.2575 0.1536 0.2227 0.1701 0.0958 0.0000 0.1538 0.2733 0.0779 0.1829 0.2163 (N.B. The series in this table are summed, one line at a time, starting '..with the bottom entry of the table, to arrive at the values of the plotted lines in Figure 62. Thus, the differences between the plotted lines are the entries in Table 67.) 208 1.60 -I 1.40 -A BASE CASE CHEAP ELEC. AUTO PRIMARY FUEL SHARES: SOLAR X BIOMASS + HYDRO O NUCLEAR X GAS + OIL A COAL © 1.20 H 1.00 H O i—i O 0.80 H CE DZ 0.60 H 0.40 H 0.20 H 0.0 1975 1985 35 l2i5 2obl 20*15 20^5 Figure 62. Primary Energy Fuel Shares, Electric Auto Case. 209 Chapter 9. Summary and Conclusions This dissertation describes the construction of a model of the energy sector in the Canadian economy using a nonlinear programming algorithm to equilibrate energy supplies and demands in three five-year periods and three ten-year periods, from 1975 to 2020. A linear process model of energy supply, conversion and distribution is linked to a model of the demands for services provided by energy in combination with other inputs such as capital. Upper limits on energy exports in the model present current policies and imply a two price system (domestic and international), which also represents current policies. Other important features of the model are the distinction of two regions, western and eastern (the main energy producing and consuming regions, respectively), and the linear approximations to long-run marginal cost curves for exhaustible hydrocarbon resources. The main efforts to date have been in the collection of data for the "base case", in the construction of a structure for which data exist, in the computer coding (including routines for reporting the results), and in the testing and debugging of the model. Apart from the base case, data for low demand and high demand cases were used in other solutions of the model. Examination of the low, base and high cases shed some light on the dates of introduction of various new tech nologies and frontier petroleum resources, on energy pricing, and on the competitiveness of certain new technologies. As well, some energy policy questions have been analyzed with the aid of the model, namely the questions of banning further nuclear power development and of allowing district heating by cogeneration with nuclear electricity, the effects of higher oil costs (a sensitivity analysis), the impacts of competitive coal gasification, and the impacts of competitive electric automobiles. Some important conclusions drawn 210 from the results of the model are summarized below. It was found that oil from the northwest Arctic and northeast offshore will not likely be needed until after 2000, although northeast offshore oil is required after 1990 under the high demand assumptions. Coal liquefaction appears to be uneconomical in all periods in the base case. Even under the most favourable assumption about the cost of the coal input, the cost of the oil output would be higher than the price of oil until after the year 2000. The assumption of restricted exports, with the resulting two price system, is a key assumption in all conclusions. For example, if unrestricted exports, or even much higher oil export restrictions were allowed, frontier oil production would begin earlier and coal liquefaction may become competitive. Oil production and use were found to be approx imately constant after 1980, due to increasing fuel efficiency in the trans portation sectors, and to substitution of other fuels in the other sectors. Frontier natural gas sources will not be needed until after 2000 under the three demand scenarios (low, base, and high). Gas is a transitional fuel, to be used in place of oil in the medium term, but it will eventually be replaced by other energy sources. Canadian use of natural gas peaks in the period 1991 to 2000, and production (including for export) peaks in the period 1986-to 1990. It was found that the "competitive relationship" 'of gas and oil is quite different in the two regions — the ratio of the gas price to the oil price rises over time in each region, but it is higher in the east. Coal gasification is nearly competitive in the base case. Sensitivity analysis indicates that gasification of coal may play an important role after 2000, displacing some electricity, solar heat and heat by cogeneration, compared to the base case. The model indicates strong demands for coal in industry, for the gener-211 ation of electricity and heat by cogeneration in the west, and possibly, for synthetic fuel production as discussed above. Hydroelectricity is important in both regions, since it is the least expensive source of electricity. The existence of large supplies of inexpensive coal for electricity in the west and of low cost nuclear electricity in the east ensure fairly stable electricity prices in both regions. The eastern picture changes dramatically under the assumption of no new nuclear development after 1985. The alternate source of eastern electricity - from coal - is so expensive that there is a large switch from electricity to oil in the no-new-nuclear case, compared to the base case. Oil from the tar sands is especially important in this switch after the turn of the century. Comparison of the objective function values revealed that the economic benefits of nuclear power are not great, which indicates that the issue is not one of economics, but of the safety of nuclear power. The electric automobile will not likely be competitive unless there are technical breakthroughs which lower the initial cost differences between the electric and conventional cars, or the road tax burden is less for electric cars than for conventional ones. Under the assumptions of improvements in the fuel efficiency of conventional cars, the price of transportation (price per mile) decreases until 2010, even though the fuel price (price per gallon) increases. Heating in the domestic, farm and commercial sector of the west will likely be done mainly by gas until 2010, with solar and cogeneration taking the place of gas later. In the eastern region, oil and gas are important heating fuels until 2000 and 2010, respectively. Electric resistance and solar heating are the important types of heating in later periods. It appears that the heat pump is not competitive in either region. If district heating by 212 cogeneration with nuclear electricity is allowed (it is not allowed in the base case), total electricity production is lower in the east, particularly nuclear electricity, because electricity for resistance heating is not re quired in such large amounts. This indicates that one route to improving nuclear safety may be to distribute the waste heat from nuclear stations for residential and commercial heating, provided, of course, that any new risks from circulating radioactive hot water, or from building nuclear stations closer to population centres do not outweigh the safety benefits of decreased nuclear power development. There are many possible directions for future research. A major effort to construct a data base on the functional end uses of energy in Canada, particularly in industry, would allow the revision of the structures of models such as this one to a more theoretically satisfying structure. The market shares of fuels in the end use sectors could be made more endogenous, for example, by a more detailed process modelling in the end use sectors. This data base work can likely be carried out only by a government agency such as Statistics Canada. The existing areas of end use process modelling — DFC heating and road transportation — could benefit by explicit representation of "vintage effects" in the energy-using processes. For example, automobiles might be distinguished by period of production, with a new-car fuel efficiency for each period. In the present formulation of the model, average fuel efficiency is projected for each period for all cars, regardless of when they were produced. However, this average in reality depends on the rate of introduction of new cars. The vintage approach would avoid this problem. The policies of unrestricted energy exports and world pricing could be explored by incorporating increasing, marginal costs of capacity expansion in 213 key energy sectors (e.g. oil and gas). Apart from straightforward structural changes, the work would involve careful estimation of the cost escalations which can occur by a too rapid construction of, say, tar sands plants. A stochastic model of oil production might shed light on the optimal rate of development of tar sands, given the uncertainties surrounding the alternative, less costly conventional oil resources. Stochastic modelling may also give insight into optimal export policies, without exogenously restricting exports. The model discussed here is a partial equilibrium model, viewing the energy - economy linkages as only one-way. It is assumed that the various macroeconomic variables used in the energy demand functions are not them selves affected by events in the energy sector. The model would benefit by an extension to include automatic two-way energy economy interactions. In the early development of this model, a representation of energy economy interactions was attempted, by the method of ETA-MACRO (Manne, 1977). How ever, this approach had to be abandoned to keep the process detail in the end use sectors because there was no apparent way to make each end-use sector's share of total output energy endogenous. Probably the most important area of energy-economy interactions is the effect of the demand for investment capital by energy investments, particularly the large projects. Several recent investigations (Energy, Mines and Re sources, 1977h,Downs 1977, Rothman, 1980, Waddingham, 1980 and Kalymon, 1980 -also see the discussion by Schwartz, 1980a) have been made by forecasting energy capital needs, total capital investment, and economic growth, and judging whether energy investments will cause any strains to develop. Most conclude that there will be no great difficulties, provided the federal and provincial governments adopt certain policies. Waddingham (1980), however, 214 is relatively pessimistic, forseeing the possibility of capital supply limitations for energy investments. A fruitful area of further research, therefore, would involve the extension of the model to account for constraints on capital availability for energy investments. Ideally, such an extension should include the feedback effect of a large energy-related capital re quirement driving up the economy-wide cost of capital, which in turn raises the cost of energy, thus dampening the demand for energy. As a first step, a data base on initial capital costs of new capacities of energy production and conversion processes could be developed, including the data on the lead-time required between investment and beginning of operation. Investment require ments for the solution in each period could then be calculated, examined for "bulges", and compared to projections of capital availability to look for capital supply constraints, as in the approach of the other studies mentioned above. However, the base case results in this dissertation are unlikely to be constrained by capital requirements. Total secondary energy in the base case increases at an average rate of 2.9% per year between 1978 and 1995, while the rates of growth of secondary energy projected by EMR (1977a) in the various scenarios range from 2.7% to 3.9% per year between 1975 and 1990. The energy projections here are at the low end of the EMR ranges, and the above-mentioned studies were mostly based on the same EMR energy demand projections (except Rothman, 1980). Since the studies were mostly optimistic about financing, the energy projections here should cause even less concern about financing. Nevertheless, a detailed, careful look at the problem would certainly be worthwhile, particularly if the unrestricted trade policy is to be investigated thoroughly. A systematic study by Canadian energy analysts of the various Canadian 215 energy models, with a careful examination of the structural and data assumptions, would be a great help in assessing the confidence which may be attached to the conclusions of the models. As well, the design of future models could be improved with the suggestions arising from such a study. Survey papers such as those by Fuller and Ziemba (1980), and Manne et al. (1979) can be useful steps in the evaluation process, but the Energy Modeling Forum in the United States provides an example of the method and bene fits of deeper studies by researchers from industry, government and universities. If many new details are incorporated into the model in future research, closer attention will have to be paid to computing methods, to minimize computation costs. Decomposition by region might be attempted, particularly if more than two regions are distinguished (perhaps for a better represent ation of electricity generation). Time period decomposition might proceed by solving a series of two-period problems — at each step, one period would be the "present", and the second "period" would represent all time beyond the first period, in the manner of the dual equilibrium method of Grinold (1980). It is possible that the solution obtained by stepping through the time periods in this way may be a good, inexpensively-obtained starting basis for the full problem, in which the optimal solution in all time periods is to be found by a single optimization. The interim solution found by this time decomposition may be of interest itself -- it might be interpreted as a "myopic" solution, representing the behaviour of decision makers who act on the basis of somewhat vague, average notions about the future. If this model and its variants are to be used continually for analysis of energy policies, it will be necessary to revise the data base periodically as new facts come to light. 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EPRI Journal, 4_, 9:6-15, Electric Power Research Institute, Palo Alto, California. Ziemba, W.T. 1980. "The Process of Energy Policy Modeling." In Energy Policy Modeling: United States and Canadian Experiences, Volume II, eds. W.T. Ziemba and S.L. Schwartz, Martinus Nijhoff Publishing, Boston. Ziemba, W.T.; and Schwartz, S.L. (eds.). 1980. Energy Policy Modeling: United States and Canadian Experiences, Volume II, Martinus Nijhoff Publishing, Boston. Ziemba, W.T.; Schwartz, S.L.; and Koenigsberg, E. (eds.). 1980. Energy Policy Modeling: United States and Canadian Experiences, Volume I, Martinus Nijhoff Publishing, Boston. Appendix A. Derivation of the Demand Equations. The model calculates equilibrium prices and energy quantities in each region, for every time period, for four end-use sectors — road transportation, other transportation, industrial, and DFC (domestic, farm and commercial). The bulk of the model is a linear process model of energy supply and distribution. The demands for output energy in each of the four end use sectors are determined as functions of the respective prices, and of exogenous economic and demographic variables. Except for road transportation, the demand equations are adapted from those estimated by Energy, Mines and Resources (EMR). No new econometric estimation of demand equations has been carried out here. Instead, the work of other researchers, especially at EMR, has been used as a guide in the selection of independent variables and elasticities to derive the demand equations used here. These demand equations have been calibrated with data on demands and independent variables from 1970 and 1971, which were assumed to be equilibrium years for the energy sector. The EMR demand equations, described in Sahi and Erdmann (1980) and Sahi (1979), all incorporate lagged demands as determinants of present demands since the effects of changes in prices and other variables are not immediate. Long term versions of the EMR demand equations can be easily derived, with the interpretation that the calculated demands would be the demands at the given prices, etc., after sufficient time has elapsed for the full response to be made. The long term versions of the demand equations have been used because 1) the model has five and ten-year periods, but typical adjustment times range from 4.6 years to 7.3 years for 90% of the adjustment to be made; and, v 2) the linear process model of energy supply incorporates lag .effects by forcing the continued use of established capacity of many energy supply and end-use technologies for specified lifetimes. There is some evidence (Schwartz, 1980b) that the long term elasticities of demand for total output energy in each end use sector reported by Sahi and Erdmann are too low, and represent shorter term responses. The problem may be in the little variation in time series used for estimation. Cross country studies, with wider variation in the data, generally indicate larger long term elasticities. Sahi and Erdmann (1980) treat residential and commercial demands separately in the EMR model. The present model combines these two sectors in the DFC sector. Hence, it is necessary to combine the two EMR demand equations in a reasonable way. The EMR demand equation for the residential sector is ln (RDEM) = lh-(.R ) + ln(H) + (.0927)ln(IPH) + y'ln(SDPH) - (.1077)ln(P) + (.5282)ln(DD) - (.7279)ln(H ) - (.3845)In(DD ^ + (.7279)ln(RDEM where RDEM = demand for output energy in the residential sector, RQ = a regional constant, H = number of households, IPH = disposable income per household, SDPH = single dwellings per household, y' = .1276 (for Ontario), .2337 (for Manitoba), 0 (elsewhere), DD = degree days (a weather factor), and P = price of output energy in the residential sector. The subscript "-1" in the above equation indicates that the variable is 2 lagged one year. Sahi and Erdmann report that R = .998 for this equation. All equations were estimated over the period 1963-1974, pooling time series for seven regions. The long term version of the above equation may be derived by assuming that lagged variables equal the present year variables in the long term. If the weather factor is incorporated into the constant (since long range weather forecasting is impossible), the long term residential demand equation is 3407 V - 3958 -RDEM = RQ X H X (IPH)' X (SDPH) X P " , where, now, y = .469 (for Ontario), .859 (for Manitoba), and 0 elsewhere. When this equation is combined with the EMR long term commercial energy demand equation and used in the present model, the energy demand and price variables are endogenous. The EMR equation for commercial energy demand, in long term form, and incorporating the weather factor into the constant, is CDEM = CQ X (POP) x (IPC)'9060 x (MDPH) •1565:,.xP "•3823 where, CDEM = demand for output energy in the commercial sector, CQ = a constant POP = population IPC = disposable income per capita MDPH = number of multiple dwellings per household, and, P = price of output energy. The commercial sector's estimated income and price elasticities were altered by EMR judgementally to the above more reasonable values, according to Sahi (1980). In combining the residential and commercial sectors for the purpose of long-range forecasting, several simplifying assumptions can be made. The first is the elimination of the weather factor. .Secondly, the MDPH variable may be dropped from the combined equation, since its positive elasticity suggests that it is more a measure of the amount of residential energy falling under the statistical class "commercial" than a measure of energy efficiency due to multiple dwellings. Thirdly, the SDPH' variable may be dropped from the combined equation since it has a non-zero elasticity for only two provinces, indicating that its inclusion is primarily to explain the data classification problem associated with large multiple dwellings falling under the commercial classification. (This problem should disappear when the two sectors are combined.) Fourthly, the price elasticities for the residential and commercial sectors are very close, suggesting a price elasticity of -.39 for the combined demands would be a good choice. Lastly, although there has been a higher rate of growth of the number of households than that of population in recent decades (due to such factors as increasing divorce rate, the "baby boom" children growing to adulthood, and a lower birth rate), it is difficult to justify making a distinction between fore casts of these two growth rates over the long term of the present model (45 years). Therefore, output energy demand in the DFC sector is taken to be proportional to population, and to income per capita raised to some power z - 39 DFC = AQ x (POP) x (IPC) x P * where DFC = demand for output energy in the DFC sector, and = a constant. The elasticity, z, is taken to be 0.9060 by EMR for the commercial sector. 3407 In the EMR equation for residential demand, the factor H x (IPH)* z corresponds to the factor (POP) x (IPC) in the above combined DFC equation. . 3407 If z is chosen to make the average annual rates of growth of H x (IPH)" and (POP) x (IPC) equal in the historical period 1960-1976, then, using the data for these growth rates presented by the National Energy Board (1979 , p.84), z = .58. Thus, if the above combined equation were to re present only the residential sector, the elasticity with respect to income 22.9 per capita ought to be .58. The average of .58 and .906, weighted by the 1973 input energy to the residential and commercialsectors, respect ively, is z = .71. .^Indices of -population (pop) and of income per capita (ipc) are used/.with a base year of 1973 in the: DFC demand equations, giving 71 - 39 DFC = DQ x (pop) x (ipc)* x p-where DQ = a constant, different for the east and west. The constant factors are chosen using data of 1970, which is assumed to be an equilibrium year. One further adjustment is necessary to make the DFC demand equation appropriate for the model. In the DFC sector of the linear process model of energy supply, the non-fuel costs of space heating are taken into account, as well as the fuel costs. However, in the demand equation derived above, only the fuel cost is represented in the price variable. In section 8 of Appendix C, "Data for the Base Case", the output energy prices are derived for the base year, 1970. The weighted average of the western and eastern DFC output prices (weighted by output energy in the two DFC sectors), in cluding non-fuel costs of heating, was 0.5074, in model units. The weighted average of the DFC output fuel prices, not including non-fuel heating costs, was 0.2431, in model units. An elasticity of 0.39 with respect to fuel price means that a 1% change in fuel price leads to a 0.39% change in output energy demand. However, a 1% change in fuel price alone implies a 0.48% '.':•(•= .01 x .2431/.5074 x 100%) change in total output energy price, including non-fuel heating costs. Therefore, since a change of 0.48% in total output energy price leads to a 0.39% change in output energy demand, the elasticity of demand for output energy with respect to total price is - (0.39)/(0.48) = ---.-'81. Therefore, the demand equation for the DFC sectors of the present model is 71 — 81 DFC = D x(pop)x(ipc)" xP ' The EMR industrial energy demand equation excludes the demands for coke, coke oven gas and non-energy use of oil, but includes the demand for natural gas as a petrochemical feedstock. The EMR variables and elasticities have been used in an equation which includes all of industry's demands for energy commodities, including for the above special uses. EMR makes separate projections for coke, coke oven gas and petrochemical use of oil, but here the approach adopted is that of Hedlin, Menzies and Associates (1976), of projecting the upper and lower limits of the fractions of industrial output energy (including the special uses) supplied by coal, oil, gas and electricity. The EMR equation uses industrial real domestic product as an explanatory variable, but since it is difficult to make a distinction between the growth rates of industrial RDP and total RDP over the long range of the present model, total real domestic product has been used here. Using indices (1973 = 1) of real domestic product and capital-output ratio, and combining the weather factor into the constant, the long term EMR equation is altered to the form used here: IND = I x (rdp) x (cor) xP "48 , where,IND = output energy demand of industrial sector, I = constant, different for each region rdp = index (1973 = 1) of real domestic product, cor = index (1973 =1) of the capital/output ratio (manufacturing capital stock divided by industrial output) , and P = price of output energy, industrial sector. Again, the constant factors are chosen using the variables' values in 1970, an equilibrium year. The EMR model of demand for motor gasoline, in Sahi (1979), has been estimated using as data the econometric-judgemental forecasts for 1976-1990 prepared by the National Energy Board (NEB) with the aid of the NEB's complex motor gasoline model. The interpretation of EMR's long-term income and price elasticities for use in the present model is complicated because EMR is estimating input energy requirements, and they use a lagged, new-car fuel economy standard as an explanatory variable. This model requires an equation of the demand for output energy requirements, where the average fuel economy of all cars is projected in the linear process supply model. Therefore, in the model discussed here, income and price elasticities are assumed to be in the ranges found by Dewees, Hyndman, and Waverman (1975), who estimated five different models of demand for gasoline (input energy) using Canadian data for 1956-1972. Although these researchers used an urbanization index and automobile price as explanatory variables (as well as gasoline price and income per capita), it has been assumed here that these two variables will be relatively constant over the time period covered by the model. In addition, it has been assumed that average fuel economy was constant over their estimation period, so that their elasticities are applicable to the estimation of demand for output energy. Since diesel fuel supplied only about 6% of the input energy to road transportation in 1973, it has been assumed here that the same income and price elasticities apply to the demands for both gasoline and road-diesel. The equation for the demand for output energy in the road transport sector is then: 8 — 36 RTR = RQ x (pop) x (ipc)* x P. where, RTR = demand for output energy in the road transport sector, RQ = a regional constant, pop = an index of population (1973 = 1), ipc = index of disposable income per capita (1973 = 1), and, P = price of output energy in the road transport sector. The long term income and price elasticities, .8 and -.36, respectively, are the midpoints of the ranges reported by Dewees, Hyndman and Waverman (1975) for all of Canada —.69 to .91, and -.26 to -.45. -The regional constants are derived from 1970 data. The demands for input energy to the rail, aviation and marine sub-sectors of the transportation sector together accounted for 23% of the input energy demands of the whole transportation sector in 1973. It is therefore worthwhile to have a separate demand equation for the rail-aviation-marine sector, which is labelled "other tansportation" in this model. EMR has estimated demand equations, in Sahi (1979), for each of these three subsectors, using a 1976-1990 projection by the NEB. The long term price elasticities fall between -.067 and -.71, with an average (weighted by the 1973 input energy to the three subsectors) of -.36. The income variables are either real domestic product per capita (aviation) or real domestic product in industry and agriculture (the others). Population is also an explanatory variable in the aviation equation. Considering the average price elasticity above, and the similarity in the growth rate of real domestic product (RDP) and RDP in industry and agriculture, it is reasonable, upon examination of the three EMR equations, to adopt the following demand equation for other transportation: 30 OTR = 0Q x (rdp) x P , where, OTR = output energy demand in the sector of other transportation, 0Q = a regional constant rdp = an index of real domestic product (1973 = 1), and, P = price of output energy, in the other transportation sector. The regional constants are derived from 1970 data. The following chart summarizes the four long- term,-demand questions used in the present model. Table 68. Demand Equations Used in the Model. Sector Equation 71 — 81 1. Domestic, Farm DFC = DQ x (pop) x (ipc)" x P and Commercial , -, x -667 -.48 2. Industrial IND = I x (rdp) x (cor) X P 8 — 3 6 3. Road Transportation RTR = RQ x (pop) x (ipc)" x p — 36 4. Other Transportation OTR = 0Q x (rdp) x P Definitions of Symbols DFC, IND, RTR, OTR = output energy demands in the various sectors D , I , RQ, 0Q = regional (east or west) constants pop = index of population in each region (1973 = 1) ipc = index of disposable income per capita (1973 = 1) rdp = index of real domestic product in each region (1973 = 1) cor = index of capital/output ratio . (1973 = 1) - i.e. manufacturing capital stock divided by industrial output. Appendix B. Detailed Structure of the Model. In this section, the detailed equations of the model are given. Endo genous variables are represented by upper case letters. Exogenous parameters are represented by lower case letters or by upper case letters with a bar above. There are six time periods — three five-year periods, three 10-year periods, all labelled by the last year. The periods are Tn{l980, 1985, 1990, 2000, 2010, 2020J . In listing the model contraints, the time index, t, appears in the inter-period constraints, and is otherwise suppressed, for the sake of clarity. Furthermore, because of the complications introduced into inter-period constraints by the unequal lengths of the time periods, the constraints are first presented as if the time periods are of equal length, i.e. T1 = {1980, 1985, 1990, 1995, 2005, 2000, 2010, 2015, 2020 } . In a later section, alterations to inter-period constraints due to time period aggregation are discussed. The forms of intra-period constraints do not change when time periods are aggregated. The names of variables generally obey the following pattern: the first letter indicates the region (W for west — B.C., the prairie provinces, and northern territories — E for east); the second letter indicates the type of energy commodity or the end-use sector (e.g., 0 for oil, G for gas, T for transportation, etc.); the letter X in the third place indicates a flow and capacity of an energy commodity; and the letter D in the third place indicates an addition to capacity. In addition, there are numerals appearing in some variable names, and in the computer implementation, there are 2 numerals pre fixing the variable name to indicate the time period. 235 In addition to the parameters listed in the following sections, there are exogenously-assigned parameter values for pre-1980-period variables which occur in inter-period constraints. Constraint names obey the following pattern: (1) (2) (3) (4) (5) (6) (7) (1_) (2) - two numerals indicate the time period. (_3) - the letters W, E, or N stand for west, east, or non-regional. C4J C5J - two letters indicate constraint type: PR - production decline (oil or gas) CP - capacity expansion and replacement SB - supply-demand balance SE - share eguation SL - share, lower bound SU - share, upper bound • RL - reserves limit M - miscellaneous (.7) - this may be a letter, numeral, or blank. The constraint names appear to the left of the constraints in this appendix (without the first two numerals, indicating time period). Constraints which are upper or lower limits on single variables are not given names. The letters "DFC" stand for the Domestic, Farm and Commercial end-use sector. B.l. Coal a) List of Variables western production, low cost western production, high cost coal for liquefaction in west coal for gasification in west coal for electricity production in west coal for industrial use in west capacity increases of low and high cost western production western coal transported to eastern region WCX1 = WCX2 = WCX3 = WCX4 = WCX5 = WCX6 = WCD1,= WCD2 WCE = 236 b) c) WCEX ECX1 ECX2 ECX3 ECX4 ECD1, ECD2 ECIM coal exports eastern production, low cost eastern production, high cost coal for electricity production in east coal for industrial use in east capacity increases of low and high cost eastern production coal imports List of Parameters mciw, mcie = cwcl,cwc2 = cecl,cec2 = pcex = pcimcctr = WCRi, (i=l,2) = ECRi, (i=l,2) = WCE bwc, bee ECXl distribution margin for coal to industrial sector, liquefaction and gasification costs of corresponding western coal production costs of corresponding eastern coal production price of coal exports price of coal imports cost of transporting coal from west to east reserves of corresponding western production type remaining after 1975. reserves of corresponding eastern production type remaining after 1975 maximum capacity of west-to east coal transportation system fraction of coal supply remaining after deduction of coal use by energy supply industries, in the west and east, respectively upper limit on production of low cost eastern coal Constraints (i) Capacity Expansion and Retirement WCCPi: WCXi(t) = WCXi(t-5) + WCDi(t) - WCDi(t-30), i = 1,2 ECCPi: ECXi(t) = ECXi(t-5) + ECDi(t) - ECDi(t-30), i = 1,2 (ii) Reserve Limits WCRLi: E WCXi(t) <_ WCRi, i = 1,2 t£T' ECRLi: E ECXi(t) . <_ ECRi, i = 1,2 t£T" (iii) Supply-Demand Balances 2 6 , WCSB: bwc'1 E WCXi = E WCXi + WCEX + WCE i=l i=3 237 Civ) B.2. a) b) ECSB: bee ( I ECXi + ECIM + WCE) = i=l Bounds 4 I i=3 ECXi WCE < WCE — west-to-east coal transport limits ECXl <_ ECXl — limit on rate of production of eastern coal Oil List of Variables ("LHF" stands for "liquid hydrocarbon fuels") W0X1 W0X2 W0X3 W0X4 W0X5 W0X6 WODi,(i=l,..,6)= WOEX WOE WOG E0X1 E0X2 E0X3 EODi,(i=l,2,3) = EOIM EOG WLX1,ELX1 WLX2,ELX2 WLX3,ELX3 WLX4,ELX4 WLDC List of Parameters mltw,mlrw,mldw,"\ = mliw, mite,mire, mlde,mlie J cwoi,(i=l,,.., 6) = poex = cotrWORi,(i=l,2,.. .5) = conventional production, low cost, west conventional production, high cost, west northwest frontier production, low cost northwest frontier production, high cost tar sands production western methanol production, from biomass capacity expansions of above oil exports (to USA) western oil transported to eastern region oil to western refinery gate eastern production, low cost (mostly southeast offshore) eastern production, high cost (mostly northeast offshore) eastern methanol production, from biomass capacity expansions of above oil imports oil to eastern refinery gate LHF for electricity production in west & east LHF for domestic, farm and commercial use in west & east LHF for industrial use in west & east LHF for transportation use in west & east capacity expansion of coal liquefaction, in west oil distribution & refining margins to Transporta tion, Road Transportation, DFC and to Industrial sectors, respectively, west and east costs of corresponding western oil production price of oil exports cost of transporting oil from west to east reserves of corresponding western production type remaining after 1975. 238 ao (s) opipe WOEX foim ceoi, (i=l,2^3) poim EORi, (i=l,2) clc bwl,bel acl WLDC W0X6, E0X3 W0X5 E0X1, E0X2 c) Constraints (i) Oil Production Decline Curves 25 WOPRi: WOXi(t) = £ ao(s) '• WODi(t-s) , i=. 1,2,3,4 s=0,5,... 25 EOPRi: EOXi(t) = £ ao(s) • EODi(t-s) , i = 1,2 s=0,5,... (ii) Capacity Expansion and Retirement WOCPi: WOXi(t) = W0Xi(t-5) + WODi(t) - WODi(t-30) , 1 = 5,6 E0CP3: E0X3(t) = EOX3(t-5) + E0D3 (t) - E0D3(t-30) WOCPL: WCX3(t) = WCX3(t-5) + WLDC(t) - WLDC(t-30) = parameters for oil production decline curve = fraction of capacity established s years ago which is still producing now = fraction of eastern crude market accessible to western oil production = upper limit on oil exports = maximum fraction of Canadian crude oil market served by net imports = costs of corresponding eastern production = price of oil imports = reserves of corresponding eastern production type remaining after 1975 = cost per unit output of coal liquefaction, not including cost of the coal = fraction of oil supply remaining after deduction of oil use by energy supply industries, west and east = oil output per unit of coal input to coal liquefaction = upper limit on capacity expansion of western coal liquefaction = upper limits on production of methanol from biomass, in west and east = exogenously fixed tar sands production = upper limits on eastern oil production 239 (iii) Reserves Limits (v) WORLi: E WOXi(t) <_ WORi, i = 1, , 5 teT' EORLi: E EOXi(.t) <_ EORi, i = 1,2 teT' (iv) Supply-Demand Balances WOSBO: E WOXi + acl-WCX3 = WOE + WOG + WOEX i=l 2 EOSBO: WOE + E EOXi + EOIM = EOG i=l 4 WOSBL: bwl•(WOG + W0X6) = E WLXi i=l 4 EOSBL: bel'(EOG + E0X3) = E ELXi i=l Other Constraints NOMSS: EOIM - WOEX <_ foim • (WOG + EOG) — target of net self-sufficiency for security of oil supply NOMEM: WOE <_ opipe • EOG — all of eastern market is accessible to western oil when opipe = 1 (vi) Bounds WLDC < WLDC W0X6 < W0X6 E0X3 < E0X3 WOEX < WOEX W0X5 = WOX5 EOXI <_ EOXI E0X2 < E0X2 Limits on introduction of coal liquefaction Limits on introduction of methanol from biomass, in west Limits on introduction of methanol from biomass, in east Export limits Fixing of tar sands production to 2000 Limits on eastern oil production 240 B.3. Gas — Natural and Synthetic a) List of Variables WGX1 = western natural gas production, conventional areas, low cost WGX2 = western natural gas production, conventional areas, high cost WGX3 = northwest frontier natural gas production, low cost WGX4 = northwest frontier natural gas production, high cost WGX5 = synthetic gas (from biomass) production, in west WGDi, (i=l,2,...,5) = capacity expansions of above WGD6 = capacity expansion of syn. gas production from coal,..west WGX7 = gas for electricity production in west WGX8 = gas for domestic, farm and commercial use in west WGX9 = gas for industrial use in west WGE = western gas transported to western region WGEX = gas exports (to USA) EGX1 = eastern natural, gas production, low cost EGX2 = eastern natural gas production, high cost EGX3 = synthetic gas (from biomass) production, in east EGDi, (i=l,2,3) = capacity expansions of above EGX4 = gas for electricity production in east EGX5 = gas for domestic, farm and commercial use in east EGX6 = gas for industrial use in east b) List of Parameters cwgl,cwg2,cwg3 y cwg4,cwg5 pgex cgc cgtr WGRi, (i=l,...,4) acg bwg,beg WGX5 WGD6 WGE cegl,ceg2,ceg3 ag(s) WGEX EGRi, (i=l,2) EGX3 mgdw, mgiw, -^ mgde, mdie EGX1, EGX2 = costs of corresponding western gas sources = price of gas exports = cost per unit output of coal gasification, not including cost of the coal = cost of transporting gas from west to east = reserves of corresponding western production type remaining after 1975 = gas output per unit of coal input to gasification = fraction of gas supply remaining after deduction of gas use by energy supply industries, in the west and east, respectively = upper limit on production of synthetic gas from biomass in west = upper limit on capacity expansion of western coal gas'n = maximum capacity of west-to-east gas pipeline = costs of corresponding eastern gas sources = parameters for natural gas production decline curve = fraction of capacity established s years ago which is still producing now = upper limit on gas exports = reserves of corresponding eastern production type remaining after 1975 = upper limit on production of synthetic gas from biomass in east = gas distribution margins, to DFC and to Industrial sectors, respectively, west and east = upper limits on production of eastern gas 241 Constraints (i) Gas Production Decline Curves 30 WGPRi: WGXi(t) = E ag(s)• WGDi(t-s), i=l,...,4 s=0,5, 30 EGPRi: EGXi(t) = £ ag(s) • EGDi(t-s), i = 1,2 s=0,5,.. . (ii) Capacity Expansion and Retirement WGCP6: WCX4(t) = WCX4(t-5) + WGD6(t) - WGD6(t-30) WGCP5: WGX5(t) = WGX5(t-5) + WGD5(t) - WGD5(t-30) EGCP3: EGX3(t) = EGX3(t-5) + EGD3(t) - EGD3(t-30) (iii) Reserves Limits WGRLi: Z WGXi(t) £ WGRi, i = 1,...,4 t£T' EGRLi: Z ,EGXi(t) < EGRi, i = 1,2 teT' — (iv) Supply-Demand Balances 5 9 WGSB: bwg • ( Z WGXi + acg • WCX4) = Z WGXi + WGE + WGEX 1=1 i=7 3 6 EGSB: beg • ( Z EGXi + WGE) = Z EGXi i=l i=4 (v) Bounds WGEX <_ WGEX — exports limit WGE <_ WGE — capacity of west-to-east pipeline WGD6 <_ WGD6 — limit on capacity expansion of coal gasification WGX5 _£ WGX5 — limit on production of gas from biomass, west EGX3 <_ EGX3 — limit on production of gas from biomass, east EGXI <_ EGXI ) — limits on production from eastern sources EGX2 < EGX2 ' 242 B.4. Electricity a) List of Variables WEX4,EEX4 = electricity from nuclear, west and east WEX5,EEX5 = hydroelectricity production, west and east WEX6,EEX6 = electricity from biomass, wind, tidal, etc., west & east WEDi,EEDi, (i=4,5,6) = capacity expansions of above WED1,EED1 = capacity expansion of electricity from coal, west & east WED2,EED2 = capacity expansion of electricity from oil, west & east WED3,EED3 = capacity expansion of electricity from gas, west & east WEX9,EEX9 = electricity for industrial use, west and east WEX10,EEX10 = electricity for transportation (electric car), west & east WEX11,EEX11 = electricity for DFC use, west and east WEEX, EEEX = electricity exports from west and east b) List of Parameters ce4 = cost of electricity from nuclear ce5 = cost of hydroelectricity ce6 = cost of electricity from biomass, etc. peex = price of electricity exports cec = cost of. electricity from coal, '.excluding coal cost cel = cost of electricity from oil, excluding oil cost ceg = cost of electricity from gas, excluding gas cost bwe, bee = fraction of electricity supply remaining after deduction of electricity use by energy supply industries, west and east ace = electricity output per unit of coal input ale = electricity output per unit of oil input age = electricity output per unit of gas input medw,meiw,j= electricity distribution margins, to DFC and to Industrial mede,meie sectors, respectively, west and east met = electricity road tax for transportation WEX5,EEX5 = maximum hydro electric capacities in west and east WED4,EED4 = maximum:rate of nuclear electric capacity expansion in west and east hdw, hde = maximum fractions of total electric capacity expansion which can be filled by hydro, in west and east c) Constraints (i) Capacity Expansion and Retirement fWCX5(t) = WCX5(t-5) + WEDl(t) - WEDl(t-30) ECX3(tj = ECX3(t-5) + EED1(t) - EED1(t-30) WLXl(t) = WLXl(t-5) + WED2(t) - WED2(t-30) V ELXl(t) = ELXl(t-5) + EED2(t) - EED2(t-30) WECPi EECPi: (i=l,...,6) 243 WGX7(t) = WGX7(t-•5) + WED3(t) - WED3(t-30) EGX4(t) = EGX4 (t-5) + EED3(t) - EED3(t-30) WEXi(t) = WEXi(t-•5) + WEDi(t) - WEDi(t-30) , i = 4,5,6 EEXi (t) = EEXi(t-•5) + EEDi(t) - EEDi(t-30) , i = 4,5,6 (ii) Supply-Demand Balances 6 11 WESBE: bwe-(ace?WCX5 + ale-WLXl + age-WGX7 + E WEXi) = E WEXi + WEEX i=4 i=9 6 11 EESBE: bee•(ace-ECX3 + ale-ELXl + age-EGX4 + £ EEXi) = E EEXi + EEEX i=4 i=9 (iii) Other Constraints 6 WEMH: WED5 «• hdw(ace-WEDl + ale-WED2 + age-WED3 + E WEDi) i=4 6 EEMH: EED5 £ hdes(ace-EEDI + ale-EED2 + age-EED3 + E EEDi) i=4 (iv) Bounds <_ WEEX <_ EEEX J WEX5 < WEX5 maximum hydro capacities EEX5 < EEX5 WEEX — i export limits EEEX 244 B.5. ' Transportation End Use Sectors a) List of Variables WLA, ELA = oil for automobiles, west and east WTD1, ETD1 = capacity additions for electric autos, west and east WTD2, ETD2 = capacity additions for conventional autos, west and east WRTR, ERTR = total output energy, road transportation, west and east WOTR, EOTR = output energy, other transportation, west and east b) List of Parameters aea = output energy per unit electricity input, for electric autos ala = output energy per unit oil input, for conventional autos alo = output energy per unit oil input, for other transportation el = maximum fraction of new autos that can be electric cea = differential cost of electric auto over conventional c) Constraints (i) Capacity Expansion and Retirement WTCP1: WEXlO(t) = WTDl(t) + WTDl(t-5) ETCP1: EEXlO(t) = ETDl(t) + ETDl(t-5) WTCP2: WLA(t) = WTD2(t) + WTD2(t-5) ETCP2: ELA(t) = ETD2(t) + ETD2(t-5) (ii) Supply-Demand Balances WTSBL: WLA + (1/alo)-WOTR = WLX4 ETSBL: ELA + (1/alo)-EOTR = ELX4 WTSBA: aea-WEX10 + ala-WLA = WRTR ETSBA: aea"EEX10 + ala'ELA = ERTR (iii) Electric Auto Constraints WTMEA: aea • WTDl « el • (aea • WTDl + ala • WTD2) ETMEA: aea • ETD1 ^ el • (aea . ETD1 + ala • ETD2) 245 B.6. Industrial" End 'Use - Sector WIND, EIND = Total output energy, industrial sector, in west and east, respectively b) List of Parameters agi = output energy per unit gas input, in industry ali  output energy per unit oil input, in industry aci = output energy per unit coal input, in industry aei  output energy per unit electricity input, in industry lwg, leg = lower limit on fraction of total output energy from gas, west and east lwl, lei = lower limit on fraction of total output energy from oil, west and east lwc, lec = lower limit on fraction of total output energy from coal, west and east lwe, lee = lower limit on fraction of total output energy from electricity, west and east uwg, ueg = upper limit on fraction of total output energy from gas, west and east uwl, uel = upper limit on fraction of total output energy from oil, west and east uwc, uec = upper limit on fraction of total output energy from coal west and east uwe, uee = upper limit on fraction of total output energy from electricity, west and east c) Constraints (i) Supply-Demand Balance WISB: agi • WGX9 + ali • WLX3 + aci • WCX6 + aei EISB: agi • EGX6 + ali • ELX3 + aci • ECX4 + aei Market Share Bounds WISLG, WISUG : lwg ' • WIND^agi • WGX9*= uwg • WIND WISLL, WISUL : lwl ' • WIND^ali • WLX3^ uwl • WIND WISLC, WISUC : lwc • WIND< aci • WCX6 ^ uwc " WIND WISLE, WISUE : lwe • WIND<aei • WEX9i£ uwe • WIND EISLG, EISUG : leg • EINDSagi • EGX6 ueg • EIND EISLL, EISUL : lei • EINDSjali ' ELX3'£ uel • EIND EISLC, EISUC : lec • EIND€ aci • ECX4 £ uec • EIND EISLE, EISUE: lee•• EINDi aei • EEX9 S uee • EIND 246 B.7. Domestic, Farm and Commercial (DFC) End Use Sector a) List of Variables WER, EER = WEH, EEH = WEO, EEO = WDD1, EDD1 = WDD2, EDD2 = WDD3, EDD3 = WDD4, EDD4 WDX5, EDX5 -WDX6, EDX6 = WDD5, EDD5 = WDD6, EDD6 = WDFC, EDFC = electricity for DFC electric resistance heating, west & east electricity for DFC heat pump, west and east electricity for DFC non-heating uses, west and east capacity expansions of DFC gas heating, west & east capacity expansions of DFC oil heating, west & east capacity expansions of DFC electric resistance heating, west and east capacity expansions of DFC electric heat pump, west & east output energy of district heating by cogeneration, west & east output energy of solar heating, west and east capacity expansions of WDX5, EDX5 capacity expansions of WDX6, EDX6 total output energy, DFC sector, west and east b) List of Parameters chp, crh,| = non-fuel costs of heating by heat pump, electric resistance, coh, cgh oil, gas, respectively chs = cost of solar heat cdh = cost of district heating by cogeneration agh = output energy per unit gas input, for DFC heating alh = output energy per unit oil input, for DFC heating aeh = output energy per unit electricity input, for DFC heat pump aer = output energy per unit electricity input, for DFC electric resistance heating aeo = output energy per unit electricity input, for DFC a >>. non-heating uses gwh, geh = fraction of total DFC output energy for heating, west a .'.east hpw, hpe = maximum fraction of heating due to heat pump, west & east sw, se = maximum fraction of heating due to solar, west and east gw, ge = maximum fraction of heating due to cogeneration, west & east fc = fraction of new coal-electric capacity available for cogeneration fn = fraction of new nuclear-electric capacity available for cogeneration c) Constraints (i) Capacity Expansion and Retirement WDCP1: WGX8(t) = WGX8(t-•5) + WDD1(t) - WDDl(t-•15) EDCPl: EGX5(t) = EGX5(t-•5) + EDD1(t) - EDD1(t-•15) WDCP2: WLX2(t) = WLX2(t-•5) + WDD2(t) - WDD2(t--15) EDCP2: ELX2(t) = ELX2(t-•5) + EDD2(t) - EDD2(t--15) WDCP3: WER(t) = WER(t-5) + WDD3(t) - WDD3(t-15) EDCP3: EER(t) = EER(t-5) + EDD3(t) - EDD3(t-15) WDCP4: WEH(t) = WEH(t-5) + WDD4(t) - WDD4(t-15) EDCP4: EEH(t) = EEH(t-5) + EDD4(t) - EDD4(t-15) WDCP5: WDX5(t) = WDX5(t-5) + WDD5(t) - WDD5(t-30) EDCP5: EDX5(t) == EDX5 (t-5) + EDD5(t) :'• -)EDD5 (t-30) WDCP6: WDX6(t) = WDX6(t-5) + WDD6(t) - WDD6(t-15) EDCP6: EDX6(t) = EDX6(t-5) + EDD6(t) - EDD6(t-15) Supply--Demand Balances WDSBE: WEX11 = WEH + WEO + WER EDSBE: EEX11 = EEH + EEO + EER 6 WDSBH: aer • WER + agh • WGX8 + alh • WLX2 + aeh • WEH + £ WDXi = gwh*WDFC i=5 6 •EDSBH: aer • EER + agh • EGX5 + alh • ELX2 + aeh • EEH + £ EDXi = geh-EDFC i=5 WDSEO: aeo • WEO = (1-gwh) • WDFC EDSEO: aeo • EEO = (1-geh) ' EDFC (iii) Heat Pump Constraints WDSUP: aeh • WEH £ hpw • gwh • WDFC EDSUP: aeh • EEH ^ hpe • geh • EDFC (iv) Solar Heat Constraints WDSUS: WDX6 ^ sw - gwh • WDFC EDSUS: EDX6 ^ se • geh • EDFC (v) District Heat by Cogeneration Constraints WDSUC, EDSUC: WDX5^gw • gwh • WDFC , EDX5 ^ ge • geh • EDFC WDMCG: WDD5 $:fc-WEDl + fn• WED4 EDMCG: EDD5'$'."fc-EED'l + fn-EED4 248 B.8. Objective Function a) List of Variables EC " energy cost b) List of Parameters d = social discount rate ed, ei,j = price elasticities of demand for output energy in the er, eo sectors DFC, industry, road transportation and other transportation, respectively dwdjdwi,-^ = parameters derived from demand equation parameters for dwr,dwo, / the sectors DFC, industry, road transportation and ded,dei, j other transportation, in west and east der,deo J c) Objective Function (Maximand) t-1975 (1-1/ed) (1-1/ed) OBJECTIV: E [l/(l+d)] • (dwd -WDFC^ + ded -EDFC m. t t t t t £ T (1-1/ei) (1-1/ei) (1-1/er) + dwi -WIND^ + dei -EIND^ + dwr 'WRTR t t ..t t t t (1-1/er) (1-1/eo) (1-1/eo) + der :ERTR + dwo -WOTR + deo -EOTR - ECt) d) Constraint 2/ NMMEC: EC-= E (cwci-WCXi + ceci-ECXi) + pcim-ECIM - pcex-WCEX 1=1 6 + cctr-WCE + mciw-WCX6 + mcie-ECX4 + E cwoi-WOXi + E ceoi-EOXi + (mciw + clc-acl)-WCX3 + poim-EOIM i=l - poex-WOEX + cotr-WOE + (mldw + coh-alh)-WLX2 + (mlde + coh-alh)-ELX2 + mliw-WLX3 + mlie-ELX3 + mltw-WLX4 5 3 + mlte-ELX4 + mlrw-WLA + mlre-ELA + E cwgi-WGXi + E cegi-EGXi i=l i=l + (mciw + cgc-acg)-WCX4 - pgex-WGEX + cgtr-WGE 249 + (mgdw + cgh-agh)-WGX8 + (mgde + cgh-agh)>EGX5 + mgiw-WGX9 + mgie-EGX6 + cec-ace- (WCX5 + ECX3) + cel-aler(WLX1 + ELX1) + ceg•age•(WGX7 + EGX4) 2 + E cei-(WEXi + EEXi) - peex-(WEEX + EEEX) + meiw-WEX9 i=l + meie-EEX9 + (met + cea-aea)•(WEX10 + EEXlO) + medw-WEXll + mede-EEXll + crh-aer-(WER + EER) + chp-aeh-(WEH + EEH) + cdh-(WDX5 + EDX5) + chs-(WDX6 + EDX6) B.9. Time Period Aggregation In the previous eight sections, it was assumed that there were nine 5-year time periods. To save computation time, and since there is greater uncertainty associated with later time periods, later time periods have been aggregated in the following way: three five-year periods / -followed by three 10-year periods.- The time index, t, . which marks the last year in each period, takes on values in the set T = {l980,1985,1990,2000,2010,2020}', or alternatively, {5,10,15,25,35,45} for brevity in the computer coding. The forms of the intraperiod constraints described earlier do not change after aggregation. This-section is concerned"with changes to the inter-period constraints due to the aggregation. a) Changes to Capacity Expansion and Retirement Constraints Let X(t) be the flow, or production, and D(t) capacity expansion. For brevity, label the time periods t=5,10,15,25,35, or 45. The method followed is to consider what multiple of a capacity addition continues to produce in later periods of differing lengths. In the following, a bar on top of a variable indicates that the value of the variable is a datum, fixed at its past value (i.e. before t=5). (i) 30-Year Lifetime X(t) = X(t-5) + D(t) - D(t-30), for t=5,10,15 X(25) = D(25) + 2 • D(15) + 2 •' D(10) + 2 > D(5) + 2 • D(0) + D(-5) X(35) = D(35) + D(25) + 2 • D(15) + 2 • D(10) + D(5) X(45) = D(45) + D(35) + D(25) + D(15) (ii) 10-Year Lifetime (Automobiles) X(t) = D(t) + D(t-5) , for t=5,10,15 X(25) = D(25) + D(15) X(t) = D(t) , for t=35,45. (iii) 15-Year Lifetime (Most Heating in DFC) X(t) = D(t) + D(t-5) + D(t-10), for t=5,10,15 X(25) = D(25) +2« D (15) + D(10) X(t) = D(;t)l + (0.5) * D(t-5) , for t=35,45. bj_ Changes in Production Decline Curves Cl) Crude Oil Usilng the data assumptions presented in Appendix C, Section 2 - i.e. new capacity lasts 10 years, followed by a 15-year decline at 10% per year —the following may be derived X(t) = D(t) + D(t-S) + (.59) • D(t-10) , + (.35) • D(t-15) + (.21) • D(t-20) , for t=5,10,15 X(25) = D(25) + (.1.59) • D(;i5) + (.94) » D(10) + (.56) • D(5) + (.21) • D(0) X(35) = D(35) + (.47) « D(25) + (.56) • D(15) + (.21) . D(10) X(45) = D(45) + (.47) • D(35) + (.10) * D(25) 252 (ii) Natural Gas Using the data assumptions presented in Appendix C, Section 3 — i.e. new capacity lasts 15 years, followed by a 15-year decline at 10% per year — the following may be derived: X(t) = D(t) + D(t-5) + D(t-10) + (.59) • D(t-15) + (.35) • D(t-20) + (.21) D(t-25) for t=5,10,15 X(25) = D(25) + 2 • D(15) + (1.68) • D(10) + (.94) - D(5) + (.56) • D10) + (.21) •" D(-5) X(35) = D(35) + (.80) • D(25) + (.98) . D(15) + (.56) • D(10) + (.21) • D(5) X(45) = D(45) + (.80) • D(35) + (.28) • D(25) + (.21) • D(15) X(55) = D(55) + (.80) • D(45) + (.28) D(35) (altered for end effects correction -- see next section). c) Changes to Reserves Limits Constraints There is no change in these constraints when- time periods are aggregated. B.10. Corrections for End Effects End effects due to the finite time horizon are minimized by a pro cedure based on the dual equilibrium method of Grinold (1980). He assumes that prices are constant after the time horizon in his method for LP problems — i.e. the dual variables are constant after the time horizon, if expressed in undiscounted dollars. This method has been extended slightly to the NLP problem here by assuming that the output energy prices, derived from the gradient of the objective function, are also constant (in undiscounted dollars) after the time horizon. This ex tension affects only the nonlinear variables in the objective function. Presented below are the alterations to the linear constraints and the linear part of the objective function — that is, of Grinold's dual equilibrium method applied to the LP problem associated with the NLP problem, obtained by fixing the nonlinear variables exogenously. Next the alterations to the nonlinear part of the objective function are shown. The procedure involves the addition of an extra time period, with altered constraints. The vector of all exhaustible resource production levels in period t is represented by y , the vector of resource limits by R, and all other variables by X^. Period "0" below represents periods 5, 10 and 15 together. The matrix H defines the impact of x in period t. The matrix represents the impact of X^ on period (t+10); is the impact of X on period (t+20). Below, A and B are matrices involving relations among variables in the same time period. If d is the social discount rate, let a = l/(l+d). The right hand side vector is b = (h^,b^,h^^, . ..) . Following Grinold, let -cS^"""1 t-55 b55(a) = t=fe65,7.. \ , X__(a) = at_55X. 55 t=55,65,... t at-55 -Y_c(a) = t=55,65,... Y , and bo —K ' • •>• t Kl(a) = Kl + a " V Grinold shows that the (LP) problem of minimizing the discounted cost of meeting the specified energy demands (the nonlinear variables here)t with the dual equilibrium method is: ... 5^ t-1975 55, minimize a EC^ + a • ^EC^,. (a) subject to: A X + B :Y = b 00000 H X + AX + BY = b 25 o 25 25 25 H_CX + K.XV_ + AI, + BY = b 35 o 1 25 35 35 35 H45Xo + K2X25 + KlX35+AX45 + BY45=b, 45 K2X35 + Kl(a)X45 + (A + K!(a))x55(a) +"'BY55(a) = b55<a) Y0 + Y25 + Y35 + Y45 + Y55(a) ^ R " The. procedure involves the addition of one .variable to the objective function, EC__, and an extra set of constraints almost 55 identical in form to the constraints of period 45, but with some different coefficients and a right hand side which depend on the discount rate. In the full NLP problem, these changes to the constraints and the linear part of the objective function are made, and extra nonlinear terms are added, related to the consumers' surplus in the new, additional period 55. Since it is assumed that the' output energy prices (in undiscounted dollars) are constant after period 45, it follows that the output energy demands will increase from their period 45 levels at rates influenced only by the exogenous determinants of demand such as population, real domestic product, etc. Using the notation of chapter 4, for brevity, the objective function for the full infinite horizon problem would be: 8 . 1/ei 1-1/ei maximize £a • (. & ( , . ) * A. • E. ^ - EC ), t x=l ei-1 i,t i,t t where E. = output energy demand in sector i, in period t, r /1 ei = the price elasticity of demand in sector i, t = 5,10,15,25,35,... , and E. ^ = A • P?6* I, t l, t I, t where P. = the price of output energy in sector i and period t, and I , t A. = the product of the exogenous factors determining I , t demand in sector i and period t. The assumption of constant prices is -:. P. . = P. rr , for t > 55. i,t i,55 Assuming that the exogenous variables determining demand each grow at certain rates per year after period 55 (it is assumed that these rates are the rates of growth between t=45 and t=55 — see Appendix C for these rates), it follows that for some gi (i=l,...,8) which can easily be calculated from the rates of growth and the various elasticities with respect to income, etc., Ai,t = Ai,55 * ^1+^t~55 • and Ei,t = Ei,55 • ^t-55-Therefore, the objective function, under the constant price and the growth assumptions, is 45 ^ 8 _, 1/ei 1-1/ei maximize afc . ( £ (ei^—) • A E . - EC ) t=5 x=l ei-1 i,t i,t t + aZ • • A. (l+gi)* • E - EC.) t-55' 1=1 ei-1 i,55 i,t t Finally, the infinite sum can be collapsed into a finite sum of nine terms involving the nonlinear variables E^ (provided a * (1+gi) ^ 1), and ECpr(a) (defined above), namely 55 8 2 a55- (l/(l-a • (1+gi))).-' {SL-) • AV^ • E1"^ ei-1 1,55 i,55 - a55 • EC55(a). Viewed from another perspective, this method corrects for end effects by adding another period representing the time beyond the planni horizon. The extra constraints' coefficients, bounds and right hand sides are given values which tend to make the variables larger than they-would be if the extra period were an ordinary one. The extra period's consumers' surplus is also weighted more heavily than if it were an ordinary period, offsetting the larger energy cost (EC) asso ciated with the larger values of the other variables. The net effect is to treat the post-horizon period as one (very long) period, with appropriate weights to account for the length of the infinite period, with discounting applied. 257 Appendix C. Data for the Base Case. The following abbreviations are used for frequently mentioned organizations: HMA Hedlin, Menzies and Associates, Ltd., EMR Energy, Mines and Resources, Canada, NEB National Energy Board of Canada, CPA Canadian Petroleum Association, and SRI Stanford Research Institute, SC Statistics Canada. C.1;.0 Data for the. Coal Sector Throughout this section, the thermal contents of various grades of coal are assumed to be those reported by Statistics Canada (cat. no. 57-207), i.e., in units of 106 BTU/short ton: Anthracite 25.4 Imported Bituminous 25.8 Canadian Bituminous 25.2 Sub-bituminous 17.0 Lignite 13.2 C.l~l. .Costs and Remaining" Supplies It is assumed that the current cost of producing coal (the "low cost" in the model) is the reported at-mine price in 1974 — i.e. before the rapid rise in coal prices in 1975., to avoid, inclusion of "windfall profits" or vastly increased royalties. For bituminous coal in the west, this was about $.60/10^ (1975$), according to figures derived from EMR (1977f) and Statistics Canada ( cat. no. 26-206). However, the at-mine price of Alberta sub-bituminous coal and Saskatchewan lignite were about $.20/10^ BTU, using figures derived from the same sources. Since coal is treated as one com modity in the model, we take the lower grade cost as the cost of coal at the low price - i.e. cwcl = .02. A distribution margin of $.80/106BTU, i.e. mciw = .08, is added to coal used in western industry ( including that for liquefaction or gasification), to account for the total costs of coal to western industry in 1970, $ 1.00/106BTU in 1975 $, derived from Statistics Canada (cat. no. 57-506). The price of exported coal in 1975 at the mine, using EMR (1977f) figures, was about $1.43/106BTU, while, the production cost for this bituminous coal was about $ I60:/10^BTU , for an economic rent of about $.83/106BTU. The logic of the model requires that the export price equal production cost plus economic rent. Since c"> cwcl = .02 and rent (in 1975))= .083, the 1975 export price is taken to be -.103. This price is escalated at the rate of 2!1/2 % per year until the year 2000.(The international oil price is assumed to increase at 4% per year until 2000i The result is: Period 05 10 15 25,35 pcex .117 .132 .149 .191 The situation in the east is simpler. The coal is all bituminous, as are imports, and there are virtually no exports. The import price in 1975 was $1.37/10 BTU, using EMR (1977f) figures, and is assumed to increase in real terms at 2 1/2 % per year, the same rate as export prices, until 2000. The result, in model units, is: Period 05 10 15 25 pcim .155 .175 .198 .254 The eastern cost of (bituminous) coal production is determined in Nova Scotia, where the largest production is. The 1974 at-mine price was $.80/106BTU, using EMR (1977f) figures. Therefore, ceci = .08 . The 1975 coal costs to electric utilities reported by Ellison (1978. p.71), in the cases where the coal used is mined locally, are reasonably close to the above values for cwcl and ceci. The distribution margin for.":coal to eastern industry ±s derived by subtracting the weighted average of the 1970 production and import costs from the cost of coal to eastern industry, as reported by Statistics Canada (cat. no. 57-506). The result is, mcie = .04 . The cost of transporting coal to the east from the west is arrived at by subtracting the production cost from the price paid by Ontario Hydro for western coal. According to Ellison ( 1978,p.65) Ontario Hydro' imported 2.7 x 10^ tons of bituminous coal from B.C. 6 and Alberta, and 1 x 10 tons of lignite from Saskatchewan in 1975:,'. at costs of 135.8<V106BTU and 55.2C/106BTU respectively. Calculating an average weighted by the total BTU contents of the two types gives a price of 122.8<yi06BTU paid by Ontario Hydro. Subtracting 20C/106 BTU production cost leaves an average transport margin of 102.8C/106 BTU — i.e. cctr = 0.103 HMA (1976, p.241) present an estimate of remaining coal reserves 15 of 660 x 10 BTU at a cost of .055 (in model units), and a further 44 x 10"*"^ BTU at a cost of 0.11 . The discussion concludes with the comment that the reserves figures are probably low. Therefore, the reserves data chosen for the model are midway between the above total amount, and the Latour-Christmas estimate mentioned in HMA (1976, p.241), with the same proportional split of reserves'between cost levels. The proportional split of the reserves between east and west is the same as that in HMA (1976, p.240) for coal potential reserves, by region (i.e. west, 98.66%, east, 1.34%). Finally, the lower costs in each region are those established above, and the higher cost levels are double the lower. The results are (in model units): cwcl = .02 WCR1 =1,587 , cwc2 = .04 WCR2 = 106 ceci = .08 ECR1 = 22 cec2 = .16 ECR2 = 1.4 C.1.2 Energy Supply Industry Use Let bwc,bec = fractions of western and eastern coal supplies not used by western and eastern energy supply industries. These parameters are equal in all periods to their 1971-1975 values of .9996 (west) and .9994 (east), using data from Statistics Canada (cat. no. 57-207). 261 C.1.3 Miscellaneous Limits In an EMR document (1976d, pp.96-97), it is stated that the coal 6 terminal at Thunder Bay is to open in 1979 at a capacity of 3.5 x 10 6 6 tons/year, of which 25 x 10 tons are bituminous coal, and 1 x 10 tons 6 are lignite. The capacity can be expanded quickly to 6 x 10 tons, and eventually to 9 x 106 tons/year. Using this information, and adding the 1971-75 amount transported through existing facilities, expressed in model units and 5-year capacities puts upper limits oh west-to-east coal transportation for the first three periods as shown below. Period 05 10 15 WCE .215 .579 .879 Because of the costs chosen, the model has a tendency to expand eastern coal production unrealistically quickly. Therefore, the following upper limits have been placed on ECXl, corresponding to a doubling in production every 5 years (about 15% increase per year): Period 05 10 15 ECXl .506 1.012 2.024 Because of the large size of the coal reserves, and because the international price of coal is so much higher than its cost of production, the model tends to export coal at an unrealistically high rate. There fore, upper limits are placed on coal exports in all periods, allowing exports to increase at about 5% per year (assuming a levelling-off of the rapid growth in the early 1970's): 262 Period 05 10 15 25 35 45 WCEX 1.7 2.2 2.8 9.2 14.8 24.2 C.2.0 Data for the Oil Sector C.2.1 Primary Costs and Remaining Supplies Until a study on long-run supply curves for oil and natural gas is completed by EMR, the cost and supply data must be based on various sources. The cost of the "low cost" conventional oil (cwol) of western Canada is taken to be the wellhead price before the rapid price rise after 1973, based on data presented by the CPA (1977) - i.e. cwol = .4, in model units, or $4/bbl. Based on estimates by EMR (1977c, p.31) of the costs of Lloydminster heavy oil, using an 8% rate of return over a 15-year production time span, the higher cost of western "conventional" oil is taken to be cwo2 = .8, or $8/bbl. The total remaining reserves (after 1975) of conventional western 9 oil, at both cost levels, are taken to be 12 x 10 bbl, which is the total of remaining reserves at the 100% probability, plus undiscovered resources at the 40% probability level reported by EMR (1977b) for western Canada. The amount of these reserves allocated to the lower cost level is taken to be sufficient to allow existing conventional western oil producing capacity to run the course of the oil production decline curve (i.e. to ensure model feasibility). The allocation WOR1 = 6.0, W0R2 = 6.0 works well. The total remaining reserves of northern frontier oil (not in cluding northeast offshore-Labrador oil, which is allocated to the east in the model) are taken to be 7.7 x 10^" bbl, based on the 40% probability level in EMR (1977b). The low and high costs for these reserves (i.e. including transportation to southern Alberta) are based on various sources, namely an early draft of the EMR (1977d) study on long run supply curves, and figures in the report by HMA (1976). The costs chosen are $10/bbl and $14/bbl, or in model units cwo3 = 1.0 cwo4 = 1.4 Based on the general shape of the tentative long-run supply curves in EMR (1977d), the following allocation of reserves between the two cost levels has been made: W0R3 = 4.4 W0R4 =3.3 Using cost estimates on tar sands mining, by EMR (1977c, p. 31), and a rate of return on capital of 8% over 30 years, the cost of syncrude is set at $12/bbl, or in model units, cwo 5 = 1.2. (This is the 1975 price of crude oil imported to eastern Canada, as well.) The remaining reserves of syncrude from the tar sands are taken to be 9 200 x 10 bbl, based on estimates in EMR (1978c), or in model units, W0R5 = 200.0. The "low cost" eastern oil is taken to be represented mostly by southeast offshore oil, and the "high cost" by northeast offshore oil. Based on the 40% probability level of potential resources in these two areas, reported by EMR (1977b), the reserves are taken to be E0R1 = 3.0, E0R2 = 2.0. Based on various sources — namely estimates by Millan (1980) of development and operating costs for the Hibernia discovery at an 8% rate 264 of return, the EMR draft (1977d), and HMA (1976) — the landed costs of these are set at $7/bbl and $10/bbl, respectively, i.e. ceol = 0.7 ceo2 = 1.0. Once again, limits are placed on the rate of expansion of these sources in the model (see the last section, on limits). C.2.2 Import and Export Prices The prices of imports and exports are taken to be the same except for the oil import subsidy in the first three periods. The 1975 price of imported oil, at North America, of $12/bbl, is increased at the rate of 4% per year until the year 2000. Recall that all values are expressed in 1975$ in the model, and that the 4% per year figure is therefore net of inflation. The figure of 4% has been chosen to reflect expectations of continuing rapid increases in the price of inter national oil, and because 4% per year is a rate which would be in the best interests of consuming and producing countries, according to Manne (1978). With a subsidized eastern domestic price of about $10.80/bbl (calculated from Helliwell (1979)) in 1978, the mid-year of the first period, and assuming the subsidy reaches zero by the fourth period, the price series are: Period 0.5 10 15 25,35,45. . poex 1.46 1.78 2.16 3.20 poim 1.08 1.48 1.93 3.20 C.2.3 Oil Production Decline Curves The standard production time-profile presented by EMR (1973, p.80) is a two-year buildup to a peak lasting seven years, followed by a decline at the rate of 15% per year. This rate of decline appears to be 265 too rapid when compared to the NEB (1978) projection of producibility from established light and heavy crude oil reserves. The latter suggests a decline rate of 10% per year, which is adopted in this model. In deriving the parameters ao(s), it is assumed as an approximation that new capacity established in one year lasts at the same level for ten years, then declines at 10% per year for the next 15 years. See Appendix B, section 9, "Time Period Aggregation" for the detailed results, taking into account the varying lengths of the time periods. C. 2.4. Coal Liquefaction 9 15 Let acl = 10 bbl of liquefied product per 10 BTU of coal input; and clc = cost of liquefaction of coal, not including coal feed cost, in units of 1012$ per 109 bbl. Using estimates by the SRI (1976, Vol. II, p.IV-7), and a real rate of return on capital of 8% per annum, the parameters are set at acl = 0.1072 and clc = .79, in the model's units. The conversion efficiency corresponding to the above acl is 0.622. The earliest date of introduction of coal liquefaction, according to SRI (1976), is 1987. It is assumed in the model, therefore, that coal liquefaction can be introduced after 1985 — i.e. WLDC = 0.0 for t = 0.5, 10. C.2.5 Methanol from Biomass Let cwo6, ceo3 = cost of producing methanol from biomass. Using figures from Middleton Associates (1976, p. 316) $30/bbl is the approximate cost. Since in the model methanol from biomass enters the oil stream, which is subject to refining charges, it is necessary to subtract a refining charge of $4.20/bbl (from EMR (1977a, p. 53)). from the cost of methanol, a finished product. The result, in model 12 9 units of 10 $ per 10 bbl, is cwo6 - ceo3 = 2.5. It is assumed that this technology can be introduced after 1980, i.e. W0X6 = E0X3 =0.0 for t = 05 . C.2.6 West-to-East Oil Transportation Let cotr = cost of transporting oil from west to east. An EMR report (1978a, p.50) gives $.60/bbl for this oil trans portation margin in 1977, from Edmonton to Port Credit. In 1975$ and model units, this is cotr = .05. Let opipe = fraction of eastern crude oil market accessible to western c rud e supply. According to estimates in Oilweek (Feb. 12, 1979, p. 31, table entitled "Canadian Petroleum Consumption") the fraction of eastern crude oil supplied from western sources was 0.5355 in 1978 (i.e. after the ex tension of the pipeline to Montreal). In the model, the following grad ual approach towards full accessibility of western oil to eastern markets is assumed: period, t = 0.5 10 15,25... opipe .54 .77 1.0 C.2.7 Distribution and Refining Margins These costs have been estimated as the differences between the retail prices in the end use sectors and the refinery-gate price of crude oil, in a pre-"crisis" year, reduced by an amount to prevent double-counting of the cost of crude oil used by the energy supply industry 267 (mostly the still gas used in the refining process). Used in the DFC sector was the weighted average of the 1973 retail prices of light and heavy fuel oils for industry, as reported by Statistics Canada (cat. no. 57-506), adjusted downward by the difference between the 1970 and 1973 wellhead prices of oil, in 1975$, as reported by the CPA (1977). The margins are mldw = 0.32, mlde = 0.21. Used in the industrial sector was the 1970 average retail price for all industrial fuel oils, as reported by Statistics Canada (cat. no. 57-506). The margins are mliw = 0.04, mlie = 0.01. Used for the "other" transportation sector were the 1973 retail prices to industry for heavy fuel oil and disel oil, adjusted downward by the difference between the 1973 and 1970 western Canadian wellhead oil prices. An average price to "other" transportation was arrived at by weighting these prices by the 1970 consumption of heavy fuel oil, and diesel oil plus aviation turbine fuel. It was assumed that the price of aviation turbine fuel was the same as the diesel price, since the 1970 values per barrel shipped from refineries, derived from Statistics Canada (cat. no. 45-205, Table 6) for the two fuels, were almost equal (within 1% of each other). The margins are: mltw = 0.77, mite = 0.69. Used in the road transportation sector was the 1970 retail gasoline price reported by EMR (1977a, Appendix C). Since the "other" transportation margins, mltw and mite, are applied to oil products going to both "other" and "road" transportation sectors — i.e. to the variables WLX4 and ELX4 - it is necessary to deduct mltw and mite from 268 the margins for the road transportation sector. The net margins are mlrw = 1.15, mire = 1.36, applied to the variables WLA and ELA. C.2.8 Energy Supply Industry Use of Oil Let bwl, bel = fractions of the western and eastern supplies of oil not used by the western energy supply industries (including refining). These parameters are equal in all periods to their 1971-1975 values of .9272 (west) and .9262 (east), using data from Statistics Canada (cat. no. 57-207) . C.2.9. Miscellaneous Limits Using the NEB (1978) figures for the "base case" expansion of tar sands capacity to 1995, the following values of tar sands production are imposed: Period 05 10 15 25 W0X5 .181 .372 .767 2.756 Upper limits on oil exports (including net product exports) are taken from the NEB reports (1977, 1978), and, for 1976 and 1977, from EMR (1978c) . The limits are assumed to be zero after 2000. The limits are Period 05 10 15 25 35,45 WOEX .597 .152 .073 .067 0.0 It is assumed that production from eastern onshore and southeast offshore sources is no higher than the 1971-75 level, in 1976-1980, and that it can increase to 50 million barrels per year in the 1986-1990 period, with a buildup in the 1981-1985 period: 269 Period 05 10 15 E0X1 .004 .050 .250 It is assumed that production from northeast offshore sources cannot begin until after 1985, and that for t = 15, 25, it is no greater than southeast production is allowed to be one period earlier, i.e.: Period 05 10 15 25 E0X2 0.0 0.0 .050 .500 C.3.0 Data for the Gas Sector C.3.1 Primary Costs and Supplies Until a study by EMR on long-run supply curves is completed, the cost and supply data must be based on several sources. The cost of "low cost" conventional western gas is taken to be $.30/Mcf. According to CPA (1977) data, the average wellhead price during 1971-1975 was $.21/Mcf (1975$). Thus $.30/Mcf is a little farther along the long-run supply curve. In model units, this cost is: cwgl = .03 The higher cost western conventional gas is taken to be cwg2 = .08, somewhat arbitrarily. The remaining reserve (after 1975) at the above cost levels are estimated roughly from the shape of the tentative long run supply curve of the EMR draft (1977d), and using the total of remaining known reserves plus undiscovered resources, at the 40% probability level, from EMR (1977b). They are: WGR1 = 39.0 WGR2 = 59.0. 270 The total remaining reserves of northern frontier gas (not including northeast offshore gas, which is allocated to eastern production) 12 are taken to be 137 x 10 cu. ft., which is the figure for potential resources, at the 40% probability level, from EMR (1977b). The low and high cost levels (including transportation to southern Alberta) are based on various sources, namely an early draft of the EMR study (1977d) on long-run supply curves, and figures in the report by HMA (1976). The costs chosen are $2.50/Mcf and $3/Mcf, or, in model units: cwg3 = .25 cwg4 = .30. Based on the shapes of the tentative long-run supply curves of EMR (1977d), the following allocation of reserves between the two cost levels has been made: WGR3 =44.4 WGR4 = 93.0. The low cost eastern gas is taken to be represented by southeast off-shore gas, and the high cost eastern gas by northeast offshore gas. Based on the 40% probability level of potential resources in these two areas, reported by EMR (1977b), the reserves are taken to be EGR1 =16.0 EGR2 = 29.0. Based on the EMR draft (1977d) and HMA (1976), the landed costs of these are set at $.60/Mcf and $3.00/Mcf, respectively. In model units, these are eegl = .06 ceg2 = .30 Limits are placed on the rate of increase of production of the low cost eastern gas (see the section on miscellaneous limits). C.3.2 Export Price The 1976 EMR "Energy Strategy" report (1976a) lays out the policy 271 that prices of gas exports should be competitive in the markets where they are sold. The 1978 (mid-year of first period) gas export price was $1.92/Mcf, according to Helliwell (1979X. Assuming gas export prices follow the same pattern assumed for oil prices, the real gas price is escalated at the rate of 4% per year until the year 2000. Since the logic of the model requires export prices to be equal to production cost plus economic rent, and since there is no provision in the model for gas transport charges from the wellhead to the border., the trans port charge — about $.25/Mcf — must be subtracted from the above. The result, in model units, is: Period 05 10 15 25,35,45 pgex .167 .209 .259 .396 C.3.3 Gas Production Decline Curves The standard production time-profile presented by EMR (1973, p. 80) has the peak rate being achieved in the first year and maintained for 15 years, followed by a decline at the rate of 15% per year. This rate of decline appears to be too rapid. As with oil production, it is assumed that production declines at 10% per year. The detailed results for the values ag(s), based on the assumptions that capacity established in one year lasts 15 years, followed by a decline of 10% per year for X another 15 years, are in Appendix B> section 9, "Time Period Aggregation". C.3.4 Coal Gasification 12 15 Let acg = 10 cu.ft. of gas output per 10 BTU coal input; and cgc = cost of coal gasification, not including coal feed cost, in units of 1012 $ per 1015cu. ft. Using estimates by the SRI (1976, Vol. II, pp. IV-4,5), the parameters are set at acg = 0.567 and cgc = 0.124. These are arrived at by averaging the conversion efficiencies and costs for the Lurgi process, and an "Advanced" process, as estimated by SRI (1976), and converting to model units. The average conversion efficiency corresponding to the above acg is 0.587. The earliest dates of introduction of coal gasification, according to SRI (1976), are 1984 for the Lurgi process, and 1987 for the "Advanced" process. The approximate date of 1985-86 is modeled by fixing capacity additions at the zero level for the periods ending 1980 and 1985, i.e. WGDG = and setting initial capacity equal to zero. C.3.5 Synthetic Gas from Biomass Middleton Associates (1976, pp. 300-301) give a cost range for pyrolysis (gas and liquid output) of $1.50-$3.50 per million BTU(MMBTU). An average value of $2.50 per MMBTU (or $2.50 per MCF of gas) is taken for the model. In model units, this is cwg5 = ceg3 -= 0.25. It is assumed that this technology is available after 1980. In order to model this, production is set equal to 0.0 in the first period. For later periods, low upper limits are placed on production from this source, as shown below: Period 05 10 15 25,35,45 WGX5 0.0 .0005 .001 .002 EGX3 0.0 .001 .002 .004 C.3.6 West-to-East Gas Transportation Let cgtr = cost of transporting gas from west to east. 273 Helliwell (1976, appendices) gives $.44/mcf for this cost. In model units, this is cgtr = .044. It is assumed that the west-to-east transportation of gas can increase from the 1971-1975 level up to 3.5% per year until 1985, when the Quebec & Maritimes pipeline may be built. Since this pipeline will make the eastern market potentially 43% larger (based on population shares), an additional amount (above 3.5% growth) is added, equal to 1/2 the potential increase (i.e. 21.5% more), since it takes time to establish the new markets. There is no upper limit after 1990. The results are: Period 05 10 15 WGE 4.092 4.860 7.008 C.3.7 Distribution Margins The margins for the two sectors industrial (mgiw, mgie) and DFC (mgdw, mgde), are taken to be the differences between the average revenues and wellhead price (Toronto city gate, for the east) in 1970, a pre-"crisis" year. The average revenues were derived from Statistics Canada (cat. no. 57-205), the wellhead price from the CPA (1977) and the Toronto city gate price from the sum of the wellhead price and the west-to-east gas transport chafge. The margins are: mgiw = 0.0155, mgie = 0.0055, and mgdw = 0.0744, mgde = 0.08S1. C.3.8 Energy Supply Industry Use of Gas Let bwg, beg = fractions of the western and eastern supplies of gas not used by the western and eastern energy supply industries. These parameters are equal in all periods to their 1971-1975 values of .8832 (west) and .958 (east), using data from Statistics Canada (cat. no. 57-207). 274 C.3.9 Miscellaneous Limits Upper limits on future gas exports are set at the level of currently approved exports, according to the NEB (1979, Table G-12) — i.e., in model units, Period 05 10 15 25 35,45 WGEX 5.4 8.4 3.7 0.3 0.0 Eastern production (mostly offshore) is assumed to be able to reach up to 0.8 Tcf per year in the year 1988, following comments by Walters (1979) on the availability of Sable Island gas, and assuming all eastern offshore gas is available, starting in 1988. It is assumed that the northeast offshore gas is available after 1990 (existing onshore production makes a small contribution in the first two periods). The upper limits are: Period 05 10 15 25 35, -45 EGX1 0.001 0.001 2.4 no limit no limit EGX2 0.0 0.0 0.0 4.8 no limit C.4.0 Data for the Electricity Sector C.4.1 Capital and Non-fuel Operating Costs for Secondary Electricity Production The source for the basic data is the report by HMA (1976, p. 250). The data given below, in model units, were derived using a real rate of return of 8% over 30 years. (Multiplication by 10 yields the costs in mills/kWh.). Fuel Gas Coal Oil Cost ceg==.54 cec = .76 cel = .66 275 C.4.2 Fuel-to-Electricity Conversion Coefficients 12 12 Let age = 10 kWh electricity output per 10 cu. ft. gas input? 12 5 ace = 10 kWh electricity output per 10 BTU coal input, and 12 9 ale = 10 kWfe electricity output per 10 bbl oil input. From data compiled by Statistics Canada (cat. no. 57-207) for 1971-1975, the above parameters can be estimated. The parameter values, with approximate corresponding conversion efficiencies are: Parameter age ale ace Value in Model .0788 .4621 .09396 Corresponding .2689 .2718 .32 Conversion Efficiency For the base case, the conversion factors for gas, oil and coal are increased in the first three periods in approximately the same amount as assumed by EMR (1977a, p. 68). In addition, coal electric production is assumed to increase in efficiency to 38%, due to introduction of fluidized bed combustion (using estimates by Keairns, et al. (1975, p. 10)), by the period 2000. The results are: \. Period Parameter 05 10 15 age .0850. .0879 .0879 .0879 ale .4942 .5746 .5900 .5900 ace .0954 .0998 .1028 .1113 C.4.3 Nuclear Power The cost of electricity from nuclear power is taken to be 10 mills/kwh, or ce4 = 1.0, in model units. This figure is based on capital and non-fuel operating costs of 8.9 mills/kwh, derived from estimates by HMA (1976), with a real rate of return of 8% over 30 years, and 276 fuelling costs of 1.1 mills/kwh, converted to 1975$ from a 1976 estimate by Kee and Woodhead (1977). Since Canada has abundant reserves of uranium, no cost increase over time is assumed for nuclear electricity. In later time periods, this technology may be thought of as the thorium near-breeder, or a fusion system. Because of the long lead times in establishing nuclear capacity, and because there is no nuclear power yet in the west, the following restriction is specified: WED4 = 0.0 , t = 05,10 . C.4.4 Cost of Hydroelectricity -Protti (1978, p.56) gives the capital cost of a recent, large hydro installation in Manitoba. Using this information, in 1975 dollars, and a rate of return on capital of 8% over 30 years, together with the non-fuel operating costs assumed for coal-electric production by HMA (1976, p. 250), the cost of hydro-electricity is taken to be 7.7 mills/kwh, or in model units, ce5 = .77 C.4.5 Limitations on Hydroelectricity Using estimates in the report by HMA (1976, p.242), the maximum hydroelectric production, per 5-year period, that can be realized in 12 12 the future is about 1.27 x 10 kwh in the west, and 2.21 x 10 kwh in the east. From Statistics Canada (cat. no. 57-207), the 1971-1975 hydro 12 12 productions were 0.24 x 10 kwh for the west and 0.71 x 10 kwh for the east. Assuming that the future potential can be reached no sooner than the period ending 2000, and allowing a linear increase in capacity until then, the values for the parameters in the model are (recall that the first 277 3 periods are 5 years long, and the rest are 10): Period 05 10 15 25 f35 f•• • WEX5 0.45 0.65 0.86 2.54 EEX5 1.01 1.31 1.61 4.42 To account for the relative lack of hydro potential in some provinces of each region, it is assumed that the proportion of electric capacity expansion due to hydro cannot exceed the 1971-1975 fraction of total electricity production coming from hydro — i.e., using figures from Statistics Canada (cat. no. 57-207, and 57-204) , hdw = .753, hde = .779. C.4.6 Cost of Electricity from Biomass According to Middleton Associates (1976, p. 287), the cost of wood chip input is approximately $1.50/MMBTU, if we reduce Middleton's figures somewhat to account for the higher capital cost (10%) than is assumed in this model (8%). The thermal efficiency of generation is 34%. Therefore, the fuel cost is $1.50 = $4.50 per MMBTU of output. .34 Converting to units of mills/kwh, the fuel cost is 15.3. Assuming the capital and non-fuel operating costs are the same as for coal (7.6 mills/ kWK), the total cost, expressed in model units is ce6 = 2.29. C.4.7 Electricity Exports Manne (1976) presents a projection of U.S. electricity prices, which can be approximated by 18 mills/kWh in the period 1975-1990T and 23 millsAWh in the period 2000-2025, expressed in 1970$. The CPA (1977, Section XI, Table 3), presents statistics on quantity and value of electricity exports. The 1975 average export price is 14.5 mills/ kWh. Appling a factor of 14.5/18.0 to the Manne (1976) projection 278 produces the projection used in the model (model units are presented in the table): Period 05 10 15 25,35,45 peex 1.45 1.45 1.45 1.86 Electricity exports are allowed to be no greater than the level in 1971-75, increased at a rate of 1% per year, i.e. Period 05 10 15 25 35 45 WEEX .0161 .0169 .0178 .0393 .0434 .0480 EEEX .0333 .0350 .0368 .0814 .0898 .0992 C.4.8 Electricity Distribution Margins The margins for the two sectors industrial (meiw, meie) and DFC (medw, mede) are taken to be the differences between the average revenues and average generation costs in 1971, a pre-"crisis" year. The average revenues were derived from Statistics Canada (cat. no. 57-202), and the average generation costs from Statistics Canada (cat. no. 57-207), using the unit generation costs and fuel costs derived above. The margin for electricity used'in road transportation (met) — i.e. for electric automobiles — is based on two assumptions: first, that there would be a road tax equivalent to the road tax on gasoline, and second that the recharging of electric autos would receive off-peak price discounts. Specifically, the road tax of approximately 13 cents per gallon across the country (according to Statistics Canada (cat. no. 68-201)) is converted to dollars per output BTU, and then converted to dollars per kWh of electricity used for electric autos. It is assumed that revenue from electricity sales to the road transportation sector covers only generation costs and the road tax — i.e. there is no distribution margin. 279 The margins are: meiw = 0.18, meie = -0.10, medw = 1.55, mede = 1.00, and met =1.03 C.4.9 Energy Supply Industry Use of Electricity Let bw, bee = fractions of the western and eastern supplies of electricity not used by the western and eastern energy supply industries (including transmission losses). These parameters are equal in the period 1971-1975 to .8938 (west) and .9096 (east), using data from Statistics Canada (cat. no. 57-207). They are altered in the first three periods roughly in accordance with the assumptions of EMR (1977a, p. 71). The results are: 1— Period Parame ter 05 10 15, 25, 35 ... bwe .8984 .9034 .9083 bee .9143 .9193 .9244 Data for Transportation End Use Sector C.5.1 Conversion Factors 15 9 Let ala = 10 BTU output per 10 bbl input, conventional autos, 15 2 aea = 10 BTU output per 10 kWh input, electric autos, and 15 9 alo = 10 BTU output per 10 bbl input, non-auto transportation. EMR (1977a, p. 28) estimates the utilization efficiency for gasoline to be 20%. Using the factor for conversion of gasoline units to BTU's; ala = .2 x 5.222 = 1.0444. Assuming an improvement in fuel economy bringing average mileage from the present 17.5 miles per gallon to 33 miles per gallon after 1985 as projected by EMR (1976b, p. 2), and increasing to 50 m.p.g. by 2020, the values are: 280 Period 05 10 15 25 35 45 ala 1.3527 1.6611 1.9694 2.3076 2.6457 2.9839 The comparable conversion efficiency for electric autos is the basic operating efficiency of 70%, given by Swinton (1976, p. 29). Multiplying by the factor for conversion of electrical units to BTUs, aea = .7 x 3.412 = 2.388. For non-auto transportation, a weighted average of utilization efficiencies given by EMR (1977a, p. 28) for rail, air and marine transport, using liquid fuels, yields a conversion efficiency of 24%. (Coal, already in little use by 1975 in transportation, is assumed not to be used in transportation.) With an approximate average factor for conversion of liquid fuel units to BTUs, alo = .24 x 5.8 = 1.41. Air, truck and bus energy efficiency measures discussed in EMR (1977e, p. 28) are expected to amount to 18%-20% fuel savings in 1990. Assuming the fuel savings will actually be 15%, by 2000, and more modest improve ments after 2000, the conversion factor, alo, takes the following values: Period 05 10 15 25 35, 45 alo 1.46 1.51 1.66 1.71 1.71 C.5.2 Electric Auto Growth Restrictions Let el = maximum fraction of new autos that can be electric, in west and east. From the discussion by Hedley, et al. (1976, p. 13) on the "free market" penetration of electric autos, it is assumed that / 0, t = 05, 10 el = J I .15, t = 15 but that a 60% penetration can be achieved by 2010, i.e. 281 .375, t = 25 el = ^.6, t = 35, 45. C.5.3 Differential Cost of Electric Auto over Conventional Auto The latest information on the U.S. electric test vehicle, ETV-1, suggests an initial cost difference of approximately $1500 extra for the electric auto, in Canadian 1975$, according to Wayne (1979, p. 13). Lower maintenance costs for the electric car would be offset by battery replacement charges. Amortized over 10 years, at a rate of return on capital of 8%, the annual extra cost is $224. Assuming the vehicle travels 10,000 miles in a year, this is $0.0224 per mile extra for the electric car. Since ala = 1.0444 corresponds to 17.5 miles per gallon, the quantity of output energy per mile driven is (1.0444/(35 x 109 x 17.5) = (1.705 x 10~12) x 1015BTU per mile. (Dividing by aea = 2.388 gives the number of kwh per mile, 0.714 kwh per mile. This falls within the range given by Wayne (1979, p. 10), of 0.5 -1.5 kwh per mile.) Therefore, the differential cost of electric auto output energy 3 is $.0224/1.705 = $.0132 per 10 BTU, or in model units, cea = 1.32. C.6.0 Data for Industrial End-Use Sector C.6.1 Conversion Factors ^ nn" 12 agi = 10 BTU per 10 cu. ft. gas used in industrial sector, 15 9 ali = 10 BTU per 10 bbl liquid hydrocarbon (oil) used in industrial sector, 15 15 aci •= 10 BTU per 10 BTU coal used in industrial sector, and 15 12 aei = 10 BTU per 10 kWh electricity used in industrial sector. 282 EMR (1977a, p. 28) has estimated average utilization efficiencies for the different fuels in the industrial sector. The above parameters are set at EMR estimates, expressed in model units, for all time periods. Since EMR deals separately with different liquid fuels, it is necessary to take a weighted average of the liquid fuel conversion efficiencies, for the model. The parameter values, and associated conversion efficiencies, are: Parameter agi ali aci \ aei Value in Model .85 • .4.13 .87 ; 3.412 Corresponding Con version Efficiency .85 '• .70 ,87 1.00 C.6.2 Upper and Lower Limits on Fractions of Total Industrial Output' Energy Available from the Different Fuels HMA (1976, p. 148) present estimates of these upper and lower limits for the year 2000. It is assumed that these parameters change linearly from their 1971-1975 values (when upper limit = lower limit = actual fraction), estimated from Statistics Canada (cat. no. 57-207), to the HMA (1976) values for 2000, and remain constant after this. The results are presented in Table 69. Non-energy uses of oil and gas (e.g. for petrochemicals, asphalt, etc.) are included in industrial uses. 283 Table 69. Bounds on Industrial Fuel Shares Period Fuel Limit Base 05 10 15 25,35,... Coal lwc .030 .044 .058 .072 .10 lec .172 .158 .143 .129 .10 uwc .030 0084 .138 .192 .30 uec .172 .198 .223 .249 .30 Oil lwl .279 .243 .207 .172 .10 lei .348 .298 .249 .199 .10 uwl .279 .343 .407 .472 .60 uel .348 .398 .449 .499 .60 Gas lwg .455 . 384 .313 .242 .10 leg .242 .214 .185 1.157 .10 uwg .455 .484 .513 .542 .60 ueg .242 .314 .385 .457 .60 Electricity lwe .236 .229 .222 .214 .20 lee .238 .230 .223 .215 .20 uwe .236 .289 .342 .394 .50 uee .238 .290 .343 .395 .50 C.7.0 Data for Domestic, Farm and Commercial (DFC) Sector C.7.1 Conversion Factors The conversion efficiencies for fuels in the DFC sector are presented below, along with the corresponding values for the conversion factors. The efficiencies are taken from EMR (1977a, p. 28), except in the case of the heat pump, for which the SRI (1976, Vol. II, pp. IX-14,15) figure is used. There is close agreement between the EMR and SRI efficiency values for electric resistance heating, oil heat, and gas heat. 284 Process Thermal Efficiency Conversion Factor Electrical, non-heating 1.0 aeo = 3.412 Electric-heat pump 2.0 aeh = 6.824 Electric-resistance 1.0 aer = 3.412 heating Gas heat 0.76 agh = 0.76 Oil heat 0.65 alh = 3.835 C.7.2 Heating Costs Except for district heating by cogeneration, the following costs are taken from SRI (1976, Vol. II, pp. IX-14,15). The heat pump cost is reduced to 5/6 of the SRI value, under the assumptions that 1/2 of the users would have air conditioning even without a heat pump, and that the air conditioning function of the heat pump would be used 1/3 of the time, for a total credit of 1/6 of the non-fuel cost. The district heat cost is taken from estimates by Berthin (1980) of capital costs for plant equipment changes, piping, and in-home heat exchangers, amortized over 30 years at an 8% rate of return, plus system maintenance costs of $25/ yr./house, plus in-home maintenance costs of $37/yr./home (the maintenance cost for gas heat assumed by SRI (1976)), with the same annual heating load of 94.7 x 106BTU/yr. as assumed by SRI (1976). 3 Process Non-Fuel Cost ($/10 BTU) Electric Resistance crh = .105 Heating Gas Heat cgh = .251 Oil Heat coh = .336 Heat Pump chp = .466 Solar Heat chs = .706 District Heat cdh = .662 by Cogeneration 285 C.7.3 Heat Pump Limits It is assumed that the heat pump is commercially available only after 1980, and that the upper limit on the fraction of heating done by heat pump rises linearly from 0 in 1980 to 1 in 2000 — i.e. hpw = hpe = 0, t = 05 .2S, t = 10 .50, t = 15 1/ t — 2 5 ^ 35 f • • • • C.7.4 Solar Heating Limits Berkowitz (1977, p. 7) deals with a partial solar system providing 70% of a structure's heating and hot water demands. He further assumes (p. 119) a 15% penetration of solar home heating by 2000. Using the 70% and the latter criteria puts an upper limit on the fraction of heating that can be done by solar. It is assumed that this level is achievable by 2000, that a further doubling can take place by 2010, another doubling by 2020, that solar heating is at virtually zero level until after 1980, and that the solar potential increases linearly between 1980 and 2000 - i.e. Period 05 10 15 25 35 45 sw = se 0 .0263 .0S25 .105 .21 .42 C.7.5 Limits on District Heating by Cogeneration According to Berthin (1980) the total combined efficiency of coal-steam-electric plus district heat is 72%, with 27% for electricity and 45% for heating. To simplify matters, it is assumed that 32% is used for electricity (as with no district heating), and that 40% (= 72% - 32%) of the input energy is available for'district heating. Therefore, the coefficient relating new coal-electric capacity to the maximum new capacity of district heating is fc = .40. 286 Assuming that heat from waste heat of nuclear power generation would be publically unacceptable, the coefficient relating new nuclear electricity capacity to the maximum new capacity of district heating is zero in the base case: fn = 0.0. It is assumed that district heating by cogeneration is not possible in Newfoundland, Quebec, Manitoba or B.C., where electricity is produced mainly by hydro. If these areas are elminated in proportion to their populations, as given by Statistics Canada,(1978, p. 186), and the resulting upper limits are taken to be achievable by 2000, with linear increase from 0 in 1980 then the maximum fractions of total heating due to district heat by cogeneration are: Period 05 10 15 25,35, gw 0 .1125 .225 .45 ge 0 .15 .3 .6 • C.7.6 Proportion of DFC Output Energy for Heating The values (for 1974 of energy used by end-use function, pre sented by EMR (1977a, pp. 20-21), adjusted for end use efficiencies using EMR (1977a, p. 28) data gives gwh = geh = .8661. This value is taken to be constant in all time periods. C.8.0 Data for the Objective Function C.8.1 Social Discount Rate The.real social discount rate is taken to be 10%, that is d = 0.10. This is the figure derived by Jenkins (1977, p. 140) for the social opportunity cost of government funds. A real discount rate of 10% is also 287 the rate preferred by the NEB (1979) in the calculations of costs and benefits of proposed exports of natural gas. C.8.2 Price Elasticities of Demand The derivation of the price elasticities of demand is discussed in Appendix A. For completeness of this section, they are presented here: ed = 0.81, for DFC, ei = 0.48, for industry, er = 0.36, for road transportation, and eo = 0.36, for other transportation. C.8.3 Base Year Prices and Quantities For the calculation of the parameters dwd, dwi, etc., it is necessary to have estimates of the prices and quantities of output energy used in a base year. The base year chosen is 19$0, since this year was before the rapid escalation of petroleum prices and was thus likely an equilibrium year in energy markets. The base year quantities of output,energy were calculated from Statistics Canada (cat. no. 57-207), which gives the input energy to the end use sectors, and from the end use conversion efficiencies specified in sections 5, 6 and 7 above, which were adapted mostly from EMR (1977a, p. 28) . The base year prices were calculated in two stages. First, the base year prices of the fuels, in natural units and in 1975$, were calculated for each end use sector. Secondly, the total energy costs in each end use sector were calculated, using the base year fuel prices and input energy quantities, then divided by the total output energy quantities for each sector. In the DFC sectors, the non-fuel costs of heating, as presented in section 7 above, are also incorporated into the price. The base year natural gas prices in the DFC and industrial sectors of the west and east were estimated by calculating the average revenues, from data in Statistics Canada (cat. no. 57-205). The residential and commercial categories were combined for the DFC calculation. The base year electricity prices in the DFC and industrial sectors of the west and east were estimated by calculating the average revenues, from data in Statistics Canada (cat. no. 57-202). The residential, commercial and street lighting categories were combined for the DFC cal culation. The 1971 data were used to calculate electricity prices. This should not introduce much error since, as is well known, real energy prices were quite stable between 1970 and 1971. The base year coal prices for industry in the west and east were estimated by calculating the average cost to industry of coal and coke, from data in Statistics Canada (cat. no. 57-506). Weighted averages of the gasoline prices in five regions, from EMR (1977a, Appendix C), were used for the base year fuel prices in the road transportation sectors of the west and east. The base year prices of oil used in the western and eastern in= dustrial sectors were estimated by calculating the average cost to industry of all oil products consumed, from data in Statistics Canada (cat. no. 57-506). There are no readily available statistics for the base year prices of oil in the DFC sector. The prices of light fuel oil and heavy fuel oil to western and eastern industry were calculated from Statistics 289 Canada (cat. no. 57-506). Since light and heavy fuel oils are the pre dominant oil fuels used in the DFC sector, averages of these two prices were calculated for the west and the east, weighted by the proportions of the 1970 consumption of the two fuels in each region. Since Statistics Canada (cat. no. 57-506) does not distinguish between light and heavy fuel oils until 1973, the 1973 prices were used, but adjusted downward by the difference between the 1973 and 1970 western Canadian wellhead oil prices, in 1975$, as reported by the CPA (1977). The base year prices of oil products in "other" transportation are weighted averages of the prices to industry of heavy fuel oil, diesel oil and aviation turbo fuel. The prices of heavy fuel oil and diesel oil were calculated from Statistics Canada (cat. no. 57-506) for 1973, when these products were first distinguished separately, but adjusted downward by the difference between the 1973 and 1970 western Canadian wellhead oil prices, as reported by the CPA (1977). The price of aviation turbine fuel was taken to be the same as the price of diesel fuel oil, since the values per barrel shipped from refineries in 1970 of the two commodities were very nearly equal, according to data in Statistics Canada (cat. no. 45-205, Table 6). A summary of the calculations for the output energy prices is presented in the tables below. The input fuel prices are expressed in familiar units, but all other quantities and monetary values are expressed in model units. 290 Sector Fuel Input Price Output Energy Total Cost Road Transportation, oil $.67/gallon .056951 .1281 West Output Price = 2.2501 Road Transportation, oil $.70/gallon .127151 .2995 East Output Price = 2.3554 Other Transportation, oil $.33/gallon .019503 .0161 West Output Price = .8261 Other Transportation, oil $.32/gallon .049652 .0400 East Output Price = .8046 Industry, West coal $1T00/106BTU .0110254 .00127 gas $.386/mcf .131535 .00597 oil $.13/galIon .09044 .01007 electricity 1.17*r/kwh .0806339 .02765 Totals: .3136343 .04496 Output Price .14335 Industry, East coal $.88/106BTU .2170946 .02196 gas $.774/mcf .2076631 .01891 oil $.12/gallon .42497 .04219 electricity 1.06<r/kwh .2503984 .07779 Totals: 1.1001261 .16085 Output Price .14621 DFC, West gas $.975/mcf . .175376 .379 (Note: Total Cost oil $.21/gallon .103850 .512 electricity 2 ..54<r/kwh .073094 .782 Total: .352320 Output Price = .5018 DFC, East gas $1.57/mcf .154927 .458 (Note: Total Cost oil $.17/gallon .940832 .482 is per unit of electricity 2.16 <r/kwh .225452 .656 output energy, *i npl nH"i i-i rr nnn — Total: 1.321211 iiiui n^-Liiy iiwii fuel cost) Output Price = .5089 C.8.4 Base Year Values of Exogenous Parameters For the calculation of the objective function parameters dwd, dwi, etc., it is necessary to have base year (1970) estimates ofrthe indices (1973 = 1) of population, income per capita, real domestic product and capital output ratio. It is assumed that the 1970 indices of population 291 and real domestic product are the same in the west and the east — i.e. that there was not much difference between west and east in the percentage changes of these quantities from 1970 to 1973. Income per capita is personal disposable income, divided by population. The indices and data sources are shown below. Source Index- Value population .9662 income per capita .8217 real domestic product .8249 Capital output ratio 1.0343 Statistics Canada (cat. no. 91-201) Statistics Canada (cat. no. 13-531, and cat. no. 91-201) Statistics Canada (cat. no. 13-531) EMR (1977a, Appendix C) C.8.5 Projections of Exogeneous Parameters For the calculation of the parameters dwd, dwi, etc., projections are needed for the indices of western and eastern population, income per capita, western and eastern real domestic product, and capital output ratio. The population indices for the base case are arrived at by taking slightly lower values than the NEB's base case projections for all of Canada, in Douglas and Nichols (1979), until the year 2000, and applying the regional population proportions in EMR (1977a, Appendix C) to derive separate indices for the west and east. The NEB's base case projections have been lowered slightly because they are deliberately a little on the high side. Population growth after 2000 is taken to be at the same rate in both regions, using the midpoint of the four main projections in Statistics Canada (cat. no. 91-520). The projections, expressed in per cent change per year, are shown below. Period 1980 1985 1990 2000 2010 2020 2030 Population, West, %/yr. 1.5 1.2 1.1 0.9 0.6 0.5 0.3 Population, East, %/yr, 1.2 0.9 0.8 0.7 0.6 0.5 0.3 292 The projection of income per capita- until 2000 is slightly lower than the base case NEB projections, in Douglas and Nichols (1979), which are a little on the high side. (Because the NEB is evaluating proposed new gas exports, any errors in domestic demand projection should be on the high side). After 2000, the rate of growth of income per capita is 2.3% per year, under the assumptions that the proportion of the population in the work force will have stabilized by that time, and that the main source of the increase in income per capita will be the increase in output per worker due to technological change, which has typically been about 2% per year. The projection is: Period 1980 1985 1990 2000 2010 2020 2030 Income per Capita, ' 3.7 1.9 2.3 2.5 2.3 2.3 2.3 %/yr. The projections of the western and eastern real domestic product until 2000 are slightly lower than the NEB projections for all of Canada, in Douglas and Nichols (1979X , with the split between west and east chosen to make the real domestic product per capita increase at the same rate in each region. After 2000, the rates of growth in the two regions are taken to be equal to the rate of growth of population plus that of income per capita. The projections are: Period 1980 1985 1990 2000 2010 2020 2030 Real Domestic 3.5 4.0 3.7 3.8 2.9 2.8 2.6 Product, West, %/yr. Real Domestic 3.2 3.7 3.4 3.6 2.9 2.8 2.6 Product, East, %/yr. The projection of the capital output ratio (i.e. capital stock divided by output) is based on the projections by EMR (1977a, Appendix C) of 293 industrial capital stock and industrial real domestic product, until 1990. After 1990, the rate of growth of the capital output ratio is assumed to gradually slow to zero — i.e. that industrial capital stock and output eventually grow at the same rate. The projection is: Period 1980 1985 1990 : 2000 : 2010 : 2020 2030 Capital Output Ratio, %/yr. 2.0 2.1 2.8 1.0 0.5 0.0 0.0 In all of the above projections, the rate of growth in the period ending 2030 is used in the end effects modifications as the rate of growth in every period after the time horizon, 2020. C.9.0 Right-Hand Side Values (Initial Conditions) The interperiod constraints of the first few time periods relate the values of variables to historical (pre-1976) values. These histo rical values combine in various ways to form the non-zero right hand sides of the model's constraints. (The values of various bounds on variables have been outlined in earlier sections). These right hand sides involve combinations of production levels and capacity additions in historical periods. Since statistics for production levels are easy to obtain, but statistics for capacity additions are not, estimates of the capacity additions are made by a simple procedure from the data on production levels. The annual growth: rate of a production level in historical periods is estimated using two years separated by several years. It is then assumed that the growth rate of capacity additions is the same as that estimated for the production level, and a simple expression relating the capacity additions to the production level in the period 1971-1975 is derived. It is then a simple matter to evaluate the right hand side. 294 In the following, let X(t)"represent a-production level, and D(t) represent., a capacity addition. C.9.1 'Capacity Expansion and Retirement — 30 Year Lifetime The equations with non-zero right hand sides, separated into unknowns on the left and historical values on the right hand side, are X(5) - D(5) = X(0) - D(-25) , X(10) - X(5) - D(10) = - D(-20) , X(15) - X(10) - D(15) = - D(-15) , and X(25) - D(25) - 2 • D(15) - 2 • D(10) - 2 • D(5) = 2.- D(0) + D(-5) . Assuming an annual growth rate r in both X and D , X(0) = D(0) + D(-?5) + D(-10) + D(-15) + D(-20) + D(-25) = D(0) • [1-:-+ (1+r)"5 + (l+r)~10 + (1+r)"15 + (l+r)~2° + (1+r)"25] = D(0) ' [l-(l+r)"3°] / [1 - (1+r)"5] . Therefore, D(0) =X(0) - [1 - (1+r)"5] / [1 - (1+r)"30], and D(t) = D(0) • (l+r)fc , for t= -5,-10,-15,-20,-25 . The calculations for each of the technologies having 30-year lifetimes and existing in the past are 295 Right Hand Side, for t = Production of r X(0) D(0) 5 10 25,.., coal, west ...121. ,2.-159 .971- 2.103. ..--.-099 ~fi-75 2 - 491 coal, east -.057 .253 .018 .175 -.058 -.043 .060 electricity, hydro, west .049 .239 .067 ' , 219 -.026 -.033 .187 electricity, hydro, east .049 .708 .169 .657 -.065 -.083 .471 coal for electricity, west .099 .562 .225 .541 -.034 -.055 .590 coal for electricity, east .099 1.240 .496 1.193 -.075 -.120 1.301 gas for electricity, west .099 .449 .180 .432 -.027 -.044 .472 gas for electricity, east .099 .317 .127 .305 -.019 -.031 .333 oil for electricity, west .099 .014 .006 .013 -.001 -.002 .016 oil for electricity, east .099 .076 .030 .073 -.005 -.007 .079 electricity, wood, west .099 .004 .0016 .004 0 0 .004 electricity, nuclear, east(*) .051 .046 .051 0 0 .096 oil from tar sands(*) .088 .059 .088 0 0 .147 (*) - right hand side take directly from data sources. The estimates for r and X(0) are based upon statistics in SC(26-206) for coal, CPA (1977) for oil from the tar sands, and SC(57-207) for the rest. 0.9,-2 - Capacity Expansion and Retirement - IQ Year Lifetime These are conventional and electric automobiles. The only relevant equation is X(5) - D(5) = D(0) , with a non-zero right hand side only for conventional autos in each region, since there have been virtually no electric autos in recent history. Since X(0) = D(0) + DJt-5)-= D(0) • [1 + (1+r)"5] , it follows that D(0) = X(0) / [-1+ (1+r)"5] . From SC(57-207) , r = 0.057 , WLA(0) = .426, and ELA(0) = .909.. 296 Therefore, WTD2(0) = 0.2423, and ETD2(0) = 0.5171 , which are the right hand sides. C.9.3 Capacity Expansion .and Retirement - 15-Year Lifetime These technologies are all of the DFC heating, except district heat by cogeneration. The relevant equations are X(5) - D(5) = D(0) + D(-5) , and X(10) - D(10) - D(5) = D(0). It is easy to show that D(0) = X(0) / [1 + (1+r)"5 + (1+r)"10] , and D(-5) = D(0) • (1+r)"5 . The chart below shows the estimates for r and X(0), taken from SC(57-207), and the calculated right hand sides for the three historical heating fuels - gas, oil and electric resistance. In the calculations for electric resistance, it is necessary first to estimate the proportion of DFC electricity use which is for heating purposes, since the statistics in SC(57-207) are for all electricity used in the DFC sector. This is done by estimating the quantities of total output energy used in the western and eastern DFC sectors during the period 1971 - 1975, subtracting non-heating output energy according to the proportion derived-.in section 7.6 above, subtracting the output energy supplied by gas and oil to arrive at a residual which is presumed to be heating output energy supplied by electricity. This quantity is converted to secondary energy in the form of input kilowatt-hours of electricity using the end-use conversion coefficient listed in section 7.1 above. The results are 297 Right Hand Side, for t = Heating by r X(0) 5 10 gas, west .045 1.534 : 1.13 .627 gas, east .073 1.329 1.03 .605 oil, west -.006 .155 .102 .05 oil, east -.047 .664 .388 .171 elec. resistance, west .091 .088 .07 .043 elec. resistance, east .081 .293 .23 .137 C.9.4 Oil Production Decline Curves The relevant equations are X(5) - D(5) = D(0) + (0.59) • D(-5) + (0.35) • D(-10) + (0.21) X(10) - D(10) - D(5) = (0.59) • D(0) + (0.35) • D(-5) + (0.21) X(15) - D(15) - ... = (0.35) • D(0) + (0.21) - D(-5), X(25) - ... = (0.21) • D(0) . The relationship between X(0) and D(0) is D(0) = X(0) / [1 + (1+r)"5 + (0.59) (1+r)"10 + (0.35)(1+r)"15 + (0.21)(l+r)"20]. As above, D(t) = D(0) • (1+r)1, for t = -5,-10,-15 . The values of r are estimated from data in CPA (1977), and X(0) from SC(57-207). The chart below shows the results for the low cost conventional oil of each region, which is assumed to be the only historically existing oil production (oil from the tar sands is covered in section 9.1 above). • D(-15), • D(-10) , 298 Oil from .. r X(0) 5 10 15 25 west, low cost east, low cost .082 -.021 3.121 .004 2.417 .0026 1.374 .0014 .733 .0006 .3131 .0002 C.9.5 Natural Gas Production Decline Curves The relevant equations are X(5) - D(5) = D(0) + D(-5) + (0.59)D(-10) + (0.35)D(-15) + (0.21)D(-20), X(10) - ... = D(0) + (0.59)D(-5) + (0.35)D(-10) + (0.21)D(-15) , X(15) - ... = (0.59)D(0) + (0.35)D(-5) + (0.21)D(-10) , X(25) - ... = (0.56)D(0) + (0.21)D(-5) . It is easy to show that D(0) = X(0) / [1 + (1+r)"5 + (1+r)"10 + (0.59)(1+r)"15 + (0.35)(1+r)"2° + (0.21)(1+r)"25] and D(t) = D(0) • (l+rjS for t = -5,-10,-15,-20. The value of r is estimated from CPA (1977), and X(0) from SC (57-207). The chart below shows the results for the low cost conventional gas production in the two regions. Gas from r X(0) R 5 ight Hand S: 10 Lde, for t = 15 25 west, low cost east, low cost .138 -.023 12.77 .00078 11.665 .0006 9.557 .0004 5.533 .0002 4.461 .0001 . 299 Appendix D. DETAILED-'OUTPUT FOR THE BASE CASE. The following table gives the optimal values of the.base case variables, and sixteen prices, in undiscounted, 1975$. The first eight rows in the table are prices, whose names begin with "P", followed by the name of the constraint from which the dual activity was taken for the price calculation. The next eight rows are the variables which enter nonlinearly into the objective function, expressed as average annual flows in each period. The next eight rows in the table are prices calculated from the objective function gradient; the name of each begins with "P", followed by the name of the associated nonlinear variable. The remaining rows in the table are all the other variables, expressed as average values for each period. 300 BASE CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects PWCSB 0. 0200 0. 0200 0. 0200 0. 0200 0.0200 0.0200 0.0200 PECSB 0. 1551 0. 1751 0. 1697 0. 1231 0.1231 0.1231 0.1231 PHOSBL 0. 5557 0. 8843 0. 9305 0. 9141 1.1397 1.2942 1.2942 PEOSBL 0. 8659 1. 0907 0. 9855 0. 969 1 1.1949 1.3496 1.3496 PWGSB 0. 1041 0. 1093 0. 1158 0. 166 9 0.2 560 0.2831 0.2831 PEGSB 0. 2243 0. 2615 0. 1994 0. 2201 0.3132 0.3132 0.3132 PWESBE 0.9123 0. 9075 0. 9060 0. 9180 0.8755 0.8572 0.8572 PEESBE 0. 9014 0. 9524 0. 9224 0. 9088 1.0818 1.0818 1.0818 8 DFC 0. 5013 0. 5639 0. 6379 0. 7156 0.7837 0.9514 1.9146 EDFC 1. 5635 1. 6543 2. 0748 2. 3592 2.7751 3.4348 6.9249 WIND 0. 4223 0. 5287 0. 6964 0. 9409 1.2019 1.5498 2.7902 EIND 1. 3072 1. 5744 2. 1365 3. 0259 3.8367 5.0235 9.0439 WRTE 0. 0926 0. 1091 0.1334 0. 1756 0.2285 0.2831 0.4417 ERTE 0. 1952 0. 2308 0. 2831 0. 3670 0.4783 0.5930 0.9254 WOTB 0. 0271 0. 0309 0. 0371 0. 0503 0.0647 0.0829 0.1374 EOTB 0. 0637 0. 0737 0. 0901 0. 1205 0.1549 0.1984 0.3288 PWDFC 0. 5172 0. 5228 0. 5307 0. 5886 0.6913 0.7064 0.7080 PEDFC 0. 6466 0. 6922 0. 6074 0. 6503 0.6994 0.6977 0.6977 PWIND 0. 1805 0. 1965 0. 1958 0. 2078 0.2426 0.2539 0.2539 PEIND 0. 2317 0. 2653 0. 2410 0. 2250 0.2668 0.2705 0.2705 PWETB 1. 8302 1. 6882 1. 4474 1. 2282 1.1565 1.2149 1.2149 PERTR 2. 1557 1. 8908 1. 5413 1. 3083 1.2265 1.2850 1.2850 PWOTR 0. 9080 1-0956 1. 0900 1. 0145 1.1168 1.2072 1.2072 PEOTB 1. 0657 1. 1794 1. 0740 0. 9994 1.1023 1.1928 1.1928 WCX3 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 8CX4 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WCX6 0. 0408 0. 0839 0. 1537 0. 3245 0.4144 0.5344 0.9621 WCD1 0. 1351 0. 2511 0. 3035 0. 9668 1.2091 2.6140 4.9594 WCD2 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WCE 0. 0430 0. 1158 0. 1758 0. 4491 0.6378 1.2986 3.1205 WCEX 0. 3400 0. 4400 0. 5600 0. 9200 1.4800 2.4200 10.7068 ECX4 0. 2374 0. 4035 0. 3807 1. 0434 1.3230 1.7322 3.1186 ECD1 0. 0662 0. 1128 0. 2110 0. 3291 0.0000 0.0000 0.0000 ECD2 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 ECIM 0. 3321 0. 3093 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOX6 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOD1 0. 0733 0. 0005 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOD2 0. 0000 0. 1470 0. 1635 0. 0000 0.0706 0.0000 0.0000 WOD3 0. 0000 0. 0000 0. 0000 0. 0000 0.0635 0.2256 0.0000 WOD4 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOD5 0. 0186 0. 0382 0. 0790 0. 1251 0.0000 0.1796 0.3234 WOD6 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOEX 0. 1194 0. 0304 0. 0146 0. 0067 0.0000 0.0000 0.0000 WOE 0. 3280 0. 4048 0. 5076 0. 3790 0.1875 0.4247 0.8090 WOG 0. 1455 0. 1349 0. 1321 0. 1411 0.2595 0.2082 0.3396 301 BASE CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects EOX3 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 EOD1 0. 0003 0. 0094 0. 0403 0. 1406 0.0000 0.0000 0.0000 EOD2 0. 0000 0. 0000 0. 0000 0.0000 0.1274 0.0000 0.0000 EOD3 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 EOIM 0. 2786 0. 1109 0. 0000 0. 0000 0.0000 0.0000 0.0000 EOG 0. 6075 0. 5257 0. 5576 0. 5562 0.3933 0.4986 0.8217 HLX1 0. 0026 0. 0024 0. 0020 0. 0016 0.0000 0.0000 0.0000 WLX2 0. 0204 0. 0100 0. 0000 0. 0000 0.0000 0.0000 0.0000 WLX3 0. 0248 0. 0265 0. 0290 0. 0228 0.1164 0.0375 0.0676 WLX4 0. 0871 0. 0861 0. 0915 0. 1064 0.1242 0.1555 0.2473 WLDC 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 ELX1 0. 0146 0. 0136 0. 0122 0. 0079 0.0000 0.0000 0.0000 ELX2 0. 2341 0. 1907 0. 1565 0. 0000 0.0000 0.0000 0.0000 ELX3 0. 1260 0. 0949 0. 1463 0. 2756 0.0929 0.1216 0.2190 ELX4 0. 1880 0. 1877 0. 2015 0. 2316 0.2713 0.3402 0.5421 WGX5 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WGD1 0. 3751 0.0000 0. 0000 0.0000 0.0000 0.0000 0.0000 WGD2 0. 2480 1. 4916 0. 4998 0. 6025 0.0000 0.0000 0.0000 WGD3 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.3428 0. 2000 WGD4 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 HGD5 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 HGD6 0.0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 HGX7 0. 0864 0. 0810 0. 0722 0. 0472 0.0000 0.0000 0.0000 HGX8 0. 4055 0. 5536 0. 7270 0. 8155 0.8278 0.3158 0.2837 WGX9 0. 2206 0. 2693 0. 3457 0. 4428 0.1414 0.1823 0.3283 BGE 0. 8184 0. 9720 1. 4016 1. 3381 0.0907 0.0000 0.0000 WGEX 1. 0800 1. 6800 0. 7400 0. 0300 0.0000 0.0000 0.0000 EGX3 0. 0000 0. 0000 0. 0000 0. 0000 0.0004 0.0004 0.0006 EGD1 0. 0001 0. 0000 0. 4798 0. 2904 0.0000 0.0000 0.0000 EGD2 0. 0000 0. 0000 0. 0000 0. 0000 0.2476 0.2867 0.4090 EGD3 0. 0000 0. 0000 0. 0000 0. 0000 0.0004 0.0000 0.0001 EGX4 0. 0610 0. 0572 0. 0510 0. 0333 0.0000 0.0000 0.0000 EGX5 0. 3941 0. 5315 1. 3064 1. 6305 0.3117 O.OOOO 0.0000 EGX6 0. 3291 0. 3427 0. 4452 0. 3560 0.4514 0.5910 1.0640 wExa 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 EEX4 0. 0201 0. 0509 0. 0726 0. 1216 0.8277 1.0650 2.1433 HEX5 0. 0506 0. 0522 0. 0548 0. 0677 0.0877 0.2224 0.3392 HEX6 0. 0008 0. 0008 0. 0008 0. 0004 0.0000 0.00 00 0.0000 WED 5 0. 0068 0. 0067 0. 0093 0. 0262 0.0421 0.1495 0.0377 HED6 0. 0000 0. 0000 0. 0000 o.oooo 0.0000 0.0000 0.0000 HED1 0. 0235 0. 0221 , 0. 0296 0. 0771 0.1241 0.4706 0.4566 8ED2 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 HED3 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WED4 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WEX9 0. 0283 0. 0344 0. 0437 0. 0552 0.0705 0.2271 0.4089 302 BASE CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects WEX10 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WEX11 0. 0337 0. 0307 0. 0250 0.0281 0. 0308 0.0373 0. 0751 WEEX 0. 0032 0. 0034 0. 0036 0.0039 0. 0043 0.0048 0. 0093 WCX5 0. 1317 0. 1470 0. 1656 0.2113 0. 2647 0.6866 1. 8653 EEX5 0. 1666 0. 2620 0. 3220 0.4420 0. 4420 0.4420 0. 7193 EEX6 0. 0000 0. 0000 0. 0000 0.000 0 0. 0000 0.0000 0. 0000 EED5 0. 0352 0. 1084 0. 0766 0.1747 0. 0647 0.1643 0. 1790 E ED 6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED1 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED2 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED4 0. 0100 0. 0307 0. 0217 0.0496 0. 7207 0.2839 0. 4315 EEX9 0. 0881 0. 1583 0. 2412 0. 1985 0. 5622 0.7361 1. 3253 EEX10 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EEX11 0. 1074 0. 1521 0. 1412 0.3282 0. 5959 0.6405 1. 2912 EEEX 0. 0067 0. 0070 0. 0074 0.0081 0. 0090 0.0099 0. 0191 ECX3 0. 2386 0. 2236 0. 1996 0.1301 0. 0000 0.0000 0. 0000 WLA 0. 0685 0. 0657 0. 0678 0.0761 0. 0864 0.1070 0. 1670 RTD1 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 HTD2 0. 0201 0. 0456 0. 0221 0.0650 0. 0864 0.1070 0. 1670 ELA 0. 1443 0. 1389 0. 1437 0. 1590 0. 1808 0.2241 0. 3498 ETD1 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 ETD2 0.0409 0. 0980 0. 0457 0.1361 0. 1808 0.2241 0. 3498 WEE 0. 0140 0. 0086 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WEH 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WEO 0. 0197 0. 0221 0. 0250 0.0281 0. 0308 0.0373 0. 0751 WDD1 0. 1795 0. 2487 0.2988 0.3924 0. 6316 0.0000 0. 1891 WDD2 0. 0000 0.0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WDD3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WDD4 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WDX5 0. 0000 0. 0000 0. 0000 0.0000 0. 0497 0.2379 0. 7461 WDX6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.3461 0. 6965 WDD5 0. 0000 0. 0000 0. 0000 0.0000 0. 0497 0.1882 0. 1826 WDD6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.34 61 0. 3490 EES 0. 0460 0. 0872 0. 0598 0.2357 0. 4870 0.5057 1. 0195 EEH 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EEO 0. 0614 0. 0649 0. 0814 0.0926 0. 1089 0.1348 0. 2718 EDD1 0. 1881 0. 2224 0. 8959 0.6234 0. 0000 0.0000 0. 0000 EDD2 0. 1565 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EDD3 0. 0000 0. 0598 0. 0000 0.2058 0. 3842 0.3136 0. 5751 EDD4 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EDX5 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EDX6 0. 0000 0. 0000 0. 0000 0.0000 0.5048 1.24 96 2. 5193 EDD5 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EDD6 0. 0000 0. 0000 0. 0000 0.0000 0. 5048 0.9972 1. 3471 303 BASE CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects HCX1 0. 5557 0. 7870 1. 0555 1. 9057 2. 7981 4.9417 16.6613 BCX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 ECX1 0. 1012 0. 2024 0. 4048 ; 0. 7251 0. 6860 0.4346 0.0000 ECX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 IOX1 0. 5567 0. 3486 0. 1904 0. 0521 0. 0001 0.0000 0.0000 B0X2 0. 0000 0. 1470 0. 3106 0. 199 1 0. 1318 0.0332 0.0071 WOX3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0 635 0.2554 0. 1211 W0X4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 80X5 0. 0362 0. 0744 0. 1534 0. 2756 0. 2516 0.3442 1.0204 E0X1 0. 0008 0. 0100 0. 0500 0. 1772 0. 0784 0.0141 0.0000 E0X2 0. 0000 0. 0000 0. 0000 0. 0000 0. 1274 0.0599 0.0127 HGX1 2. 7081 2. 2865 1. 4817 0. 6224 0. 0394 0.0000 0.0000 HGX2 0. 2480 1. 7396 2. 2394 2. 4047 1. 1606 0.2212 0.0000 WGX3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.3428 0.6928 SGX4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 EGX1 0. 0002 0. 0002 0. 4800 0. 7703 0. 4578 0.1317 0.0000 EGX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 2476 0.4848 1.1100 EC 1. 9109 2. 0743 2. 5462 3. 1702 4. 1829 5.5728 9.5867 304 Appendix E. Detailed Output for the High and Low Cases The following two tables list the values of .the variables, and sixteen prices for the high, and low demand cases. The prices, prefixed by "P", are derived in the same manner as for the Base Case detailed output listing, in Appendix D." 305 HIGH CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects PWCSB 0. 0200 0. 0200 0. 0200 0. 0200 0.0200 0.0200 0.0200 PEC SB 0. 1551 0. 1751 0. 1715 0. 1231 0.1231 0.1231 0.1231 P'iOSBL 0. 5817 0. 9202 0. 9389 1. 0802 1.2165 1.2942 1.2942 PEOSBL 0. 8800 1. 1184 0. 9939 1. 1353 1.2718 1.3496 1.3496 PWGSB 0. 1081 0. 1135 0. 1173 0. 1964 0.2693 0.2831 0.2831 . PEGSB 0. 2193 0. 2691 0. 2177 0. 2509 0.3173 0.3240 0.3414 PWESBE 0. 9110 0. 9083 0. 9071 0. 9223 0.8580 0.9223 0.9223 PEESBE 0. 9014 1. 0323 0. 9294 1. 0509 1.0818 1.0818 1.0818 WDFC 0. 4978 0. 5703 0. 6651 0. 7504 0.9113 1.1973 2.5997 EDFC 1. 5743 1. 6623 2. 1124 2. 4435 3.2583 4.27 17 9.2929 WIND 0. 4184 0. 5466 0. 7461 1. 0501 1.6114 2.3613 4.9302 EIND 1. 3069 1. 6035 2. 2625 3. 3081 5.1790 7.7377 16.0981 WRTR 0. 0923 0. 1109 0. 1400 0.1902 0.2718 0.3611 0.5990 ERTR 0. 1949 0. 2348 0. 2970 0. 3950 0.5651 0.7511 1.2458 WOTR 0. 0269 0. 0320 0. 0398 0. 0538 0.0800 0.1145 0.2174 EOTR 0. 0635 0. 0762 0. 0962 0. 1282 0.1906 0.2729 0.5178 PWDFC 0. 5217 0. 5277 0. 5326 0. 6223 0.7060 0.7024 0.7041 PEDFC 0. 6412 0. 7043 0. 6277 0. 6920 0.6994 0.6977 0.6977 PWIND 0. 1840 0. 2005 0. 1970 0. 2259 0.2505 0.2634 0.2634 PEIND 0. 2318 0. 2767 0. 2462 0. 2531 0.2691 0.2718 0.2?38 PWRTR 1. 8494 1. 7099 1. 4517 1. 3001 1.1855 1.2149 1.2149 PERTR 2. 1661 1. 9074 1. 5456 1. 3804 1.2555 1.2850 1.2850 PWOTR 0. 9258 1. 1194 1. 0954 1. 1145 1.1617 1.2072 1.2072 PEOTR 1. 0753 1. 1977 1. 0794 1. 0996 1.1472 1.1928 1.1928 WCX3 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WCX4 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 8CX6 0. 0404 0. 0867 0. 1647 0. 3621 0.5556 0.8142 1.7001 8CD1 0.1336 0. 2593 0. 3190 1. 0995 1.7621 3.7217 5.6943 WCD2 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WCE 0. 0430 0. 1158 0. 1758 0. 5464 1.1009 2.2352 5.5544 WCEX 0. 3400 0. 4400 0. 5600 0. 9200 1.4800 2.4200 10.7068 ECX4 0. 2373 0. 4110 0. 3807 1. 1407 1.7859 2.6682 5.5511 ECD1 0. 0662 0. 1128 0. 2110 0. 3291 0.0000 0.0000 0.0000 ECD2 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 ECIM 0. 3320 0. 3168 0. 0000 0.0000 0.0000 0.0000 0.0000 WOX6 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOD1 0. 0738 0.0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOD2 0. 0000 0. 1595 0. 2143 0. 0071 0.0000 0.0000 0.0000 WOD3 0. 0000 0. 0000 0. 0000 0. 0000 0.2803 0.0000 0.0000 WOD4 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 WOD5 0. 0186 0. 0382 0. 0790 0. 1251 0.0000 0.6372 0.4313 WOD6 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 O.QOOO 0.0000 WOEX 0. 1194 0. 0304 0. 0146 0. 006 7 0.0000 0.0000 0.0000 WGE 0. 3292 0. 4144 0. 5630 0. 4204 0.2939 0.6164 1.2460 WOG 0.1448 0. 1378 0. 1398 0. 1530 0.3181 0.3178 0.6939 306 HIGH CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects E0X3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 EOD1 0. 0003 0. 0094 0. 0403 0. 1406 0. 0000 0.0000 0.0000 E0D2 0. 0000 0. 0000 0. 0000 0. 0251 0. 1022 0.0000 0.0000 EOD3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 EOIM 0. 2796 0. 1138 0.0000 0.0000 0. 0000 0.0000 0.0000 EOG 0. 6096 0. 5382 0. 6130 0. 6227 0. 4863 0.6811 1.2562 WLX1 0. 0026 0. 0024 0. 0020 0. 0016 0. 0000 0.0000 0.0000 WLX2 0. 0204 0. 0100 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WLX3 0. 0246 0. 0274 0. 0311 0. 0254 0. 1454 0.0912 0.2899 1LX4 0. 0867 0. 0879 0. 0966 0. 1148 0. 1495 0.2035 0.3535 WLDC 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.00 00 0.0000 ELX1 0. 0146 0. 0136 0. 0122 0. 0079 0. 0000 0.0000 0.0000 ELX2 0. 2365 0. 1931 0. 1589 0. 0000 0. 0000 0.0000 0.0000 ELX3 0. 1259 0. 1000 0. 1842 0. 3204 0. 1254 0.1874 0.3898 ELX4 0. 1876 0. 1918 0. 2125 0. 2484 0. 3250 0.4435 0.7737 WGX5 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WGD1 0. 3751 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WGD2 0. 2412 1. 5170 0. 5442 0. 5397 0. 0000 0.0000 0.0000 WGD3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.4734 0.5363 WGD4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WGD5 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WGD6 0. 0000 0.0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WGX7 0. 0864 0. 0810 0. 0722 0. 0472 0. 0000 0.0000 0.0000 WGX8 0. 4015 0.5609 0. 7579 0. 8552 0.8499 0.3243 0.3852 WGX9 0. 2186 0. 2784 0. 3704 0. 4942 0. 1896 0.2778 0.5800 WGE 0. 8184 0. 9720 1. 4016 1. 2457 0. 0000 0.0000 0.3182 WGEX 1. 0800 1. 6800 0.7400 0. 0300 0. 0000 0.0000 0.0000 EGX3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0004 0.0004 0.0006 EGD1 0. 0001 0.0000 0. 4798 0. 2904 0. 0000 0.0000 0.0000 EGD2 0. 0000 0. 0000 0. 0000 0. 0000 0. 4238 0.4791 0.5788 EGD3 0. 0000 0. 0000 0. 0000 0. 0000 0.0004 0.0000 0.0001 EGX4 0. 0610 0. 0572 0. 0510 0. 0333 0. 0000 0.0000 0.0000 EGX5 0. 3942 0. 5252 1. 3337 1. 5088 0. 2357 0.0000 0.0000 EGX6 0. 3290 0. 3490 0. 4179 0. 3892 0. 6093 0.9103 1.8939 HEX 4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 EEX4 0. 0202 0. 0509 0. 0726 0. 1216 1. 1841 1.6641 3.7393 WEX5 0. 0503 0. 0533 0. 0583 0. 0741 0. 1227 0.2540 0.4134 WEX6 0. 00 08 0. 0008 0. 0008 0. 0004 0. 0000 0.0000 0.0000 WED5 0. 0065 0. 0083 0. 0116 0. 0291 0. 0705 0.1486 0.0574 WED 6 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WED1 0. 0223 0. 0271 0. 0369 0. 0858 0. 2078 0.9587 0.4178 WED2 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WED3 0. 0000 0. 0000 0. 0000 0. 0000 0. ,0000 0.0000 0.0000 WED4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WEX9 0. 0281 0. 0356 0. 0468 0. 0616 0. 1074 0.3049 0.5161 307 HIGH CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects W EX 10 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 HEX 11 0.0335 0. 0310 0. 0261 0.0294 0. 0358 0.04 70 0.1020 HE EX 0.0032 0. 0034 0. 0036 0.0039 0. 0043 0.0048 0.0093 HCX5 0.1305 0. 1509 0. 1768 0.2312 0. 3688 1.2707 2.5327 EEX5 0.1670 0. 2620 0. 3220 0.4420 0. 4420 0.4420 0.7193 EEX6 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EED5 0.0356 0. 1080 0. 0766 0. 1747 0. 0649 0.1641 0.1790 EED6 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EED1 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EED2 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EED3 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EED4 0.0101 . 0. 0306 0. 0217 0.0496 1. 0772 0.5265 0.8102 EEX9 0.0881 0. 1572 0. 2390 0.1939 0. 7589 1-1339 2.3590 EEX10 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EEX11 0.1078 0. 1532 0. 1434 0.3328 0. 7288 0.7965 1.7328 EEEX 0.0067 0. 0070 0. 0074 0.0081 0. 0090 0.0099 0.0191 ECX3 0.2386 0. 2236 0. 1996 0.1301 0. 0000 0.0000 0.0000 WLA 0.0682 0. 0668 0. 0711 0.0824 0. 1027 0.1365 0.2264 WTD1 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 HTD2 0.0198 0. 0469 0. 0241 0.0704 0. 1027 0.1365 0.2264 ELA 0.1441 0. 1414 0. 1508 0.1712 0. 2136 0.2839 0.4709 ETD1 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 ETD2 0.0407 0. 1007 0. 0501 0. 1461 0. 2136 0.2839 0.4709 WER 0.0140 0. 0086 0. 0000 0.0000 0. 0000 0.0000 0.0000 WEH 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WEO 0.0195 0. 0224 0. 0261 0.0294 0. 0358 0.0470 0.1020 HDD1 0.1755 0. 2600 0. 3224 0.4028 0. 6486 0.0000 0.2568 WDD2 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WDD3 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WDD4 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WDX5 0.0000 0. 0000 0. 0000 0.0000 0. 0831 0.4666 1.0131 WDX6 0.0000 0. 0000 0. 0000 0.0000 0. 0602 0.3240 0.9458 WDD5 0.0000 0. 0000 0. 0000 0.0000 0. 0831 0.3835 0.1671 WDD6 0.0000 0. 0000 0. 0000 0.0000 0. 0602 0.2939 0.5326 EER 0.0460 0. 0879 0. 0605 0.2369 0. 6009 0.6289 1.3681 EEH 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EEO 0.0618 0. 0652 0. 0829 0.0959 0. 1279 0.1676 0.3647 EDD1 0.1882 0. 2160 0. 9295 0.4713 0. ,0000 0.0000 0.0000 EDD2 0.1589 0.0000 0. 0000 0.0000 0. ,0000 0.0000 0.0000 EDD3 0.0000 0. 0605 0. 0000 0.2067 0. ,4976 0.3801 0.7853 EDD4 0.0000 0. 0000 0. 0000 0.0000 0. ,0000 0.0000 0.0000 EDX5 0.0000 0. 0000 0. 0000 0.0000 0. ,0000 0.0000 0.0000 EDX6 0.0000 0. 0000 0. 0000 0. 1612 0.5927 1.5540 3-3808 EDD5 0.0000 0. ,0000 0. ,0000 0.0000 0. ,0000 0.0000 0.0000 EDD6 0.0000 0. 0000 0. 0000 0. 1612 0. 5121 1.2980 1.8212 308 HIGH CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects BCX1 0. 5542 0. 7937 1-0777 2. 0606 3. 5068 6.7428 20.5022 8CX2 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 ECX1 0. 1012 0. 2024 0. 4048 0. 7251 0. 6860 0.4346 0.0000 ECX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 WOX1 0. 5572 0. 3486 0. 1902 0. 0520 0. 0000 0.0000 0.0000 WOX2 0. 0000 0. 1595 0.3739 0. 2525 0. 0801 0.0007 0.0000 80X3 0. 0000 0. 0000 0. 0000 0. 0000 0. 2803 0.1317 0.0280 80X4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 80X5 0. 0362 0. 0744 0. 1534 0. 2756 0. 2516 0.8018 1.9118 EOXI 0. 0008 0. 0100 0. 0500 0. 1772 0. 0784 0.0141 0.0000 E0X2 0. 0000 0. 0000 0. 0000 0. 0251 0. 1141 0.0506 0.0102 8GX1 2. 7081 2. 2865 1. 4817 0. 6224 0. 0394 0.0000 0.0000 8GX2 0. 2412 1. 7582 2. 3024 2. 4032 1. 1376 0.2083 0.0000 8GX3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.4734 1.4531 BGX4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 0.0000 EGX1 0. 0002 0. 0002 0. 4800 0. 7703 0. 4578 0. 1317 0.0000 EGX2 0. 0000 0. 0000 0.0000 0. 0000 0. 4238 0.8181 1.6581 EC 1. 9134 2. 1088 2. 6596 3. 4055 5. 2842 7.7410 15.1445 309 LOW CASE Period end Ending: 1980 1985 1990 2000 2010 2020 effects PWCSB 0.0200 0. 0200 0. 0200 0.0200 0. 0200 0.0200 0.0200 PECSB 0.1551 0. 1751 0. 1707 0.1231 0. 1231 0.1231 0.1231 PWOSBL 0.5554 0. 8813 0. 9351 0.9024 1. 1232 1.2942 1.2942 PEOSBL 0.8657 1. 0884 0.9901 0.9573 1. 1784 1.3496 1.3496 PWGSB 0.1039 0. 1090 0. 1158 0.1648 0. 2560 0.2831 0.2831 PEG SB 0.2256 0* 2589 0. 2003 0.2180 0. 3132 0.3132 0.3132 P8ESBE 0.9123 0. 9075 0. 9060 0.9180 0. 8755 0.8572 0.8572 PEESBE 0.9014 0. 9576 0. 8992 0.8992 1. 0818 1.0818 1.0818 WDFC 0.5015 0. 5536 0. 6100 0.6541 0. 6855 0.7910 1.4618 EDFC 1.5606 1. 6286 1. 9836 2.1730 2. 4454 2.8770 5.3266 WIND 0.4225 0. 5164 0. 6462 0.8147 0. 9915 1.2020 1.9875 EIND 1.3063 1. 5373 1. 9912 2.6227 3. 1564 3.8949 6.4402 WBTB 0.0926 0. 1069 0. 1270 0.1590 0. 1982 0.2323 0.3380 ERIE 0.1952 0. 2261 0. 2694 0.3347 0. 4179 0.4903 0.7133 WOTB 0.0271 0. 0301 0. 0353 0.0447 0. 0548 0.0660 0.1011 EOTB 0.0637 0. 0720 0. 0858 0. 1071 0. 1311 0.1579 0.2419 P WDFC 0.5169 0. 5225 0. 5307 0.5862 0. 6913 0.7064 0.7080 PEDFC 0.6481 0. 6894 0. 6075 0.6475 0. 6994 0.6977 0.6977 PWIND 0.1804 0. 1962 0. 1960 0.2065 0. 2410 0.2539 0.2539 PEIND 0.2320 0. 2651 0. 2390 0.2231 0. 2664 0.2705 0.2705 PWBSR 1.8299 1. 6864 1. 4497 1.2231 1. 1502 1.2149 1.2149 PEBTB 2.1555 1. 8894 1. 5437 1.3032 1. 2202 1.2850 1.2850 PWOTB 0.9077 1. 0937 1. 0930 1.0074 1. 1071 1.2072 1.2072 PEOTB 1.0655 1. 1779 1. 0769 0.9924 1. 0926 1.1928 1.1928 WCX3 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WCX4 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WCX6 0.0408 0. 0819 0. 1426 0.2809 0. 3419 0.4145 0.6853 ICD1 0.1351 0. 2458 0. 2863 0.7817 1. 0687 2.2972 4.5244 WCD2 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WCE 0.0430 0. 1158 0. 1758 0.3100 0. 4030 0.9092 2.2221 WCEX 0.3400 0. 4400 0. 5600 0.9200 1. 4800 2.4200 10.7068 ECX4 0.2372 0. 3941 0. 3807 0.9044 1. 0884 1.3431 2.2208 ECD1 0.0662 0. 1128 0. 2110 0.3291 0. 0000 0.0000 0.0000 ECD2 0.0000 0. 0000 0.0000 0.0000 0. 0000 0.0000 0.0000 ECIH 0.3319 0. 2998 0. 0000 0.0000 0. 0000 0.0000 0.0000 00X6 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WQD1 0.0665 0. 0073 0. 0000 0.0000 0. 0000 0.0000 0.0000 WOD2 0.0000 0. 1335 0. 1163 0.0000 0. 1316 0.0000 0.0000 WOD3 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.2917 0.0000 WOD4 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WOD5 0.0186 0. 0344 0. 0674 0.0854 o.oooo 0.0228 0.2766 WOD6 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 WOEX 0.1194 0. 0304 0. 0146 0.0067 0.0000 0.0000 0.0000 WOE 0.3212 0. 3900 0. 4412 0.2960 0. 1565 0.3277 0.5995 WOG 0.1455 0. 1323 0. 1251 0.1264 0. 2189 0.1677 0.2535 310 LOW CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects EOX3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0 0 00 0. 0000 EOD1 0. 0003 0. 0094 0. 0403 0.1406 0. 0000 0.0000 0. 0000 EOD2 0. 0000 0. 0000 0. 0000 0.0000 0. 1274 0.00 00 0. 0000 EOD3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EOIH 0. 2728 0. 1065 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EOG 0. 5949 0. 5065 0. 4912 0.4732 0. 3623 0.4016 0. 6122 WLX1 0. 0026 0. 0024 0. 0020 0.0016 0. 0000 0.0000 0. 0000 WLX2 0. 0204 0. 0100 0. 0000 0.0000 0. 0000 0.0000 0. 0000 HLX3 0. 0249 0. 0259 0. 026 9 0.0197 0. 0960 0.0291 0. 0481 WLX4 0. 0871 0. 0843 0. 0871 0.0958 0. 1069 0.1264 0. 1869 WLDC 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 ELX1 0. 0146 0. 0136 0. 0122 0.0079 0. 0000 0.0000 0. 0000 ELX2 0. 2225 0. 1791 0. 1449 0.0000 0. 0000 0.0000 0. 0000 ELX3 0. 1259 0. 0927 0. 1062 0.2208 0. 1009 0.0943 0. 1559 ELX4 0. 1880 0. 1838 0. 1917 0.2095 0. 2346 0.2777 0. 4111 WGX5 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WGD1 0. 3751 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WGD2 0. 2484 1. 4708 0. 4559 0.6666 0. 0000 0.0000 0. 0000 WGD3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.2369 0. 1545 WGD4 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WGD5 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WGD6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WGX7 0. 0864 0. 0810 0. 0722 0.0472 0. 0000 0.0000 0. 0000 WGX8 0. 4057 0. 5418 0. 6951 0.7454 0. 7241 0.2750 0. 2166 WGX9 0. 2207 0. 2631 0. 3208 0.3834 0. 1166 0.1414 0. 2338 WGE 0. 8184 0. 9720 1. 4016 1.4710 0. 2410 0.0000 0. 0000 WGEX 1. 0800 1. 6800 0. 7400 0.0300 0. 0000 0.0000 0. 0000 EGX3 0. 0000 0. 0000 0. 0000 0.0000 0. 0004 0.0004 0.0006 EGD1 0. 0001 0. 0000 0. 4798 0.2904 0. 0000 0.0000 0. 0000 EGD2 0. 0000 0. 0000 0. 0000 0.0000 0. 1419 0.2327 0. 2826 EGD3 0. 0000 0. 0000 0. 0000 0.0000 0. 0004 0.0000 0. 0001 EGX4 0. 0610 0. 0572 0. 0510 0.0333 0. 0000 0.0000 0. 0000 EGX5 0. 394 3 0. 5396 1. 2397 1.8053 0. 4345 0.0000 0. 0000 EGX6 0. 3289 0. 3346 0. 5119 0.3086 0. 3713 0.4582 0. 7577 WEX4 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EEX4 0. 0231 0. 0509 0. 0703 0.0979 0. 5727 0.7736 1. 4082 WEX5 0. 0506 0. 0512 0. 0513 0.0596 0. 0743 0.1746 0. 2381 WEX6 0. 0008 0.0008 0. 0008 0.0004 0. 0000 0.0000 0. 0000 WED5 0. 0068 0. 0057 0. 0067 0.0216 0. 0368 0.1129 0. 0188 WED6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WED1 0. 0235 0. 0188 0. 0215 0.0636 0. 1084 0.3624 0. 3411 WED2 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WED3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WED 4 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WEX9 0. 0284 0. 0336 0. 0405 0.0478 0. 0581 0.1761 0. 2912 311 LOR CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects HEX 10 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 HEX 11 0. 0337 0. 0303 0. 0239 0.0257 0. 0269 0.0310 0. 0574 HEEX 0. 0032 0. 0034 0. 0036 0.0039 0. 0043 0.0048 0. 0093 HCX5 0. 1317 0. 1437 0. 1542 0.1865 0. 2241 0.5452 1. 4242 EEX5 0. 1770 0. 2620 0. 3139 0.358 3 0. 4420 0.4420 0. 7193 EEX6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED5 0. 0456 0. 0980 0. 0685 0.0991 0. 1536 0.1551 0. 1471 EED6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED1 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED2 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EED3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0.0000 EED4 0. 0129 0. 0278 0. 0194 0.0281 0. 4908 0.2449 0. 2423 EEX9 0. 0881 0. 1545 0. 2305 0. 1939 0. 4329 0.57 08 0. 9438 EEX10 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EEX11 0. 1195 0. 1559 0. 1424 0.2348 0. 4895 0.5364 0. 9932 EEEX 0. 0067 0. 0070 0. 0074 0.0081 0. 0090 0.00 99 0. 0191 ECX3 0. 2386 0. 2236 0. 1996 0. 1301 0. 0000 0.0000 0. 0000 WLA 0. 0685 0. 0644 0. 0645 0.0689 0. 0749 0.0878 0. 1277 WTD1 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0^0000 0. 0000 WTD2 0.0201 0. 0443 0.0202 0.0588 0. 0749 0.0878 0. 1277 ELA 0. 14 43 0. 1361 0. 1368 0. 1450 0. 1579 0.1853 0. 2696 ETD1 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 ETD2 0. 0409 0. 0952 0.0416 0. 1242 0. 1579 0.1853 0. 2696 HER 0. 0140 0. 0086 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WEH 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WEO 0. 0197 0. 0217 0. 0239 0.0257 0. 0269 0.0310 0. 0574 WDD1 0. 1797 0. 2367 0. 2787 0.3483 0.5500 0.0000 0. 1444 WDD2 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WDD3 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WDD4 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 WDX5 0. 0000 0. 0000 0. 0000 0.0000 0. 0434 0.1883 0. 5697 WDX6 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.2878 0. 5318 WDD5 0. 0000 0. 0000 0. 0000 0.0000 0* 0434 0.1450 0. 1364 HDD 6 0. 0000 0. 0000 0.0000 0.0000 0. 0000 0.2878 0. 2586 EES 0. 0582 0. 0919 0. 0645 0.1495 0.3936 0.4235 0. 7842 EEH 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.00 00 0. 0000 EEO 0. 0612 0. 0639 0. 0778 0.0853 0. 0960 0.1129 0. 2090 EDD1 0. 1883 0. 2302 0. 8211 0.8691 0. 0000 0.0000 0. 0000 EDD2 0. 1449 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EDD3 0. 0122 0. 0523 0. 0000 0. 1233 0. 3319 0.2576 0. 4369 EDD4 0. 0000 0. 0000 0. 0000 0.0000 0.0000 0.0000 0. 0000 EDX5 0. 0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EDX6 0. 0000 0. 0000 0. 0000 0.0000 0. 4448 1.0466 1. 9378 EDD5 0.0000 0. 0000 0. 0000 0.0000 0. 0000 0.0000 0. 0000 EDD6 0. 0000 0. 0000 0. 0000 0.0000 0. 4448 0.82 42 1. 0171 312 LOW CASE Period Ending: 1980 1985 1990 2000 2010 2020 end effects WCX1 0. 5557 0. 7817 1. 0330 1. 6980 2. 4500 4. 29 07 15.0444 WCX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 ECX1 0. 1012 0. 2024 0. 4048 0. 7251 0. 6860 0. 4346 0.0000 ECX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 WOX1 0. 5499 0. 3486 0. 1932 0. 0534 0. 0008 0. 0000 0.0000 WOX2 0. 0000 0. 1335 0. 2498 0. 1552 0. 1782 0. 0618 0.0132 WOX3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 2917 0.1483 WOX4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 WOX5 0. 0362 0. 0706 0. 1380 0. 2205 0. 1965 0. 1419 0.6914 EOX1 . 0. 0008 0. 0100 0. 0500 0. 1772 0. 0784 0. 0141 0.0000 EOX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 1274 0. 0599 0.0127 WGX1 2. 7081 2. 2865 1. 4817 0. 6224 0. 0394 0. 0000 0.0000 WGX2 0. 2484 1. 7192 2. 1752 2. 4086 1. 1855 0.2345 0.0000 WGX3 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 2369 0.5100 WGX4 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0.0000 EGX1 0. 0002 0. 0002 0. 4800 0. 7703 0. 4578 0. 1317 0.0000 EGX2 0. 0000 0. 0000 0. 0000 0. 0000 0. 1419 0. 3462 0.7902 EC 1. 9106 2. 0226 2. 3906 2. 7956 3. 4912 4. 3925 6.6890 313 Appendix F. Computer Programs and Data Listings for the Base Case. This appendix briefly describes the computing procedure for running the model and obtaining printed and graphical output. The base case is used as the example. The steps in running the model are: 1. make any changes to the matrix (the file LPDC DATA), the right hand side (rare) or bounds (both in the file RBI DATA) for the linear process model of supply; 2. if demand data (in the file DEMAND DATA) are to be changed, then pro duce a new subroutine CALCFG (using the FORTRAN program CRCALC), then compile it to produce the new CALCFG object file which MINOS uses to evaluate the objective function and its gradient; 3. if the discount rate is to be altered (in the file DEMAND DATA), it is necessary to run the FORTRAN program ENDPROG which alters the matrix, right hand side and bounds in accordance with the procedure to mitigate and effects; 4. solve the problem using MINOS; 5. re-arrange the format of the raw output of variables and some prices from MINOS, using the REFORM FORTRAN program which also expresses all variables in annual terms (dividing by 5 or 10 as required), and expresses all prices in undiscounted dollars (the output from REFORM for the base case is in Appendix D); 6. produce a plot file (up to 2 7 plots may be chosen by inserting "1" beside the desired plot names in the file CHPLT DATA) and their printed tables of values, using the FORTRAN program GPLT; and 7. send the plot file to the Calcomp plotter, if desired. In practice, steps 4,5, and 6 are done together, in Batch mode. 314 The following is the file DEMAND DATA (base case data is entered here): LAYOOT: DFC IND RTR OTB PRELAST: 0.81 0.48 0.36 0.36 OTHELAS: 0.71 0.667 0.8 BASYPRB: 0.5018 0.1434 2.2501 0.8261 BASYPBE: 0.5089 0.1462 2.3554 0.8046 BASYQTW: 0.3523 0.3136 0.0570 0.0195 BASYQUE: 1.3212 1.1001 0.1272 0.0497 BASE YEAR VALUES OF EXOGENOUS PARAMETERS POP: 0.9662 IPC: 0.8217 RDP: 0.8249 COB: 1.0343 ANNUAL GROHIH RATE PROJECTIONS, PER CENT POPS: 1.5 1.2 1.1 0.9 0.6 0.5 0. 3 POPE: 1.2 0.9 0.8 0.7 0.6 0.5 0. 3 IPC: 3.7 1.9 2.3 2.5 2.3 2.3 2. 3 RDPH: 3.5 4.0 3.7 3.8 2.9 2.8 2. 6 RDPE: 3.2 3.7 3.4 3.6 2.9 2.8 2. 6 COB: 2.0 2. 1 2.8 1.0 0.5 0.0 0. 0 DISCOUNT RATE: 10 .0 PER CENT PER YEAR The following is the FORTRAN program CRCALC for producing the subroutine CALCFG, needed by MINOS to evaluate the objective function and its gradient. FILE: CRCALC FORTRAN A 07/25/80 18:16:00 UNIVERSITY OF WATERLOO PAGE 001 $JOB DIMENSION XPOPW(7),XPOPE(7) ,XIPC(7) ,XRDPH (7),XRDPE(7) ,XCOR(7) DIMENSION A (8,7) ,E{8) .BP (8) ,BQ(8) ,DF{7) ,TF(7) ,EX (7) READ(1,110) E(1) ,E(3) ,E(5) ,E{7) ELDI,ELIC, ELRI BPWD,BPWI,BPWR, BPHO BPED,BPEI,BPER,BPEO BQHD,BQWI,BQWR,BQWO BQED.BQEI.BQER,BQEO READ(1,110 READ(1,110 R E A D (1 „110 READ(1,110 READ(1,110 HEAD(1,110 RE A D(1,110 R EA D(1,120 REAfl(1,120 READ(1,120 R E AD(1, 120 READ(1,110 R EA D(1, 130 READ{1,130 READ(1,130 READ(1,130 REA D(1,130 READ(1,130 READ(1, 140 BPOP BIPC BRDP BCOR XPOPW XPOPE XIPC XRDPH XRDPE XCOR D 110 FORMAT(qX,«(3X.F7.1) ) 120 FORMAT (8X,F6.14) 130 FORMAT(6X,7(3X,F3. 1) ) 1U0 F0RMAT(18X,F1».1) GPOPW=(UXPOPW(7)/100.) **10 GPOPE=(UXPOPE(7)/100.) **10 GIPC= (UXIPC (7) /100.) **10 GRDPW=(1+XRDPW(7)/100.) **10 GRDPE=(1*XRDPE{7)/100.)**10 GCOR=(1+XCOR(7)/100.)**10 XPOPW (1) = (1. * XPOPW (1) /100. ) **5 XPOPE (1) = (1. * XPOPE (1) /100.) **5 XIPC (1) = (1. + XIPC (1) /100.) **5 XRDPW (1) = {1.+XRDPW (1) /100.) **5 XRDPE (1) = (1. • XRDPE (1) /100.) **5 XCOR (1) = (1. * XCOR (1) /100.) **5 DO 3 J=1,7 IF (J.LT.lJ) EX(J)=5. IF (J. EQ.4) EX (J) =7.5 IF(J.GT.<i) EX(.1)=10. 3 CONTINUE DO 5 J=2,7 XPOPW (J) =XPOPW (J-1) *( 1. +XPOPW (.1) /1 00. ) **EX (J) XPOPE (J) =XPOPE(J-1) *(1. • XPOPE (J) /100.) ** EX (J) XIPC (J) =XIPC (J-1) * (1. *XTPC(J)/100.) **EX (J) XRDPW (J) =XRDPW (J-1) *{ 1. * XRDPW (J) /100.) **E X (J) XRDPE(J)=XRDPE(J-1) *{1.+XBDPE(J)/100.)**EX(J) 5 XCOR (J) = XCOR (J-1) * (1. + XCOR (JJ/100. ) **EX (J) DO 10 1=1,7,2 10 E(I*1)=E(I) CALCULATION OF UNKNOWN CONSTANTS IN DEMAND EQUATIONS AWD=BQWD/(BPOP*BIPC**ELDI*BPWD**(-E(I)) ) 317 CM O o cc < a. o o H Z z TIO O A: O • t o n uo CN U"! CJ »— Cv Cv • f cj CJ CJ CJ cj ca Eu EH CD 1 t t i 1 z • * r— «* H HH * •» * » * a Q # » » * •» CJ _i i-l O a H W cs CC a cj CJ as Cv' 2 CJ Dt cj , , * » \ Cu cu & Cu Cb . , . z * # in m ta ca CQ ca » • H CN •» * « * • p~ co ••3 H u U H H w w 01 r- Q M M CS CE cu cj _ u CJ o un -! Cu Cu CJ cj fa u CJ w w w * * * * * * * Q • » * » » * * CJ * # «: u cs CS CJ CJ o o • a Eu ^ Cu o o a. Ou 3 CJ cn «— U n M CJ u t-t H Cu Qj II il z cn ca CO CQ CQ ca ca 1-3 s CJ «t * * » • * * * o Cu Cu CE Cu CU CU Cu o O Eu o ea c o c a a Cv, CU Cu Cu OS Oi CE CB cu ca cc Eu Eu X X o ca a a CD ca co ca r> ou r- # » Cv o » a a i &u 6u &u i Eu EH Eu * * * ' O H H I H OS B I uJ >J BMW H5C5U on O O Cu Cu ~ UUHHfc X X X X fu • * * • * CJ Cv CJ z cj ca _ a n o — Cv Cv Eu 10 » EH _ z n CJ o H EH CO CJ — z ca CJ ca ! CJ cz CJ 3E I CU Cu Cu Cu i a O o Q I CE & CU CB : x x x x »»•»»•»» CJ O CU Cb Q X CS CJ X «! CC • Q # CJ — EH Q CJ + CJ «- n — o \CB Cv ca CJ i WWWNi-QMMDSCBOO H CJDECJStCJDSCJi-a CQCOCQCacQCQCQCN II II II II II II II £5 M H CB CB O O CJ3CJ3CW3CCJC t t CJ CJ EH a •j o z Z || O Cv Cv O HHU thCOl <- p. IhflJKOOO * — . s w a &i a CJ a cj *- H \ CN II II II II II II II II O H H o »- n , . ~ — ^.„>H ~-0 || HsuKllT]']'5f}>5i5ilEio,l >-«,CN »*.«.»»»«CCN--«\'-OJ m a LCI O p CO »J MQw — —•"-W — SSO — II tvo «3 •"TlVrt,--1 < D O ' cj a • in i • U CN I 6u t-n o » Cv Z || ea o in II M — Eu O *"3 -a rn •—ij Cv D O QUO -1 CN <: CN U 1 CO H in « H CN » EH H Z o —o Q «d U m o CN m o o o o o o • ***»• »»•*»* Q ca a a a S" »- .- r- r- r- EH \\\\\\ , o MMUUHHOOtv OOMHBK--r. CJCJCJCJCJCJ4* Cv *»••** — — CJ »*»***OQi-J CjUCBCEUtJ + + < Cu Cv O C O* Cu • • CJ MHUUWM«-«-UC3 U (J U U — —»o »»»#»»\\H COCuCuCuCuCuCuCuCvC hooacoocc<( CJCUCuCBCBOiCvCBCBCB WCJOUUUUUtiO Cv I I I I I I I I O Cv • • I • I • < • CE Cj>-«-<-'-'-'-<-<-Cu C3\\WXWXZ Z ^^-.^—.^ .^rt! cjp-r^p^r-r-P-r^p-cs^-. ...... »»fu>-CSf-CMmslOlOPCOCfiO Cv«:<rt:'<<<«:<iCv . II II II II II II II II CN Z nnn^.^.^-.~„Cv — or^f*-r^r*p»r*r-r*-ow M. Eu «: wwwwn e CC4<<<44<<Cu3: CJ EH EH =3 ^ O CS I z I M CB CJ CJ EH CO Z CO —H ». . CN - m • o » o X CN X CN 13 *VCJ . — CN Tl EH —EH — «* CJ «: CJ = Eu E EH CE M CB M O CB O CB Cv 31 Cv 3B r~ CO O ca — a - cr . * o X CN X t- t- CN l£) *>IC If II « CJ "N-IHNO EH —EH — Z < CJ < O O CJ M c H c m H h CB M CE M Z O CB O O O CB O Cv 31 Cv C3 Q SB CJ O O un ic FILE: CBCALC FORTRAN A 07/25/80 18:16:00 UNIVERSITY OF WATERLOO PAGE 003 210 FORMAT(6X#,A(,,I1,',,»I1.,)=',E1t.7) DO 70 1=1,8 70 WRITE(2,220) I,E(I) 220 FORMAT (6X ,' E (•, 11, ') = • , E14. 7) WRITE (2,231) 231 FORMAT(6X,'F=0.D0') WRITE(2,232) 232 FORMAT(6X,'DO 200 J=1,7') WRITE(2,233) 233 FORMAT(6X,'DO 100 1=1,8') WRITE(2,234) 234 FORMAT(6X,•K=8*(J-1)+1') WRITE (2,235) 235 FORMAT (6X, ' F=F+A (I, J) *X (K) **E (I) ') WRITE (2,236) 236 FOR MAT (2X , ' 10 0 G (K) =E (I) * A (I, J) *X (K) ** (E (I) -1. DO) •) WRITE (2,237) 237 FORMAT(2X,'200 CONTINUE') WRITE(2,238) 238 FORMAT(6X,•RETURN') WRITE (2,239) 239 FORMAT(6X,'END') C PRODUCE EC DATA FILE, CORRECTLY DISCOUNTED K=5 WRITE(3,301) K,K,DF(1) DO 82 L=2,3 K=5*L 82 WRITE{3, 302) K,K,DF (L) DO 84 L=4,7 K=10*L-15 84 WRITE(3,302) K,K,DF (L) 301 FORMAT(4X,'0',11,•EC,6X,•0• ,11,'NMMEC',5X,*-1.0',9X,'OBJECTIV•,4X C,F8.5) 302 FOR HAT(4X,12,'EC,6X,I2,•NMMEC,5X,'-1.0',9X,•OBJECTIV,4X.F8.5) STOP END SENTRY OJ M CO The following is the FORTRAN program ENDPROG, which corrects the input files to MINOS for end effects. FILE: ENDPROG FORTRAN A 07/25/80 18:16:00 UNIVERSITY OF WATERLOO PAGE 001 JJOB WATFIV C INPUT LOGICAL UNITS: 1=DEMAND DATA A 2=LPDC DATA A 3=RBI DATA A C OUTPUT LOGICAL UNITS: 4=LPDC DATA B 7=RBI DATA D REAL*8 SS,TT,UU,YY,END/'END ATA '/ REAL D/'D V.H DIMENSION H (265) ,1(300) ,E(300) ,P(265) C READ DISCOUNT RATE DO 1 1=1,19 1 READ(1,102) SS READ(1,101) DISC 101 FORMAT (18X, Ft. 1) ALF=1/(1+DISC/100.)**10 C READ AND WRITE LPDC UP TO T=35 READ(2,201) SS WRITE(4,201) SS 201 FOR MAT (A8) DO 5 1=1,1475 READ{2,205) SS,TT,XX,UU,YY 5 WRITE(4,205) SS,TT,XX,UU,YY 205 FORMAT(4X,A8,2X,A8,4X,F7.4,6X,A8,4X,A8) DO 9 1=1,264 C READ FROM NON-EXHAUSTIBLE RESOURCE VARIABLES, T=35 READ(2,100) SS,M(I),TT,X(I),UU,YY 9 WHITE(4,100) SS,M(I),TT,X (I) ,UU,YY 100 FORMAT(4X, A8,2X,11,A8,3X,F7.4,6X,A8,4X,A8) M(265)=3 1=1 K=0 J=0 10 IF (I.GT.264) GO TO 40 IF (M (1+1) . NE. 4) GO TO 20 IF (H (1+2) . NE. 5) GO TO 30 K=K + 1 J=J + 1 C E*S ARE •A' AND 'K1+AK2' MATRICES; F IS 'A+K1+AK2' MATRIX E(K)=X(I) F(J)=X(I) + X (1*1) +ALF*X (1 + 2) K=K + 1 E (K) =X(I + 1) • ALT*X (1+2) 1 = 1+3 GO TO 10 20 K=K+1 J=J + 1 E(K)=X(I) F(J)=X(I) 1 = 1 + 1 GO TO 10 30 K=K+1 J= J + 1 E(K)=X(I) F(J)=X(I)+X(I + 1) K=K + 1 OJ E(K)=X(I+1) W 1=1+2 ° GO TO 10 FILE: ENDPBOG FORTRAN A 07/25/80 18:16:00 UNIVERSITY OP WATERLOO PAGE 002 40 CONTINUE C READ AND WRITE REMAINING T=35 DO 43 1=1,34 READ(2,205) SS,TT,XX,UU,YY 43 WRITE(4,205) SS,TT,XX,UU,YY C WRITE LPDC, T=45 DO 50 1=1,K READ(2,100) SS,MM,TT,XX,UU,YY IF (MM.EQ.5) XX=E(I) 50 WRITE(4,100) SS,MM,TT,XX,UU,YY C HEAD AND WRITE REMAINING, T=45 DO 53 1=1,34 READ(2,205) SS,TT,XX,UU,YY 53 WRITE(4,205) SS,TT,XX,UU,YY C WRITE LPDC, T=55 DO 60 1=1,J READ(2,300) SS,H,VV,TT,XX,UU,YY IP(H.EQ.D) XX=F(I) 60 WRITE{4,300) SS,H,VV,TT,XX,UU,YY 300 FORMAT(4X,A4,Al,A2,3X,A8,4X,F7.4,6X,A8,4X,A8) C BEAD AND WRITE REMAINING, T=55 DO 63 1=1,34 READ(2,205) SS,TT,XX,UU,YY 63 WRITE(4,205) SS,TT,XX,UU,YY C READ AND WRITE RHS TO BOUNDS READ(3,400) VV WRITE (7,400) VV 400 FOR MAT(A4) DO 70 1=1,47 READ(3,401) SS,TT,XX,DU,YY 70 WRITE(7,401) SS,TT,XX,UU,YY 401 FORMAT(4X,A8,2X,A8,2X,F9.4,6X,A8,3X,A8) READ(3,402) SS WRITE(7,402) SS 402 FORMAT (A8) C READ, CHANGE AND WRITE BOUNDS DO 80 1=1,300 READ(3,500) SS, MM , TT, X (I) IF(SS.EQ.END) GO TO 90 IF(MM.NE.S) GO TO 79 IF (X (1-1) . NE. 0.) GO TO 78 X(T)=0. GO TO 79 78 X (I)=X(I-1) * (X (1-1)/X (1-2) )/(1--ALF*X (1-1)/X(I-2)) 79 CONTINUE 80 WRITE(7,500) SS, MM, TT, X (I) 500 FORMAT(A8,6X,I1,A8,1X.F9.4) 90 WRITE(7,402) SS STOP Co END J°, SENTRY The following files represent the input files {other than the CALCFG object file) to MINOS. The file NLPSPEC DATA gives specifications such as tolerances, iteration limit, etc. to MINOS. The file LPDR DATA lists the rows of the linear constraints (since it repeats after the first period, changing only the time index, this listing is truncated after the end of the first period, for brevity). The file LPDC DATA gives the non-zero elements of the constraint matrix, by column, beginning with the nonlinear variables (again, when the largely repetitive part begins, the listing is truncated after the first period). The file RBI DATA contains the right hand side, the bounds, and the special bounds called INITIAL, which are used by MINOS as a first approximation to the nonlinear variables if no starting basis is specified. FILE: NLPSPEC D ATA A 05/10/80 22:25:00 UNIVERSITY OF SA1S2L00 BEGIN MINIMIZE OEJECTIVE = GEJECTIV EHS = FIRSIIE* BOUNDS = 3 BOWS 800 COLUMNS 1000 ELEMENTS (COEFFICIENTS) 5200 ITE BAT IONS 2000 LOG FJ2EQ 10 INSERT FILE 11 PUNCH FILE 12 SOLUTION FILE 13 ] NONLINEAH VAHIAELES 56 SUPEKBASICS LIMIT 57 HESSIAN DIMENSION 57 EBBOB MESSAGE LIMIT 100 DEBUG LEVEL 2 END FILE: iPDR DAI A A 04/ 1 9/80 09: 1 1:00 NAME ENEBSEC BCWS 8 OBJECTIV E 05WCCP1 E 05KCCP2 E 05ECCP1 E 05ECCP2 E 05BOPE1 E 05HOP22 1 058OPE3 E 05«OPB4 E 05HOCP5 E 05HOCP6 E 05 WOC PL E 05EC PR 1 E 05EOPE2 E 05EOCP3 E 05WGPR1 E 0 5SGPH2 E 05BGPB3 E 05KGPH4 E 05HGCP5 E 05KGCP6 E 05EGEB1 E 0 5EGPS2 E 05EGCP3 E Q5KECP1 E 05HECP2 E 05SECP3 E 05HECP4 E 05 SECP5 E 05WECP6 E 05EECP1 E 05EECP2 E 05EECP3 E 05EECP4 E 05EECP5 E 05EECP6 E 058TCP1 E 05STCP2 E 05EICP1 E 05ETCP2 E 05HDCP1 E 05WDCP2 E 05MDCP3 E 05HDCP4 E 05HDCP5 E 05WDCP6 £ 05EDCP1 E 05EECP2 E 05EDCP3 E 05EDCP4 E 05EDCP5 E 05EDCP6 E 05SCSB UNIVERSITY Or KATHHLOO F1L2: LPDH DA'iA A 04/1 9/80 09 : 1 1 :00 UNIVERSITY OF WATERLOO E 05ECSB E 05SOSBO E 05HCSBL E 05EOSBO E 05ECS3L i 05 NOMSS I 0 5 NC MEM E 0 5 KG SB E 05EGSB E 05WES3E L 05WEMH E 05EESBE I 05EEMH E 0 5KTSBL £ 05WTSEA L 05W1MEA E 05EIS31 E 05ETSBA I 05ETMEA £ 0 5HISB L 05RISLG L 05'<iISLL I 0 5SJISLC L 05WISLE G 05WISUG G 05HISUL G 05HISUC G 05SISUE E 05EISB L 05EISLG L 05EISLL L 05EISLC L 05EISLE G 05EISUG G 05EISUL G 05EISUC G 05EISUE E 05HDSBE E 05HDS3H E 0 5K.DSEO I OSBDSaP L 05HDSUS 1 05SDSOC L 05KDMCG E 05EDSBE E 05ECSBH E 05EDSEO i 05EDSUP I 05EBSUS L 05EDSUC L 05EBBCG L 0 5NHMEC E 10HCCP1 E 10SCCP2 E 10ECCP1 FILE: LPDC COLUMNS 05HDFC 05WDFC 05WDFC 05EEFC 05EDFC 05EEFC OSaiND 05HIND 058IND 05SIND 05SIND 05EIND 05EIND 05EIND 05EIND 05EIND 05ViB1:R 05EBTR 05B01H 05 ECTR 10HDFC 10HDFC 10 HDFC 10EEFC 10EDFC 1 OEDFC 10KIND 108IND 10HIND 10»IND 10«IND 10EIND 10EIND 10EIND 10EIND 10EIND 10HRTB 10ERTR 10B01R 10E0TR 15WDFC 15HDFC 15HDFC 15EDFC 15EDFC 15EDFC 15WIND 15HIND 15WIND 15HIND 15HIND 15EIND 15EIND 15EIND DATA 05WDS3H 05WDSUP 05WDSUC 0 5EDSBH 05EDSUP 05EDSUC 058IS3 05HISUG 05WIS01 05HISUC 05WIS0E 0 5EISB 05 E.I SUG 05EISUL 05EI50C 05EI5UE 05HTSBA 05EISBA 05H1S31 05 EISBL 1 0SDS3H 1 OWDSUP 1OWDSUC 10EDSBH 1 OEDSUP 10EDSUC 10WI3B 10HISUG 1 OMISUL 10WISUC ; 1OHISUE 10EISB 1OEISUG 10EISUL 10EISUC 10EISUE 10HTS3A 10ETSBA 10H1S3L 10 EISBL 15WDSBH 15WDSUP 15MDSUC 15ECSBH 15EDS0P 15EDSUC 15WIS3 1 5VMSUG 15WISUL 158ISUC 153ISUE 15EI33 - 15EISUG 15EISUL A 04/19/80 -0.366 1 0.0000 0.0000 -0. 866 1 0.0000 0.0000 - 1 . 0000 0.4840 0.3430 0.0840 0.2890 -1.0000 0.3140 0.3980 0. 1980 0.2900 -1.0000 -1.0000 0.6849 0. 6849 -0.8661 -0.2 165 -0. 0974 -0. S661 -0.216 5 -0. 1299 -1.0000 0.5130 0. 4070 0.138 0 0.3420 -1.0000 0.3850 0 .4490 0.2230 0.3430 -1.0000 - 1.0000 0.6623 0-6623 -0.8661 -0.4331 -0. 1949 -0.S661 -0.4331 -0.2598 -1.0000 0.5420 0.4720 0. 1920 0.3940 -1.0000 0-4570 0-4990 09:11:00 05SDSEO 05HDS0S 05EDSEO 05EDSUS 05HISLG 05HISLL 05HISLC 05HISLE 0 5EIS1G 0 5EISLL 0 5EIS.LC 05EISLE 1OHDSEO 10WDSU3 10ED5EO 1OEDSUS 10WISLG 1OHISIL 10HISLC 1OHISLE 1QEISLG 1 OEISLL 1OEISLC 10EISLS 15WDSE0 15HDSUS 15EDSE0 15EDSUS 15WISLG 15WISLL 15HISLC 15HISLE 15EISLG 15EI3LL 15EISLC UNIVERSITY -0.1339 -0.0 -0.1339 -0.0 + 0.384 •0.243 +0.044 +0.229 •0.214 •0.298 •0.158 +0.230 -0.1339 -0.0228 -0.1339 -0.0228 +0.3 13 +0.207 +0.058 •0.222 +0.185 +0,249 +0.143 +0.2 23 -0.1339 -0.0455 -0.1339 -0.0455 +0.242 •0.172 +0.072 •0.214 +0.157 +0.199 +0.129 327 FILE: LFDC DATA A 04/13/30 09: 1 1 : 00 UNIVERSITY OF WATSaLCO 15EIND 15EIND 158RIR 15ERTH 15HOTR 15EOTB 25WDFC 258DFC 258DFC 25EEFC 25EDFC 25EDFC 25HIHD 25HIND 25BIND 25HIND 25SIND 25EIHD 25EIND 25EIND 25EIND 25EIND 2582TB 25EBT.R 25H01R 25ECTB 35HDFC 35HDFC 35HDFC 35EDFC 35EDFC 35EDFC 358IND 35HIND 35BIND 35HIND 35SIND 35EIN.D 35EIND 35EIND 35E1ND 35EIND 3 5WH1B 35ERTR 35 5JOTR 35ECTB 4 5SDFC 458DFC 45SDFC 45EDFC USEDFC 45EDFC 45SIND 45HIND 45WIND 15EISOC 1 5EISUE 15'vlTSBA 15E1SBA 15><333L 15ETSBL 2 5SDS3H 258DSUP 25WDS0C 25EDSBU 25EDSUP 25EDSUC 25WISB 25alSUG 25HI50L 2 5BISUC 25BISDE 25EI3B 25EISUG 25EI3UL 2 5 EISUC 25EISUE 2 5 W1S 3 A 25E1S3A 25W1S3I 25ETS3L 35HDSBH 35WDSUP 3 5W.DSUC 35EBSBH 35EDS0P 35EDSUC 3 5WIS3 353ISUG 3 5 8ISU1 35WISUC 3 5 HISUE 35EISB 35EISUG 3 5EISOL 35EISUC 35EI5UE 358TSBA 3 5ElSB A 35WTS3L 35E1SBL 45WDSBH 45WDSUP 45WDSUC 45EDS3H 45EDSUP 45EDSUC 45 SISB 45HISUG 4S3ISUL 0.2490 0.3950 -1.0000 -1.000C 0.6410 0.6410 -0.8661 -0.3661 -0.3897 -0.8661 -0.366 1 -0.5197 -1.0000 0.6000 0.6000 0.3000 0.5000 -1.0000 0.6000 0.6000 0.3000 0.500C - 1.0000 -1.C00C 0.6024 0.6024 -0.8661 -0.366 1 -0.3897 -0.8661 -0. 866 1 -0.5197 -1.0000 0.6000 0.6000 0.3000 0.5000 - 1.0000 0.6000 0.6000 0.3000 0.5000 -1.0000 -1.0000 0.5848 0.5848 -0.866 1 -0.366 1 -0.3897 -0.8661 -0.8661 -0.5197 -1 .0000 0.6000 0.6000 15EISL2 •0.215 25WDSEO 25SDSUS 25EDSEO 25EDSU3 2 5HISLG 25WISLL 25BISLC 25HISLE 25EXSLG 25EISIL 25EISLC 25EISL2 35SD3EO 358DSUS 35EDSEO 35EDSUS 35WI3.LG 3 5MISLL 358I5LC 3 5HIS.LE 35EI3LG 35EISLL 3 5EISLC 35EI3LE 45'WDSEO 458DSUS 45EDSEO 45EDSUS 45WI3LG 45BISLL 4 5HIS.LC -0.1339 -0.0909 -0.1339 -0.0909 • 0. 1 • 0. 1 • 0. 1 • 0.2 • 0.1 • 0. 1 • 0.1 • 0.2 -0.1339 -0-1819 -0. 1.339 -0. 1819 • 0. 1 • 0.1 • 0. 1 • 0.2 • 0. 1 • 0. 1 + 0. 1 +0.2 -0.1339 -0.3 63 8 -0.1339 -0.3638 • 0. 1 + 0.1 +0. 1 LPDC DATA A 04/19/80 09:11:00 UNIVERSITY 0 45SIND 45WIND 45EIND 45EIND 45EIND 45EIND 45EIND 45HHTR 45ERTR 458GTH 45EOTR 55WDIC 558DFC 55HDFC 55EDFC 55EDFC 55 E DFC 558IND 5581ND 55BIND 558IND 55SIND 55EIND 55EIND 5 5 EIND 55EIND 55EIND 55SRTR 55ERTR 55WOTR 55EOTR 05BCX3 05HCX3 05HCX3 058CX4 05SCX4 05HCX4 Q5SCX6 05HCX6 05SCX6 058CD1 05SCD1 05HCD1 05WCD2 05HCC2 05BCD2 05BCE 05BCE 0SMCEX 05ECX4 05ECX4 05ECX4 05ECD1 05ECD1 05ECD1 45'riISUC 4 5WISUE 45EISB 45SISUG 45EISUL 4 5EISUC 4S3ISUE 4 5WTSBA 45E1SBA 4 5WTSB.L 45EISBL 55WDSBH 55SDSUP 55KDSUC 55EDSBH 55EDSUP 55EBSUC 55HISB 55'rflSUG 55WISUL 55WISUC 55 HISUE 55E.I5B S5SI3UG 55EISUL 55ElSUC 55 EISU £ 55B1S3A 55ETSBA 55BIS3L 55 EISBL 05HCSB 05WOSBO 10WGCPL 05SCS3 05 BGSB 10"dGC?6 0 5 8CSB 0 5SISLC 05 NMMEC 05WCCP 1 2 5 8CCP1 3 5WCC?1 05 WCCP 2 2 5 BCCP 2 35SCCP2 05HCS3 05HMMEC 0 5WCSB 05ECSB 05EISLC 05NHMEC . 05ECCP1 25ECCP1 3 5ECCP 1 0.3000 0.500G - 1 . 0000 0.6000 0.6000 0.3000 0.5000 - 1. 0000 -1.0000 0.5848 0.5848 -0.8661 -0. 866 1 -0.3897 -0.866 1 -0.866 1 -0.5197 -1.0000 0.6000 0.6000 0.3000 0.5000 - 1 .0000 0.600 0 0.6000 0.3000 0.500C -1.0000 -1.0000 0.5848 0.5848 -1.0000 0. 1072 -1 .0000 -1.0000 0.5670 -1.0000 -1.0000 -0.8700 0.0800 - 1. 0000 -2. 0000 -1.0000 -1.0000 -2.0000 -1.0000 -1.0000 0. 1030 -1 . 0000 -1.000 0 -0.8700 0.0400 -1.0000 -2.0000 -1.0000 458.ISLE 4 5-EISLG 4 5EISLL 45E.ISLC 45EISLE 55WDSEO 55WDSUS 55EDSEO 55EDSUS 55MISLG 5 58.1 SLL 55WISLC 55WISLE 5 5EIS.LG 55EI5LL 55EISLC 55EISLE 05HOCPL 0 5 N tl EC 05HGCP6 0 5 N M tl EC 058ISE 058ISUC 05ECSB 05NJiaEC 0 5EISB 0 5EISUC + 0.2 + 0. 1 + 0. 1 + 0. 1 + 0.2 -0.1339 -0.3638 -0.1339 -0.3638 + 0. 1 + 0. 1 + 0. 1 + 0.2 + 0. 1 + 0. 1 + 0. 1 + 0. 2 1.0 .1647 1.0 . 150 3 .87 -.87 .9994 -. 1 17 . 37 -.37 329 : LP DC D A'i A A 0 4/1S/S 05ECD2 05ECCP2 -1 .0000 05ECD2 2 5 ECC? 2 -2.0000 05ECD2 35ECCP2 -1.0000 05ECin 05ECSB 0.9994 05WOX6 05WCCP6 1.0000 05WOX6 0 5 NMMEC 2.500C 05WOX6 10SOCP6 -1.0000 0 5WOD1 05HOPR 1 -1.0000 05KOD1 10WOBH1 -1.0000 05HOD1 15WOPH1 -0.5.90 0 05HOD1 2 5 5JOPB1 -0.5600 05HCD2 05WOPR2 -1.0000 05HOD2 10 WO PR 2 -1.0000 05HCD2 15WQPR2 -0.5900 05SO.D2 2580PR2 -0.5600 05HOD3 05WOPR3 -1.0000 05SOD3 10HOPR3 -1.0000 O5HC03 15WOPR3 -0.5900 05SOD3 25H0PR3 -0.5600. 05801)4 05WOPR4 -1.0000 05BOD4 108OPR4 -1.0000 0580D4 15«OPR4 -0.5900 05SGD4 25 WOPH4 '-0.5600 05HCD5 0 5WOC?5 - 1 .0000 05SOD5 25WOCP5 -2-0000 05WOD5 35WOCP5 -1.0000 058OD6 05HOCP6 -1.0000 05SGD6 25WOCP6 -2.0000 05SOD6 35SCCP6 -1.0000 05HOEX Q5H03BO -1.000C 05WOEX 05NHMEC -1.4600 05HCE 05SOSBO -1.0000 05SOE 0 5 NO MEM 1.0000 0 5 WOG 05HOSBO -1.0000 05 HOG 05NGMSS -1.0000 05ECX3 0 5EOCP3 1.0000 0 5EOX3 058HMEC 2-5000 05ECX3 10EOCP3 -1.0000 05EOD1 05EQPR1 -1.0000 05EOD1 10EOPR1 -1.0000 05EOD1 15E0P31 -0.5900 05EOD1 25EOPR1 -0.5600 05EOD2 05EOPR2 -1.0000 05EOD2 10EOPH2 -1.0000 05EOD2 15EOPR2 -0.5900 05E0D2 25EOPR2 -0.5600 05EOD3 0.5EOCP3 - 1 .0000 0 5EOD3 25EOCP3 -2.0000 05EOD3 35EGCP3 -1.0000 05EOIH 0 5EOSBO 1.0000 05EOIH OSNHMEC 1.0800 05ECG 05EOSBO -1-0000 05EOG .05 NOMSS -1.0000 05WLX1 058OSBL -1.0000 Q5HLX1 05HESBE 0.4440 09: 1 1: 00 ONIV2BSITY OP WATERLOO Q 5NH3EC 05HG3EL +0.155 0.9272 05NOMSS 05EOSBO 0 5 N M il EC 05HOSBL 0 5EO3BL -1.0 1.0 .05 •0.9272 •0.9262 05NOaSS 05EOSBL 05NOaEi1 0 5WEC.P2 05N«M£C • 1.0 +0-9262 -0.54 • 1.0 •0.326 330 : LPDC DATA A 04/19/80 09:11:00 UNIVERSITY 05H1X1 103ECP2 -1.G000 0 58LX2 058O3BL -1 . 0000 0 5viDCP2 *• 1. 0 058LX2 0 5 W DSB H 3.8350 0 5NaaEC • 1. 7 1 0 5 81X3 058OSB1 -1 .0000 05HISLL -4. 13 058LX3 05SISU1 -4. 1300 os.NaaEc + 0. 04 0581X3 05 8ISB 4. 1300 0581X14 0 5WOS.BL -1.0000 05B1SB1 -1 . 0 0581X4 05Nai1EC 0.7700 05H1CC 05 3OCP1 -1.0000 05HLDC 25SOCPL -2.0000 05H1DC 35H0CP1 -1.0000 0 0 5EIX1 0 5EGSBL -1.0000 05EECP2 * 1. 05E1X1 05EE5BE 0.4518 05NaaEc + 0. 3 26 05ELX1 10EECP2 - 1 . 0000 05E1X2 05ECS31 - 1 .0000 05EDCP2 • 1. 0 05E1X2 05EDSBH 3.8350 osttaaEC * 1. 60 05E1X3 05EOSB1 -1.0000 05EI311 -4. 13 0 5EIX3 05EISU1 -4. 1300 05N«aEC • 0. 0 1 05E1X3 05EISB 4. 1300 05E1X4 05EOSBL -1.0000 05E13EL -1. 0 05E1X4 05Naa£C 0.690C 058GX5 05WGCP5 1.0000 0.5WGSE • 0. 8832 05HGX5 os.NaaEc 0.2500 • 05HGX5 1 0WGCP5 -1.0000 05HGD1 05SGPE1 -1.0000 058GD1 1 0 (iGPR 1 -1.0000 05BGD1 15WGPH 1 - 1.0000 05SGD1 • 25SGPS1 -0.9400 058GD1 35BGPR 1 -0.2100 05WGD2 0 5 8GPE2 -1.0000 05BGD2 108GPR2 - 1 .0000 05WGD2 15BGP.R2 -1 .0000 05HGD2 258GPR2 -0.940G 05MGD2 3 5 8GPR2 -0.2100 058GD3 0 5;JGPR3 -1.0000 05HGD3 108GPR3 -1.0000 05HGD3 1 58GPR 3 -1.0000 05*GD3 25SGPR3 -0.9400 05HGD3 35WGPR3 -0.2100 05SGD4 05WGPR4 -1.0000 05HGD4 10WGPR4 -1.0000 05SGD4 158GPR4 -1.0000 05BGD4 25BGPR4 -0.9400 05SGD4 353GPR4 -0.2100 05BGD5 058GCP5 -1.0000 05HGD5 25WGCP5 -2.0000 058GD5 35SGCP5 -1.0000 05BGD6 05HGCP6 -1.0000 05WGD6 2S8GCP6 -2.0000 05WGD6 35WGCP6 -1.0000 .0 058GX7 05HGSB -1.0000 05HECP3 *1 05BGX7 058ESBE 0.0764 0 5naa.EC + 0 .046 05BGX7 10HECP3 -1.0000 05HGX8 • 058GSB -1.0000 0 58DCP1 • 1 .0 058GX8 058DSBH 0.7600 05NM3EC *0 .265 331 : LPDC DA'I A A 0 4/19/80 09;11:00 UNIVERSITY 05WGX9 05WGSB -1.0000 05HISB + 0. 85 05SGX9 05HISLG -0.850 0 05WIS0G -0. 35 0 5WGX9 O5N03EC 0.0155 05WGE 05WGS8 -1.0000 05EGSB + 0. 953 05HGE 05 NHMEC 0.0440 05HGEX 05WGSB - 1.0000 QSNJiaEC -0. 167 05EGX3 05EGCP3 1.0000 05EGSB • 0. 958 05EGX3 OSNaaEC 0.2500 05EGX3 10EGCP3 -1.0000 05EGD1 05EGPE 1 -1.0000 05EGD1 10EGPR1 -1.0000 05EGD1 15EGPE1 -1.0000 05EGD1 25EGPR1 -0.9400 05EGD1 35EGPR1 -0.2 100 05EGD2 05EGPR2 -1.0000 05EGD2 10EGPR2 -1.0000 05EGD2 15EGPR2 -1.0000 05EGD2 2 5EGPH2 -0.940C 05EGD2 35EGPE2 -0.2100 05EGD3 05EGCP3 -1.0000 05EGD3 2 5EGCP3 -2.0000 05EGD3 35EGCP3 -1.0000 05EGX4 05EGSB -1.0000 05EECP3 * 1. 0 05EGX4 05EESBE 0.0777 05Nai1EC + 0. 046 05EGX4 10EECP3 - 1 .0000 05EGX5 0 SEGSB - 1 .0000 05EDCP1 • 1. 0 05EGX5 OSEDSBH 0.7600 .05NMMEC + 0. 276 05EGX6 05EGSB -1.0000 05EIS3 • 0. 85 05EGX6 05EISLG -0.8500 05EISUG -0. 85 05EGX6 05NHHEC 0.0055 05HEX4 05WESBE 0.3984 058MHEC f 1. 00 05WEX4 05WECP4 1.0000 05WEX4 10«ECP4 -1 .0000 05EEX4 05EESBE 0.9143 0 5 N M fl EC + 1. 00 05EEX4 05EECP4 1.0000 05EEX4 10EECP4 - 1.0000 05HEX5 05WECP5 1.0000 05WESBE + 0. 8983 05BEX5 0 5NI1HEC 0.770C 05BEX5 10WECP5 -1.0000 05HEX6 05HECP6 1.0000 05HE3BE • 0. 8983 05HEX6 05NMMEC 2.2900 05HEX6 10WECP6 - 1 .0000 05HED5 05WECP5 -1.0000 Q5HEMH + 0. 2 47 05HED5 25BECP5 -2.0000 056ED5 35WECP5 -1.0000 05WEE6 05SECP6 -1.0000 05WEHH -0. 7 53 05KED6 25HECP6 -2.0000 05HEE6 3 5HECP6 -1.0000 05SED1 05 MDHCG -0.4000 05HEB1 0 5HECP 1 -1.0000 0 5HEMH -0. 0718( 05KED1 2 5WECP 1 -2.0000 05WED1 35WECP 1 -1.0000 05HED2 0 5«fECP2 -1.0000 Q5WEMH -0. 372K 05HED2 2 5WECP2 -2.000C 059ED2 35HECP2 -1.0000 332 FILE: LPDC 0 5WED3 05KED3 05KED3 05HED4 05SEE4 05SED4 05KED4 05HEX9 05WEX9 05WEX9 05WEX10 05HEX10 05HEX11 05WEX11 05HEEX 05HCX5 05NCX5 05WCX5 05KCX5 05EEX5 05EEX5 05EEX5 05EEX6 05EEX6 0 5EEX6 05EED5 05EED5 05EEE5 05EED6 05EEE6 05EEB6 05EED1 05EED1 05EED1 05EED1 05EED2 05EED2 05EED2 05EED3 0 5EEE3 0 5EED3 05EED4 05EED4 05EED4 05EED4 05EEX9 05EEX9 05EEX9 05EEX10 05EEX10 05EEX11 05EEX11 05EEEX 05ECX3 05ECX3 DATA A 0 5SECP3 25WECP3 3 5UECP3 0 5 W DMCG 05HECP4 2 5 W EC? 4 3 5 H EC?4 05BES8E 0 5HISLE 05NMMEC 0 5SE53E 0 5W1SBA 05aESBE 0 5 NrtHEC 05KESBE 05WCSB 05 HECP 1 05WES8E 1OSECP 1 05EECP5 OSNMilEC 1 0EECP5 05EECP6 0 5Nai1EC 10EECP6 05EECP5 25EECP5 3 5EEC? 5 05EECP6 25EECP6 35EEC?6 05EDMCG 05EECP1 2 5EECP 1 35EECP 1 05EECP2 25EECP2 35EECP2 05EECP3 25EECP3 35EECP3 05EEMCG 0 5EECP4 25EECP4 35EECP4 05EESBE 05EISLE 05N83EC 05EESBE 05ETS3A 05EESBE 05Naa£C 05EESBE 05ECSB 05EECP 1 04/19/80 - 1 .OOOC -2.000G -1.0000 0.0000 -1.0000 -2.0000 -1.0000 - 1 .0000 -3.4120 0. 1800 -1.0000 2.3880 -1.0000 1.5500 -1.0000 -1.0000 1.0000 0.0857 -1.0000 1 .0000 0.7700 -1.0000 1.0000 2.29G0 - 1 . 0000 - 1 .0000 -2.0000 -1.0000 - 1.0000 -2.0000 -1.0000 -0.4000 - 1 . 0000 -2.0000 -1.0000 - 1. 0000 -2.0000 -1.0000 -1.0000 -2.OOOC -1.0000 0.0000 -1.0000 -2.0000 - 1 .0000 - 1 . 0000 -3.4 120 -0.1000 -1.0000 2.3880 -1.0000 1.0000 -1.0000 - 1. 0000 1.0000 09:11:00 05HEtiH 0 5 w E a H 05HIS3 05HI50E 05WTCP1 osaaaEc 05HDSEE 0 5 NBaEC 05NMHEC 0 5EESBE 05EESEE OSEEilH 05EEaH 0 5EEMH 05EE3H 0 5EEBH 0 5EEaH 05EISB 05EI3UE 05ETCP1 05NMelEC 05EBSBE 05'NMaEC UNIVERSITY OF ii AT ERLOO -0.06400 -0.753 •3.412 -3. 4 12 • 1.0 + 4. 1 8 • 1.0 -1.45 •0.0725 •0.9096 •0.9096 •0.221 -0.779 -0.07430 -0.38500 -0.06620 -0.779 +3.412 -3. 4 12 • 1.0 + 4.18 + 1.0 -1.45 333 FILE: LECC 0 5ECX3 05ECX3 05BLA 05WLA 058101 05WTD1 05STD2 05HTD.2 05ELA 05 ELA 05ETD1 05ETD1 05ETD2 05ETD2 058EE 05BEE 05 9EH 05WEH 05HEH 058EO 05BDD1 05WDD1 05HDD1 058DD2 05WDD2 05SDD2 05BDD3 0 5WBD3 05BDD3 05BDD4 05HDD4 05WDD4 05HDX5 058DX5 05HDX5 05BDX6 05BDX6 05SDD5 05BDD5 05BDD5 058DD6 05BDD6 05BDD6 05ESE 05EEB 05EEH 05EEH 05EEH 05EEO 0 5EDD1 05EDD1 05EDD1 05EDB2 05EDD2 05EDD2 DATA A 04/19/80 09:11:00 UNIVERSITY 05EESBE 0.0872 05NMHEC •0.0725 10EEC? 1 - 1 . 0000 • 1.0 0531CP2 • 1 .0000 0 5ST3E1 058T3BA 1 .3527 OSNMSEC 1.15 0 5HICP1 -1.0000 05WTMEA +2.388 10 WTCP 1 - 1 .0000 0.0 0S8TCP2 -1.0000 058taEA 10WTCP2 -1.0000 . • 1.0 05E1CP2 1 .0000 0 5EISBL 05E1SBA 1.3527 Q5NHHEC 1.36 05E1CP1 -1.0000 0 5EIHEA •2.388 10ETCP 1 -1 .0000 0.0 0 5EXCP2 - 1 . 0000 0 5EXMEA 10 ETC?2 - 1.0000 -1.0 0 5WDCP3 1.0000 058DSBE 05HBSBH 3.4120 05HMHEC •0.353 05BECP4 1.0000 05WDS8E -1.0 058D3BH 6-8240 05WDS0P +6.824 05NE1MEC 3. 1800 • 3.4 12 05WDSBE -1-0000 0 5WD32O 0 5 W DC? 1 -1.0000 1Q8DCP1 -1.0000 15HECP 1 -1.0000 05WDCP2 -1.0000 103CCP2 - 1. 0000 158DCP2 - 1 . 0000 05BDCP3 - 1.0000 10SDCP3 -1.0000 158DCP3 - 1 .0000 05»DC?4 -1.0000 10WISCP4 -1.0000 15BDCP4 -1.0000 + 1.0 05WICPS 1 .0000 05HDSBH 05NaaEC 0.6620 05HDSUC • 1.0 10WECP5 -1 .0000 + 1.0 05WDCP6 1.0000 05HDSBH 0 5NMHEC 0.7060 05BD3US + 1.0 058DCP5 -1.0000 OSHDMCS + 1.0 258DCP5 -2-0000 358DCP5 -1 .0000 0 58CCP6 -1.0000 10SDCP6 -1.0000 158 DC? 6 -1.0000 -1.0 05EDCP3 1.0000 05EDSBE 05EDS3H 3.4120 0 5suaEC +0.353 Q5EDCP4 1.0000 05EDSBE -1.0 0 5EDSBH 6-8240 05EDSUP +6.324 05NMtlEC 3. 1800 +3.412 05EBSBE -1.0000 05EDSEO 05EDCP1 -1.0000 10EECP1 -1.0000 15EDCP1 -1.0000 0 5E.CCP2 -1.0000 10EDCP2 - 1 .0000 15EDCP2 -1.0000 334 : EEDC DATA A 0 4/19/80 09:11:00 05EDD3 05EDCP3 - 1 .0000 0SEDD3 10 EDC? 3 -1.0000 05EDD3 1SEDCP3 -1 .0000 05EDD4 0 5 EEC? 4 -1.0000 05EDD4 10EDCP4 -1.0000 05EDD4 15EECP4 -1.0000 05EDX5 05EDCP5 1.0000 05ED53H Q5EEX5 0 5NMHEC 0.6620 05EDSUC 05EDX5 10 SECP5 -1.0000 05EDX6 05EDCP6 1 . 0000 05EDSBH 05EDX6 05NMHEC 0.7060 0 5EDS0S 05EDC5 05EECP5 - 1 .0000 0 5EDMCG 05EDD5, 2 5 EDC? 5 -2.0000 05EDD5 35EDCP5 -1.0000 05EDD6 05EDCP6 - 1 . 0000 05EDD6 10EECP6 -1.0000 05EDD6 15EDCP6 -1.0000 05BCX1 05SCCP 1 1.0000 05HCSB 05WCX1 OOHCBL 1 1.0000 0 5NMMEC 05HCX1 10WCC? 1 -1.0000 05HCX2 05WCCP2 1.0000 058CSB 05HCX2 0 0WCBL2 1 .0000 OSNMMEC 0 5HCX2 10WCCP2 -1.0000 05ECX1 05ECCP 1 1.0000 05EC53 05ECX1 OOECHL 1 1. 0000 05NaaEc 05ECX1 10ECCP 1 -1.0000 05ECX2 05ECCP2 1.0000 05ECSB 05ECX2 0 0ECHE2 1.0000 0 5NHMEC 05ECX2 10ECCP2 - 1 .0000 05BOX1 05MOEB1 1.0000 0 5H03BO 0580X1 05NMHEC 0.4000 OOBOfiil 05HOX2 05WOPR2 1.0000 05BOSEO 0580X2 0 5NMMEC 0.8000 008ORL2 05HOX3 05WCEH3 1.0000 05BOSBO 0580X3 0 5NSMEC 1.0000 00HOBL3 05WOX4 05 SOPH 4 1.0000 0580SBO 05HCX4 0 5NMMEC 1.400 0 008ORL4 05HOX5 05HOCP5 1.0000 058OSBO 05HOX5 05tiaaEC 1.2000 00WOR15 05BOX5 10WGCP5 -1.0000 05ECX1 0 5EOPB1 1.0000 05EOS3O 05EOX1 05 NHMEC 0.7000 00EOB11 05EOX2 05EOPH2 1.OOOC 05EOS3O 05EOX2 05Na.aEC 1.0000 00EOEL2 05HGX1 05HGPB1 1.0000 058GSB 0 5SGX1 0 5NMHEC 0.0300 00BGRL1 058GX2 05WGPR2 1.0000 05BGSB 05HGX2 05NMMSC 0.0800 0 0SGHX2 05BGX3 05BGPE3 1.0000 05BGS3 0 5BGX3 05NHBEC 0.2500 00WGRL3 05BGX4 0 5SGPR4. 1.0000 05HGSB 05BGX4 05NBMEC 0.3000 00BGRL4 05EGX1 0 5EGPR1 1.0000 0 5EGSB 05EGX1 05 NMMEC 0.0600 00EGB11 05EGX2 05EGPR2 1.0000 05EGSB UNIVERSITY OF HATEBLOO + 1.0 • 1.0 • 1.0 • 1.0 + 1.0 .9996 .02 .9996 .04 .9994 .03 .9994 . 16 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 .3832 1-0 .8832 1.0 .8832 1.0 .3832 1.0 .958 1.0 .9 58 335 : LPDC DATA A 04/19/80 09:11:00 UNIVERSITY 05EGX2 0 5 N n as c 0.300 0 O0EG2L2 1.0 10HCX3 10 8C53 -1.0000 1090CP.L 1.0 10SCX3 1 OWCSBO 0. 107 2 1 OHM3EC .1647 10WCX3 1 5WOCPI -1 . 0000 10WCX4 10WCSB - 1. 0000 1 Q8GCP6 1.0 108CX4 10 9GSB 0.5670 10NBMEC . 150.3 10BCX4 158GCP6 -1.0000 10BCX6 1OWCSB -1 .0000 1OBISE .87 10SCX6 10B.ISLC -0.8700 1 OHISUC -.87 10HCX6 10N8BEC 0.0800 10HCD1 10HCCP 1 -1.0000 10HCD1 25WCCP1 -2.0000 10BCD1 3 58CCP1 -2-0000 10BCD2 10 8CCP2 -1.0000 10HCD2 2 5SCCP2 -2-0000 10SCD2 3 5BCCP2 -2.0000 10BCE 10 3CSB -1.0000 1OECSB .9994 10BCE 1ONHMEC 0. 1030 10HCEX 10WCSB -1.0000 1ONaasc -.132 10ECX4 1OECSB -1.0000 10EXSB .37 10ECX4 1OEISLC -0.8700 1 OEXSUC -.87 10ECX4 1ONaaEC 0.04.0 0 10ECD1 1OECC? 1 -1.0000 IOECD'1 2 5ECCP1 -2.0000 10ECD1 35ECCP 1 -2.000C 10ECD2 10ECCP2 - 1 . 0000 10ECD2 25ECCP2 -2.0000 .10ECD2 35ECCP2 -2.0000 10ECIa 10ECS3 0.9994 lOSHaEC •0.175 10BOX6 108OCP6 1.0000 10WOSEL 0.9272 10BOX6 10NMMEC ' 2.5000 10BOX6 15BCCP6 -1.0000 108OD1 10WOPH 1 -1.0000 108OD1 15 MOpa i -1.0000 108CD1 2 5 HOPE 1 -0.9400 10SOD1 35HOPE1 -0.2100 10HGD2 10BOPE2 -1.0000 10BOD2 15BOPH2 -1.0000 10SOD2 2580PB2 -0.9400 10WOD2 35BOPR2 -0.2100 10BOD3 10 8OPE3 -1.0000 10BCD3 15SOPR3 -1.0000 10 SOD3 2 5HC.PE3 -0.9400 10WOD3 35WOPR3 -0.2100 10HOD4 108CPE4 -1.0000 10BCD4 15WOPB4 -1.0000 10HOD4 25WGPE4 -0. 9400 10SCD4 3580PH4 -0.2100 10BOD5 10BOCP5 -1.0000 10WCD5 25HOCP5 -2-0000 10 SOD5 35HOCP5 -2.0000 10WOD6 10MOCP6 -1.0000 108OD6 2580CP6 -2.0000 10HOD6 3 5BOCP6 -2.0000 10HOEX VOMOS30 -1 .0000 lOKoass -1.0 336 FILE: EBI DATA A 04/17/80 22:34:00 UNIVERSITY OF WATERLOO RfiS FIBSTTBY FIESTTEY FIESTIEY FIBSTTBY FIESTIEY FIBSTTBY FIBSTTRY FIBSTTBY FIESTTBY FIESTTBY FIESTTBY FIESTTBY FIBSTTBY FIBSTTBY FIESIIRY FIBSTTBY FIESTTBY FIBSTTRY FIESTTBY FIESTTBY FIESTTBY FIESTTBY FIESTTBY FIBSTTBY FIBSTTRY FIESTTBY FIESTTBY FIESTTEY FIBSTTBY FIBSTTRY FIBSTTRY FIESTTEY FIBSTTBY FIBSTTBY FIESTTBY FIBSTTBY FIBSTTBY FIESTTBY FIBSTTBY FIESTTEY FIBSTTBY FIBSTTRY FIBSTTRY FIBSTTBY FIBSTTBY FIBSTTBY FIBSTTBY BOUNDS LO B LO B LO B LO B LO B LO B 0 5tfCCP 1 1 5WCCP 1 05ECCP1 15ECCP1 05WECP5 1 5 8 E CP 5 05EECP5 15 EEC? 5 05 WECP 1 15WECP 1 05EEC? 1 1 5EEC? 1 05WECP3 1 5 Vi ECP 3 05EECP3' 1 5 E ECP3 0 58ECP2 15 H EC? 2 05EECP2 15EECP2 Q58ECP6 0 5EEC?4 0 5 WGC?5 0 5KTCP2 05wDC? 1 0 5 E EC? 1 0 5 w DCP 2 0 5 E DC? 2 0 5 8 DC ? 3 0 5 £ ECP 3 0 5WOPR 1 isaopa i 05EOP31 15EOP3 1 05BGPB1 153GPB 1 05EGPR1 15EGPB1 OOHCBL1 00ECBL1 OOHC.BL1 0080EL3 00HOBL5 00EOBL2 00HGHL2 0 0HGEL4 00EGBL2 0 5'd DFC 10 3 EEC 15BEFC 2 5WEFC 35 SDFC 458 EEC 2. -0 . 0. -0. 0 . -0. 0 . -0. 0. -0. 1. -0. 0. -0. 0. -0. 0. -0. 0. -0. 0, 0, 0, 0, 1 1 0 0 0 0 2 0 0 0 11 5 0 0 1537 22 6 4 200 2 59 93 29 103 0 1750 1750 0430 2 19 0 0330 6570 0330 5410 Q550 1930 1200 4320 0440 3050 ,0310 ,0130 ,0020 0730 .0070 ,0040 .0507 . 0880 .2420 . 1300 . 0300 . 1020 . 3880 .0700 . 2300 . 4170 .7330 .0026 .0006 . 6650 . 5330 .0006 .0002 .0000 .0000 .0000 .4000 . 0000 . 0000 .0000 .0000 . 0000 108CCP1 258CCP1 10ECCE1 25ECCP1 1 082C.E5 25HECP5 1 0EECE5 25EECE5 108ECE1 25HECP1 1GEECE1 25EECP1 109ECE3 258ECP3 10EECE3 2SEECP3 10SECP2 258ECP2 10EECP2 25EECP2 25SECP6 2 5EECP4 25WOCPS 05SICP2 1 OBBCE 1 10EDCP1 1 08DCP2 1GEDCP2 10HDCP3 1GEDCP3 1Q80EE1 2580PB1 10E0PE1 25E0PB1 10"WGEE1 25SGPR1 10EGP31 25SGPB1 O0WCa.L2 00ECBL2 00SOB.L2 0CWOBL4 OOEOBLI 0CHGBL1 0 0BG313 0 0EGBL1 -0.0 99 2.491 -0.053 0.060 -0.0 26 0.187 -0.065 0.471 -0.034 0.590 -0.075 1.301 -0.027 0.472 -0.0 19 0.333 -0.00 1 0.0 16 -0.005 0.079 0.004 0.0959 . 147 .517 .627 0.605 0.050 0.171 0.043 0. 137 1.374 0.3131 0.0014 0.0002 9.557 4.461 0.0004 0.0001 106.0 1.4 6.0 3.3 3.0 39.0 44.0 16.0 0. 0, 0. 0.6000 0.7000 1.0000 2. 6000 3.500 0 4.6000 FILE: RBI DATA A 04/17/80 22:34: 00 UNIVERSITY OF SATEBLOO IC B 558EFC 12.2561 IO B 05EDFC 1.3000 IC 8 10ECFC 1.5000 10 B 15EDFC 2.0000 LG B 2 5 E EEC 5. 2000 10 B 3 5 E DFC 6. 9000 LO B 4 5 £ DFC 9.0000 LO B 55EDFC 23.6145 LC B 0 5WIND 0. 50 0 0 LO B 108IND 0.6000 10 B 15HIND 0.8000 LO B 258IND 2.2000 LC B 358IND 2.8000 LG B 4.5 MIND 3. 800 0 LC 3 55W.IND 10.817 1 LO B 05EIND 1.3000 LO B 10 FIND 1 . 500 0 LO B 15EIND 2.0000 10 B 25EIND 5.3000 LO B 35EIND 6.9000 LC B 45EIND 9.0000 LO B 55EIND 23.6145 10 B 0SWE13 0.0838 LO B 10KBIH 0.1008 LC B 15HRI5 0.1331 LO B 25SEIR 0.3586 LC 3 35WEIE 0.4510 10 B 45HE.TH 0.597 1 LC B 55W.BIR 1.6 148 LO B 05EE1B 0. 1833 LC B 10EETR 0.2029 LO B 15EBTB 0.2608 LC B 25EBTR 0.6664 LO B 35EBIR 0.8.377 LO B 4 5 ESTE 1. 1087 LO B 55SE.IR 2.9963 LC B 05'iiOIR 0. 0352 LO B 1080IE 0.0473 LC B 15HOTR 0.0718 LO B 258CIH 0.2128 LC B 35SOTR 0.2976 LO B 45 80TB 0.3827 LG B 55W0TE 0.974 8 LO B 05EOTR 0.0749 LO B 10 E0T.3 0.C985 LO B 15ECTB _ 0 . 1451 LO B 25EOTR 0.4086 LO B 3 5ECTH 0.571 1 10 B 45EOTR 0.7345 LO B 55ECIE 1.3738 UP B 05HC.E 0.2150 UP B 10WCE 0.579 0 UP B 15WCE 0.8790 10 B 15 MCE 0.579 0 LO B 25WCE 1.7530 338 FILE: RBI DATA A 04/17/80 22:34:00 UNIVERSITY OF WATERLOO LO B 3 5«CE 1 .7530 UP 3 0 5HCEX 1.7000 UP B 10wCEX 2.2000 UP B 158CEX 2.8000 UP B 25*CEX 9.2000 UP B 35HCEX 14.8000 UP B 4 5 8CEX 24.2000 UP B 55HCEX 107.0678 DP B 05ECX1 0.5060 UP B 10ECX1 1.0120 DP B 15ECX1 2.0240 EX 3 0.5WOX6 0.C00G FX B 05WOX5 0.1810 FX B 10HCX5 0.372C FX B 15 3CX5 0.7670 FX B 25HOX5 2.756G DP B 0 5 8OEX 0.5970 UP B 1080EX 0.1520 DP B 15 8GEX 0.0730 UP B 25WOEX 0.067C FX B 35WOEX 0.0000 FX B 45 HOEX 0.0000 FX B 55 SCEX 0.0000 UP 3 05EOX1 0.0040 UP B 10EGX1 0.0500 UP B 15EOX1 0.2500 FX B 05ECX2 0.0000 FX B 10EOX2 0..000C UP B 15EOX2 0.0500 UP B 25E0X2 0.500 0 FX B 05EOX3 0.0000 IX B 0 5HLEC 0.0000 FX B 1O'SLDC 0.0000 FX B 05HGX5 0.0000 DP B 10WGX5 0.0005 UP B 15WGX5 0.0010 UP B 2 5 8GX5 0.0020 UP B 3 5WGX5 0.0020 DP B 45«GX5 0.0020 OE B 55HGX5 0.0033 FX 3 0 5 8GD6 0.0000 FX B 10WGC6 0.0000 DP B 0 5 WGE 4. 0920 DP B 108GE 4.8600 DP B 1 58GE 7.0080 UP B 0 5WGEX 5.40G0 UP B 10SGEX 3.4000 DP B 15SGEX 3.7000 DP B 25 SiGEX 0.3000 FX B 35HGEX 0.0000 FX B 458GEX 0.0000 FX B 558GEX 0.0000 DP B 05EGX1 0.0010 UP B 10EGX1 0.0010 DP B 15EGX1 2.4000 FIXE: EBI DATA A 04/17/80 22:34:00 UNIVERSITY OF WATERLOO EX B 05EGX2 0.0000 FX B 10EGX2 0.0000 FX B 15EGX2 0.0000 UP B 25EGX2 4.8000 FX B 05EGX3 0.0000 UP B 10EGX3 0.0010 UP B 15EGX3 0.0020 UP B 25EGX3 0.0040 UP B 35EGX3 0.0040 DP B 45EGX3 0.0040 QP B 55EGX3 0.0065 DP B 05SEX5 0.4500 UP B 10WEX5 . 0.6500 DP B 15HEX5 0.8600 DP B 2 5WEX5 2.5400 OP B 35WEX5 2. 5400 UP B 45SEX5 2.5400 UP B 55KEX5 4. 1337 FX B 05WED4 0.0000 FX B 10«ED4 0.0000 UP B 0 5WEEX 0.0161 DP B 1OwEEX 0.0169 UP B 1 5 M E EX 0.017S DP B 25 viEEX 0.0393 UP B 3 5 W E EX 0.0434 UP B 4 5 ViEEX 0.0480 UP B 55WEEX 0.G926 UP B 05EEX5 1.0 100 UP B 10EEX5 1.3100 UP B 15EEX5 1.6100 OP B 25EEX5 4.4200 DP B 3 5EEX5 4.4200 DP B 45EEX5 4.4200 DP B 55EEX5 7.1934 UP E 05E.EEX 0.0333 DP B 1OEEEX 0.0350 UP B 15EEEX 0.0368 DP B 25EEEX 0.0814 UP B 35EEEX 0.0898 DP 3 45EEEX 0.0992 UP B 55EEEX 0. 1909 FX INITIAL 05HCFC 2.519136 FX INITIAL 10WEFC 2.866363 FX INITIAL 15 *DFC 3.245430 FX INITIAL 2 5WDFC 7.370743 FX INITIAL 3 5 8 DFC 11.07340 FX INITIAL 4 53 DFC 14.0 FX INITIAL 55wDFC 18.8923 1 FX INITIAL 0 5 E DFC 7.835372 FX INITIAL 1OEBFC 3.480367 FX INITIAL '15EEFC 10.561S4 FX INITIAL 2 5EDFC 24.49453 FX INITIAL 3 5 EEFC 28.91066 FX INITIAL 45EDFC 35.77590 FX INITIAL 55EEFC 68. 15526 A 04/17/80 22:34: 00 ONIVEES.ITY. OF BAT ERLOO FX INITIAL 05 WIND 2. 215426 FX INITIAL 10 MIND 2. 724 187 FX INITIAL 15HIND 3. 571767 FX INITIAL 25 WIND 9. 451235 FX INITIAL 35BIND 12. 01701 FX INITIAL 4 5BIHD 15. 49 5 63 FX INITIAL 55HIND 27. 89744 FX INITIAL 05EIND 6. 236454 FX INITIAL 1OEIND 7. 998S4S FX INITIAL 15 EIND 10. 82588 FX INITIAL 25EIND 30. 57776 FX .INITIAL 35EIND 33. 3630 1 FX INITIAL 45E1ND 50. 22871 FX INITIAL 55E.IND 90. 42386 FX INITIAL 05 WEIR 0. ,4643166 FX INITIAL 1 OS RIB 0. 5542955 FX INITIAL 15 U ETR 0. ,6742355 FX INITIAL 25BETR 1. ,791336 FX INITIAL 3 5 BBTB 2. .318520 FX INITIAL 45WBTR 2. .871982 FX INITIAL 55ii BTR 4, .481712 FX INITIAL 05EBIR 0. .9786513 FX INITIAL 1OEETR 1, .171560 FX INITIAL 1.5EEIH 1, .430596 FX INITIAL 25EHTB 3. . 742 1 12 FX INITIAL 3 5 EE'IB 4. .85276 1 FX INITIAL 4 5EBTR 6. . 0 17024 FX INITIAL 55EETB 9, .389605 FX INITIAL 0.5 BOTE 0 . 1422828 FX INITIAL 10 BOTE 0, . 1590812 FX INITIAL 1 SWOTR 0 .1894716 FX INITIAL 25WCIB 0 .5077520 FX INITIAL 3 58 0TB 0 .6468614 FX INITIAL 45 BOTE 0 . 32906.94 FX INITIAL 55WCIB 1 .373961 FX INITIAL 05EOTE 0 .3343579 FX INITIAL 10ECT.R 0 .3797S60 FX INITIAL 15E0TR 0 .4604514 FX INITIAL 25EOTB 1 .216528 FX INITIAL .3 5ECTB 1 .548524 FX INITIAL 4 5EOTR 1 .983952 FX INITIAL 5 5EOTH 3 .287870 ENDATA The following is the raw output from the MINOS solution of the base case. The interested reader can look for any information on the base case not reported earlier (e.g. many dual activities and reduced costs, slack activities, etc.). FILE: SOLN DATA A 05/01/80 13: 45:00 UNIVERSITY OF WATERLOO PAGE 001 1 PROBLEM NAME STATUS ENERSEC OPTIMAL SOLN OB.TF.CTIVE VALnE PHASE 3 8.3387582555D 01 ITERATION 91 OBJECTIVE R1IS RANGES BOUNDS B OBJECTIV (MIN) FIRSTTRY SECTION 1 - ROWS NUMBER ... ROW.. AT ACTIVITY... SLACK ACTIVITY . . LOWER LIMIT. 961 OBJECTIV BS 2.019484D 01 -2.019484D 01 -9.999999E 29 962 05WCCP1 EQ 2.103000D 00 0.0 2.103000E 00 963 05WCCP2 EQ 0. 0 0.0 0.0 961 05ECCP1 EQ 1.750000D-01 0. 0 1.750000E-01 965 05ECCP2 EQ 0.0 0. 0 0.0 966 05WOPR1 EQ 2.417000D 00 0.0 2.417000E 00 967 05WOPR2 EQ 0.0 0.0 0.0 968 05WOPR3 EQ 0.0 0.0 0.0 969 05WOPR4 EQ 0.0 0.0 0.0 970 05WOCP5 EQ 8.800000D-02 0.0 8.800000E-02 971 05WOCP6 EQ 0.0 0.0 0.0 972 05WOCPL EQ 0.0 0.0 0.0 973 05EOPR1 EQ 2.600000D-03 0. 0 2.600000B-03 974 05EOPR2 EQ 0.0 0.0 0.0 975 05EOCP3 EQ 0.0 0. 0 0.0 976 05WGPR 1 EQ 1.166500D 01 0.0 1.166500E 01 977 05WGPR2 EQ 0.0 0.0 0.0 978 05WGPR3 EQ 0.0 0.0 0.0 979 05WGPR1 EQ 0.0 0.0 0.0 980 05WGCP5 EQ 0.0 0.0 0.0 981 05WGCP6 EQ 0.0 0. 0 0.0 982 05EGPR1 EQ 5.999999D-04 0.0 5.999999E-04 983 05EGPR2 EQ 0.0 0.0 0.0 981 05EGCP3 EQ 0.0 0. 0 0.0 985 05WECP1 EQ 5.109999D-01 0.0 5.409999E-01 986 05WECP2 EQ 1. 300000D-02 0.0 1.300000E-02 987 05WECP3 EQ 1.320000D-01 0.0 1.320000E-01 988 05WECP1 EQ 0.0 0.0 0.0 989 05WECP5 EQ 2.190000D-01 0.0 2.190000S-01 990 05WECP6 EQ 3.999997D-03 0. 0 3.999997E-03 991 05EECP1 EQ 1.193000D 00 0.0 1.193O0OE 00 992 05EECP2 EQ 7.299995D-02 0.0 7.299995E-02 993 05EECP3 EQ 3.049999D-01 0.0 3.049999E-01 994 05EECP4 EQ 5.070000D-02 0.0 5.070000E-02 995 05EECP5 EQ 6.569999D-01 0. 0 6.569999E-01 996 05EECP6 EQ 0.0 0. 0 0.0 997 05HTCP1 EQ 0.0 0.0 0.0 998 05WTCP2 EQ 2.120000D-01 0.0 2.420000E-01 999 05ETCP1 EQ ' 0.0 0.0 0.0 1000 05ETCP2 EQ 5. 170000D-01 0.0 5.170000E-01 1001 05WDCP1 EQ 1.129999D 00 0.0 1.129999E 00 ..UPPEI! LIMIT. 9.999999E 29 2. 103000E 00 0. 0 1. 750000E-01 0.0 2.1 17000E 00 0.0 0.0 0.0 a.aoooooE-02 0.0 0.0 2.600000E-03 0.0 0. 0 1. 166500E 01 0.0 0.0 0.0 0.0 0.0 5. 999999E-04 0.0 0. 0 5. 109999E-01 1. 3flO00OE-O2 1.320000E-01 0. 0 2.190000E-01 3.999197E-03 1. 193000E 00 7.299995K-02 3. 049999E-01 5.070000E-02 6.569999E-01 0.0 0.0 2.420000E-01 0.0 5.170OO0E-O1 1.129999E 00 DUAL ACTIVITY . . I -1.0000000 00 1 0.0 2 2.047760D-02 3 4.2887690-03 1 -6.4110400-03 5 3.2616*90-02 6 -1.0691410-03 7 1.463599D-02 8 5. 4935730-01 9 6.168713D-03 10 .2. 263300D-02 11 1.397918D-01 12 5.7446170-04 13 -3. 3362020-05 11 0.0 15 -1.5303610-02 16 -7.087722D-04 17 -9.396715H-02 18 -7.892511011-02 19 6.260280D-19 20 1. 1005720-0 1 21 -2.052871D-03 22 -6.8399580-09 23 2. 257958D-03 24 1.750115D-02 25 8.010116D-01 26 1.0344R2D-01 27 2.238535D-01 28 -5.868456D-02 29 1.8350220 00 30 1.9392090-01 31 1. 068544D 10 32 z 2.54O259D-01 3 3 < 1.9245160-01 11 --5. 45985 20-02 3 5 1.9245360-01 36 -4.4818830-01 37 -2.3865490-08 30 0 -2.379909D-01 39 i -2.0033050-07 10 > 4.7182210-05 11 JO O 0 to FILE: SOLN DATA A 05/04/80 13:45:00 UNIVERSITY OF WATERLOO PAGE 002 1002 05WDCP2 EQ 1.020000D- 01 0.0 1.020000E-•01 1.020000E- 01 2.5046370-01 42 1003 05WDCP3 EQ 6.999999D- 02 0.0 6.999999E-•02 6. 999999E- 02 7.223879D-01 4 3 1004 05WDCP4 EQ 0.0 0. 0 0.0 0.0 1.4458060 00 44 1005 05WDCP5 EQ 0.0 0.0 0.0 0.0 8.980664D-02 45 1006 05WDCP6 EQ 0.0 0.0 0.0 0. 0 1.368402D-01 46 1007 05EDCP1 EQ 1.030000D 00 0.0 1.030000E .00 1.030000E 00 -1.0320460-03 47 1008 05EDCP2 EQ 3.880000D- 01 0.0 3.880000E-•01 3. 880000E- 01 -4.1555730-02 48 1009 05EDCP3 EQ 2.300000D- 01 0.0 2.300000E-•01 2.300000E- 01 3. 651602D-03 49 1010 05EDCP4 EQ 0.0 0.0 0.0 0.0 3.5664560-01 50 1011 05EDCP5 EQ 0.0 0.0 0.0 0.0 8.133217D-03 51 1012 05EDCP6 EQ 0.0 0.0 0.0 0.0 2.8275140-02 52 1013 05WCSB EQ 0.0 0. 0 0.0 0.0 1.24-23370-02 53 1014 05ECSB EQ 0.0 0.0 0.0 0.0 9.630036D-02 54 1015 05WOSBO EQ 0. 0 0. 0 0.0 0.0 3.199354D-01 55 1016 05HOSBL EQ 0.0 0.0 0.0 0.0 3.450555D-01 56 1017 05EOSBO EQ 0.0 0.0 0.0 0.0 6.7059350-01 57 1018 05EOSBL EQ 0.0 0.0 0.0 0.0 5.3768410-01 58 1019 05NOMSS BS -2.968650D 00 2.968650D 00 -9.999999E 29 0.0 0. 0 59 1020 05NOHEM UL 0. 0 0.0 -9.999999E 29 0.0 -3. 1961210-01 60 1021 05WGSB EQ 0.0 0.0 0.0 0.0 6.4665620-03 61 1022 05EGSB EQ 0.0 0.0 0.0 0.0 1.3926580-01 62 1023 05WESBE EQ 0. 0 0.0 0.0 0.0 5.664908D-01 63 1024 05WEMII OL 0.0 0.0 -9.999999E 29 0.0 -2.9237050-01 64 1025 05EESBE EQ 0.0 0.0 0.0 0.0 5.596840D-O1 65 1026 05EEMH OL 0.0 0.0 -9.999999E 29, 0.0 -2.9517570-01 66 1027 05WTSBL EQ 0.0 0.0 0.0 0.0 -8.2316380-01 67 1028 05WTSBA EQ 0.0 0.0 0.0 0.0 1. 136410D 00 68 1029 05WTHEA BS 0.0 0.0 -9.999999E 29 0.0 0.0 69 1030 05ETSBL EQ 0.0 0.0 0.0 0.0 -9.6611880-01 70 1031 05ETSBA EQ 0.0 0.0 0.0 0.0 1. 338407D 00 " 71 1032 05ETMEA BS 0.0 0. 0 -9.999999E 29 0.0 0.0 72 1033 05WISB EQ 0.0 0.0 0.0 0.0 8.7399860-02 73 1034 05WISLG BS - 1. 26685 1D- 01 1. 266851D-•01 -9.999999E 29 0.0 0.0 74 1035 05WISLL UL 0.0 0.0 -9.999999E 29 0.0 -2.1624510-03 75 1036 05HISLC BS -8.445653D- 02 8.445653D--0 2 -9.999999E 29 0.0 0.0 76 1037 05WISLE UL 0.0 0.0 -9.999999E 29 0.0 -1. 1 1 38570-01 77 1038 05WISIIG BS 8.445634D-•02 -8. 445634D--02 0.0 9.999999E 29 0.0 78 10 39 05WISUL BS 2. 111414D-•01 -2. 111414D--01 0.0 9. 999999E 29 0.0 79 1040 05WISUC LL 0.0 0.0 0.0 9.999999E 29 1.602404D-02 80 1041 05WISUE BS 1.266848D-•01 -1.266848D--01 0.0 9. 999999E 29 0.0 81 1042 05EISB EQ 0. 0 0.0 0.0 0.0 1.3923810-01 82 1043 05EISLG UL 0.0 0.0 -9.999999E 29 0.0 -2.8621670-02 83 1044 05EISLL BS -6.535906D- 01 6.535906D--01 -9.999999E 29 0.0 0.0 8 4 1045 05EISLC BS -7.791410D-•07 7.7914100--07 -9.999999E 29 0.0 0.0 85 1046 05EISLE UL 0.0 0.0 -9.999999E 29 0.0 -6.5977800-03 86 1047 05RISUG BS 6.535906D-•01 -6.535906D--01 0.0 9.999999E 29 0.0 87 1048 05EISUL LL 0.0 0.0 0.0 9.999999E 29 7.5448050-03 88 1049 05ETSUC BS 2. 614353D-•01 -2.6 14353D--01 0.0 9. 999999E 29 0.0 89 1050 05ETSUE BS 3.921545D-•01 -3.921545D--01 0.0 9. 999999E 29 0.0 90 1051 05WDSBE EQ 0.0 0.0 0.0 0.0 1.528916D 00 91 1052 05WDSDH EQ 0.0 0.0 0.0 0.0 3.0152920-01 92 1053 05WDSEO EQ 0.0 0.0 0.0 0.0 4.4809980-0 1 9 3 1054 05WDSUP BS 0.0 0.0 -9.999999E 29 0.0 0.0 94 1055 05WDSUS BS 0.0 0.0 -9.999999E 29 0.0 0.0 95 1056 05WOSOC BS 0.0 0.0 -9.999999E 29 0.0 0. 0 96 o O OJ FILE : SOLN OATA A 05/04/80 13 1057 05WDMCG BS -4.695382D-02 1058 05EDSBE EQ 0.0 1059 05EDSBH EQ 0.0 1060 05EDSEO EQ 0.0 1061 05EDSUP BS 0.0 1062 05EDSUS BS 0.0 1063 05EDSUC DL 0.0 106") 05EDHCG BS 0.0 1065 05NHMEC UL 0.0 1066 10WCCP1 EQ -9.899998D-02 1067 10WCCP2 EQ 0.0 1068 10ECCP1 EQ -5.800000D-02 1069 10ECCP2 EQ 0.0 1070 10WOPR1 EQ 1.374000D 00 1071 10WOPH2 EQ 0.0 1072 10WOPR3 EQ 0.0 1073 10WOP R4 EQ 0.0 1071 10WOCP5 EQ 0.0 1075 10WOCP6 EQ 0.0 1076 10WOCPL EQ 0.0 1077 10EOPH1 EQ 1.400000D-03 1078 10EOPR2 EQ 0.0 1079 10EOCP3 EQ 0.0 1080 10WGPR1 EQ 9.556999D 00 1081 10WGPR2 EQ 0.0 1082 10WGPR3 EQ 0.0 1083 10WGPR4 EQ 0. 0 1084 10WGCP5 EQ 0.0 1085 10WGCP6 EQ 0.0 1086 10EGPB1 EQ 3.999998D-04 1087 10EGPR2 EQ 0.0 1088 10EGCP3 EQ 0.0 1089 10WECP1 EQ -3.1)000000-02 1090 10WECP2 EQ -9. 999999D-01) 1091 10WECP3 EQ -2.700000D-02 1092 1 OHECP4 EQ 0.0 1093 10KECP5 EQ -2. 600000D-02 1094 10WECP6 EQ 0. 0 1095 10EECP1 EQ -7.499999D-02 1096 10EECP2 EQ -1). 999999D-03 1097 10ERCP3 EQ -1.900000D-02 1098 10EECP4 EQ 0.0 1099 10EECP5 EQ -6.500000D-02 1100 10EECP6 SQ 0.0 1101 10WTCP1 EQ 0.0 1102 10WTCP2 EQ 0.0 1103 10ETCP1 EQ 0. 0 1104 10ETCP2 EQ 0. 0 1105 10WDCP1 EQ 6.270000D-01 1106 10WDCP2 EQ 5.000000D-02 1107 10WDCP3 EQ I). 300000D-02 1 108 10WDCP4 EQ 0.0 1109 10WDCP5 EQ 0.0 1110 10KDCP6 EQ 0. 0 1111 1 OEDCP1 EQ 6.050000D-01 13:1)5:00 UNIVERSITY OF WATERLOO PAGE 003 4.695382D-02 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 0.0 0.0 0. 0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -9.999999E 29 0.0 0.0 0.0 -9.999999E 29 -9.999999E 29 -9.999999E 29 -9.999999E 29 -9.999999E 29 -9.899998E-02 0.0 -5.800000E-02 0.0 1.374000E 00 0.0 0.0 0.0 0.0 0.0 0.0 1.i)OOO0OE-03 0.0 0.0 9.556999E 00 0.0 0.0 0.0 0.0 0.0 3.999998E-04 0.0 0.0 -3.400000E-02 -9.999999E-04 -2.700000E-02 0.0 -2.600000E-02 0.0 -7.499999E-02 -U.999999E-03 -1.900000E-02 0.0 -6.500000E-02 0.0 0.0 , 0.0 0.0 0.0 6.270000E-01 5.000000E-02 4.300000E-02 0.0 0. 0 0.0 6.050000E-01 0.0 0.0 0.0 0.0 0.0 • 0.0 0.0 0.0 0.0 -9.899998E-02 0.0 -5. 300000E-02 0.0 1.374000E 00 0.0 0.0 0.0 0.0 0.0 0. 0 1. 400000E-03 0.0 0.0 9. 556999E 00 0.0 0.0 0.0 0.0 0.0 3. 999998E-04 0.0 0.0 -3.U00000P.-02 -9. 999999E-0I) -2.700000E-02 0.0 -2.600000E-02 0.0 -7.499999E-02 -i). 999999E-03 -1.900000E-02 0.0 -6.500000E-02 0.0 0.0 0.0 0.0 0.0 6.270000E-01 5.000000E-02 i). 300000E-02 0.0 0.0 0.0 6.050000E-01 0. 0 1. 180601)0 00 1). 1009D3D-01 3.1)601530-01 0.0 0.0 -1.U53585n-02 0.0 -6.209199D-01 0. 0 8.0591990-03 3.654821)0-03 -8.081601)0-03 -5.771355D-02 1.963508D-O3 -3.5637660-02 2.2365210-01 -1.713513D-09 1). 526600D-02 5.940305D-02 -6. 2237460-04 -2. 31)88980-05 0. 0 -2.1)601)91)0-03 . 3.65850DD-0D 5. 9 1790(1 D-02 7.8456520-02 5. 9 17901ID-02 I). 177501D-02 9.856160D-04 2.0922070-09 1). 515915D-03 8.6093U1D-03 5.050SR10-01 5. 350011) D-02 1. 1 186880-01 -2.791D22D-02 9.2 199440-01 1.011)0830-01 5.8130D8D-01 1. 296853D-01 8.3252800-02 -2.361857D-02 8.9625520-01 . -I). 1)8 18830-01 1.5213260-07 2.3799090-01 -5.3161810-08 1). 718871)0-05 2.7232160-01 H. 3789050-01 2.077696D-01 -1.9713100-02 I. 6196890-02 -1.0320460-03 97 98 99 100 101 102 103 101) 105 106 107 108 109 110 111 112 113 11D 115 116 117 118 119 120 121 122 123 12D 125 126 127 128 129 130 131 132 133 13U 135 136 137 138 139 1tO 11) 1 142 143 144 145 146 147 11)8 149 150 151 00 it* o o PILE: SOLH DAT A A 05/04/80 13:45:00 UNIVERSITY OF WATERLOO PARE 004 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1 135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1 147 1148 1149 1 150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1 163 1 164 1165 1166 10EDCP2 10EDCP3 10EDCP4 10EOCP5 10EDCP6 10WCSB 1OECSB 10WOSBO 10WOSBL 10EOSBO 10EOSBL 10NOHSS 10NOMEM 10WGSB 10EGS3 10HESBE 10WEMH 10EESBE 10EEHH 10UTSBL 10WTSBA 10WT.1EA 10ETSBL 10ETSBA 10ETP1EA 10WISB 10WISLG 10WISLL 10WISLC 10WTSLE 10WISUG 10WISUL 10WISUC 10WISUE 10RISB 10EISLG 10EISLL 10EISLC 10EISLE 10EISUG 10EISUL 10EISUC 10EISUE 10WDSBB 10WDSBH 10WDSEO 1OWDSUP 10WDSUS 10WDSUC 10WDHCG 10EDSBE 10EDSBH 10EDSEO 1OEDSUP 10EDS0S EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ BS UL EQ EQ EQ UL EQ UL EQ EQ UL EQ EQ BS EQ BS UL BS OL BS BS LL BS EQ UL UL BS BS BS BS LL BS EQ EQ EQ BS BS BS BS EQ EQ EQ BS BS 1.709999D-01 1.3700000-01 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 0.0 0.0 -2.900331D 00 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 0.0 0. 0 0.0 -3.171957D-01 0.0 -2. 1 146330-01 0.0 2. 1 14629D-01 5. 286586D-01 0.0 3. 171952D-01 0.0 0. 0 0. 0 -6.297491D-01 -9.446241D-01 1. 5743720 00 1.5743720 00 0. 0 -9.303998D-07 0.0 0.0 0.0 -6.104429D-01 -6.428682D-02 -2.7462870-01 -4.427259D-02 0.0 0.0 0.0 -1.790738D 00 -1.885858D-01 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 2.900331D 00 0. 0 0.0 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.1719570-01 , 0.0 2.114633D-01 0.0 -2.114629D-01 -5.2865860-01 0.0 -3.1719520-01 0.0 0.0 0.0 6.2974910-01 9.4462410-01 -1.5743720 00 -1.574372D 00 0.0 9.3839880-07 0.0 0.0 0.0 6. 104429D-01 6.428682D-02 2.746287D-01 4.427259D-02 0.0 0. 0 0.0 1.790730D 00 1.8858580-01 1.709999E-01 1.370000E-01 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -9.999999E 29 -9.999999E 29 0.0 0.0 0.0 -9.999999E 29 0.0 -9.999999E 29 0.0 0.0 -9.999999E 29 0.0 0.0 -9.999999E 29 0.0 -9.999999E 29 -9.999999E 29 -9.999999E 29 -9.999999E 29 0.0 0.0 0.0 0.0 0.0 -9.999999E 29 -9.999999E 29 -9.999999E 29 -9.999999E 29 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -9.999999E 29 -9.999999E 29 -9.999999E 29 -9.999999E 29 0.0 0.0 0.0 -9.999999E 29 -9.999999E 29 1.709999E-01 -1.3550000-02 152 1.370000E-01 -4.4267080-02 153 0.0 -8.6304510-03 154 0.0 -7. 3572760-03 155 0.0 -1.8462190-03 156 0.0 7.7 1 40850-03 157 0.0 6.7511730-02 158 0.0 3. 1611770-01 159 0.0 3. 4093800-01 160 0.0 5.706 1380-0 1' 161 0.0 4. 2053060-0 1 162 0.0 0.0 163 0.0 -2.3521860-01 164 0.0 4.212914D-02 165 0.0 1. 0083000-0 1 166 0.0 3. 49880 1 0-0 1 167 0.0 -1.7081210-01 168 0.0 3. 67 19580-01 169 0.0 -1.549449D-01 170 0.0 -6.3781140-01 17 1 0.0 6.508903D-01 172 0.0 -2.4322620-02 173 0.0 -6.8656010-01 174 0.0 7.28979RO-01 175 0.0 0. 0 176 0.0 5. 65943 1D-02 177 0.0 0.0 178 0.0 -2.96914 10-02 179 0.0 0.0 180 0.0 -6.6289360-02 181 9.999999E 29 0.0 182 9.999999E 29 0.0 103 9.999999E 29 1. 2274680-02 184 9.999999E 29 0.0 185 0.0 9.631911D-02 186 0.0 -2.4799140-02 187 0.0 -6.437837D-03 188 0.0 0.0 189 0.0 0.0 190 9.999999E 29 0.0 191 9.999999E 29 0.0 192 9.999999E 29 9.9297530-04 193 9.999999E 29 0.0 194 0.0 9.4748220-01 195 0.0 1.8980620-01 196 c 0.0 2.7769120-01 197 z 0.0 0.0 198 < 0.0 0.0 199 0.0 0.0 200 0.0 0.0 20 1 0.0 7.5274570-01 202 0 0.0 2.7404450-01 203 0.0 2.2061720-01 204 i 0.0 0.0 205 > 0.0 0.0 206 TO O 0 CO : SOLM DATA A 05/04/80 13; :45:00 UNIVERSITY OF WATERLOO PAGE 005 1167 10EDSUC BS -1.074443D 00 1.0744430 00 -9.999999E 29 0.0 0.0 207 1168 10EDI1CG UL 0.0 0.0 -9.999999E 29 0.0 -1.7886660-02 208 1169 10NMMEC UL 0.0 0.0 -9.999999E 29 0.0 -3.8555000-01 209 1170 15WCCP1 EQ -1.750000D- 01 0.0 -1.750000E- 01 -1.750000E- 01 0.0 210 1171 15WCCP2 EQ 0.0 0.0 0.0 0.0 3. 482O0OD-04 211 1 172 15ECCP1 RQ -4.300000D- 02 0.0 -4.300000E- 02 -4.300000E- 02 1.827412D-03 212 1173 15ECCP2 EQ 0.0 0.0 0.0 0.0 -2.298360D-03 213 1 17U 15WOPH1 EQ 7. 3300000- 01 0.0 7.330000E- 01 7.330O00E- 01 -6.5948050-03 214 1175 15WOPR2 EQ 0.0 0. 0 0.0 0.0 -5.381751D-03 215 1 176 15WOPR3 EQ 0.0 0.0 0.0 0.0 3.5615570-02 216 1 177 15WOPR4 EQ 0.0 0.0 0.0 0.0 3.456913D-03 217 1 178 15WOCP5 EQ 0.0 0.0 0.0 0.0 -8. 567563O-10 218 1179 15WOCP6 EQ 0. 0 0.0 0.0 0.0 2. 263300D-02 219 1 180 15WOCPL EQ 0. 0 0.0 0.0 0.0 2. 2076700-02 220 1181 15EOPR1 EQ 5.999999D- 04 0.0 5.999999E-•04 5. 999999E- 04 2.2560350-03 221 1182 15EOPR2 EQ 0.0 0.0 0.0 0.0 -4.3405380-05 222 1 183 15EOCP3 EQ 0. 0 0.0 0.0 0.0 0.0 223 1 181 15WGPR1 EQ 5.533000D 00 0.0 5.533000E 00 5.5330OOE 00 5.88B804D-03 224 1185 15WGPR2 EQ 0.0 0.0 0.0 • 0.0 1.4071510-03 225 1 186 15WGPR3 EQ 0. 0 0.0 0.0 0.0 3.5373130-02 226 1187 15WGPR4 EQ 0. 0 0.0 0.0 0.0 2.507334D-03 227 1 188 15WGCP5 BS 0. 0 0.0 0.0 0.0 0.0 228 1189 15WGCP6 EQ 0.0 0.0 0.0 0.0 0.0 229 1190 15EGPR1 EQ 2.OOOOOOD- 04 0.0 2.000000E-•04 2. OOOOOOE- 04 4.7433990-03 230 1191 15EGPR2 EQ 0. 0 0.0 0.0 0.0 2. 655523D-08 23 1 1 192 15EGCP3 EQ 0. 0 0.0 0.0 0.0 1.4 122210-02 232 1 193 15WECP1 EQ -5.500000D- 02 0.0 -5.500000E-•02 -5. 500000E- 02 3. 2297550-03 233 1194 15WECP2 EQ -2.OOOOOOD- 03 0.0 -2.000000B-•03 -2.OOOOOOE-•03 1.996495D-01 234 1195 15WECP3 EQ -4.400000D- 02 0.0 -4. 400000E-•02 -4.400000E-•02 2.1416160-02 23 5 1 196 15KECP4 EQ 0.0 0.0 0.0 0.0 4.2400500-02 236 1 197 15WECP5 EQ -3.300000D- 02 0.0 -3.300000E-•02 -3.300000E-•02 -1.0490430-02 237 1198 15WECP6 EQ 0. 0 0.0 0.0 0.0 3.533S23D-01 23 8 1 199 15EECP1 EQ -1. 199999D- 01 0.0 - 1. 199999E-•01 -1. 199999E-•01 3.8343770-02 239 1200 15EECP2 EQ -6.999999D-•03 0.0 -6.999999E-•03 -6. 999999E-•03 2.0860360-01 240 1201 15EECP3 EQ -3. 100000D- 02 0.0 -3. 100000E-•02 -3. 100000E-•02 4.078939D-02 24 1 120 2 15EECP4 EQ 0.0 0.0 0.0 0.0 3. 5265390-02 242 1203 15EECP5 EQ -8.299994D-•02 0. 0 -8.299994E-•02 -8.299994E-•02 -1.000483D-O2 24 3 120 4 15EECP6 EQ 0.0 0.0 0.0 0.0 3. 4734700-01 244 1205 15WTCP1 EQ 0.0 0. 0 0.0 0.0 3.90 10580-01 245 1206 15WTCP2 EQ 0.0 0. 0 0.0 0.0 2.5009100-08 246 1207 15ETCP1 EQ 0. 0 0.0 0.0 0. 0 -2.301137D-01 247 1208 15ETCP2 EQ 0.0 0.0 0.0 0.0 5.316181D-00 248 1209 15WDCP1 EQ 0.0 0.0 0.0 0.0 -9.4370950-05 249 1210 15WDCP2 EQ 0. 0 0.0 0.0 0.0 -1.046868D-01 250 1211 15WDCP3 EQ 0.0 0.0 0.0 0.0 1. 964923D-02 251 1212 15WDCP4 EQ 0.0 0.0 0.0 0.0 -4.1553920-01 252 1213 15W0CP5 EQ 0. 0 0.0 0.0 0.0 -1.B93193D-02 253 1214 15WDCP6 EQ 0.0 0. 0 0.0 0.0 -3. 239378D-02 254 1215 15EDCP1 EQ 0.0 0.0 0.0 0.0 2.0640920-03 255 1216 15EDCP2 EQ 0. 0 0.0 0.0 0.0 5.5105730-02 256 1217 15EDCP3 EQ 0.0 0.0 0.0 0.0 4.426708O-02 257 1218 15EDCP4 EQ 0.0 0.0 0.0 0.0 1.726090D-02 258 1219 15EDCP5 EQ 0. 0 0.0 0.0 0.0 1. 1 453150-02 259 1220 15EDCP6 EQ 0.0 0.0 0.0 0.0 2. 198632D-02 260 1221 15WCSB EQ 0.0 0.0 0.0 0.0 4.789715 0-0 3 261 DATA A 05/04/80 13:45:00 UNIVERSITY OF WATERLOO PAGE 006 1222 15ECSB EQ 0.0 1223 15WOSBO EQ 0.0 1224 15WOSBL EQ 0. 0 1225 15EOSBO EQ 0.0 1226 15EOSBL EQ 0.0 1227 15NONSS BS -3.52161 ID 00 1228 15NOMEM BS -2. 500000D- 01 1229 15WGSB EQ 0.0 1230 15EGSB EQ 0.0 1231 15WESBE EQ 0. 0 1232 15WEW1 UL 0.0 1233 15EESBE EQ 0.0 1234 15EEMH UL 0.0 1235 15WTSBL EQ 0.0 1236 15WTSBA EQ 0.0 1237 15WTMEA BS -3. 269761D- 02 1238 15ETSBL EQ 0.0 1239 15ETSBA EQ 0. 0 1240 15ETMEA SBS -6.755552D- 02 1241 15WISB EQ 0.0 1212 15WISLG BS -6.267598D- 01 1213 15WISLL UL 0.0 1211 15VISLC BS -1.178397D- 01 1215 15WISLE UL 0.0 1216 15WISIIG BS 1.178395D- 01 1217 15WISUL BS 1.014599D 00 1218 15WISUC LL 0.0 1219 15WISUE BS 6.267596D-•01 1250 15EISB EQ 0.0 1251 15EISLG SBS -2. 118546D-•01 1252 15EISLL DS -8.944203D-•01 1253 15EISLC SBS -2.777718D-•01 1251 15EISLE BS -1.8177511) 00 1255 15EISUG BS 2.989941D 00 1256 15EISUL BS 2.310375D 00 1257 15EISUC BS 1.004146D 00 1258 15EISOE SBS 1.051265D--01 1259 15WDSBE EQ 0.0 1260 15WDSBII EQ 0.0 1261 15WDSEO EQ 0.0 1262 15WDSUP BS -1.381365D 00 1263 15WDSUS BS -1.451211D--01 1264 15WDSUC BS -6.216300D--01 1265 15WOMCG BS -5.918167D--02 1266 15EDSBE EQ 0.0 1267 15EDSBH EQ 0. 0 1268 15EDSEO EQ 0. 0 1269 15EDSUP BS -1.193063D 00 1270 15EDSUS BS -1.7202580- -01 1271 15EDSUC BS -2.695215D 00 1272 15EDMCG BS 0.0 127 3 15NMMEC UL 0. 0 1271 25WCCP1 EQ 2.1909990 00 1275 25WCCP2 EQ 0.0 1276 25ECCP1 EQ 6.OOOOOOD -02 0.0 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 3.5216110 00 -9.999999E 29 2.500000D- 01 -9.999999E 29 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -9.999999E 29 0.0 0.0 0.0 -9.999999E 29 0. 0 0.0 0.0 0.0 3.269761D- 02 -9.999999E 29 0. 0 0.0 0.0 0.0 6.755552D- 02 -9.999999E 29 0. 0 0.0 6.267598D- 01 -9.999999E 29 0.0 -9.999999E 29 4.178397D-•01 -9.999999E 29 0.0 -9.999999E 29 -4.178395D-•0 1 0.0 -1.044599D 00 0.0 0.0 0.0 -6. 2675960-•01 0.0 0.0 0.0 2. 1185460--0 1 -9.999999E 29 8.944203D--0 1 -9.999999E 29 2.7777180--01 -9.999999E 29 1.8177510 00 -9.999999B 29 -2.9899410 00 0.0 -2.310375D 00 0.0 -1.004146D 00 0.0 -1.051265D--01 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 1. 381 365D 00 -9.999999E 29 1.451214D -01 -9. 999999E 29 6.216300D -01 -9.999999E 29 5.918467D -02 -9.999999E 29 0.0 0.0 0.0 0.0 0. 0 0.0 1.4930630 00 -9.999999E 29 4.720258D -01 -9.999999E 29 2.6952150 00 -9.999999E 29 0. 0 -9.999999E 29 0. 0 -9.999999E 29 0.0 2.490999E 00 0.0 0.0 0.0 6.000000E -02 0.0 4.062512D-02 0.0 2. 065319D-0 1 0.0 2.2275120-01 0.0 2. 185011D-0 1 0.0 2.35914 90-01 0.0 0.0 0.0 0.0 0.0 2.7711000-02 0.0 4.772991D-02 0.0 2.1687710-01 0.0 -1.0027040-01 0.0 2.2081790-01 0. 0 -9.334424D-02 o.o -4.070815D-01 0.0 3.464913D-01 0.0 0.0 0.0 -4.0109400-01 0.0 3.689776D-01 0.0 5. 2081740-08 0.0 3.6966530-02 0.0 0.0 0.0 -1. 9286950-02 0.0 0.0 0.0 -3.9225530-02 9.999999E 29 0.0 9.999999E 29 0.0 9.999999E 29 9.448239D-03 9.999999E 29 0.0 0.0 5.7701910-02 0.0 4.515998D-08 0.0 0.0 0.0 -6.9174600-08 0.0 0. 0 9.999999E 29 0.0 9.999999E 29 0.0 9.999999E 29 0.0 9.999999E 29 -4.5981400-09 0.0 5.8793130-01 0.0 1.200575D-01 0.0 1. 7231280-01 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.602079D-01 0.0 1. 4702300-01 0.0 1. 348797D-01 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.3939000-01 2.490999E 00 0.0 0.0 -1. 2514000-03 6.OOOOOOE -02 -2.461358D-03 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 28 3 284 285 286 287 288 289 290 29 1 292 293 294 295 296 297 29R 299 300 301 30 2 303 304 30 5 306 c 307 z 300 < 309 JO 310 311 312 313 314 4 315 3> 316 X) SOLN DATA 05/04/80 13:45:00 UNIVERSITY OF WATERLOO PAGE 007 1277 25ECCP2 EQ 0.0 0.0 1278 25WOPR1 EQ 3.131000D- 01 0.0 1279 25HOPR2 EQ 0.0 0.0 1280 25WOPR3 EQ 0.0 0.0 1281 25WOPR4 EQ 0.0 0.0 1282 25WOCP5 EQ 1. 470000D- 01 0.0 1283 25WOCP6 EQ 0.0 0. 0 1284 25WOCPL EQ 0.0 0.0 1285 25EOPR1 EQ 2-000000D- 04 0.0 1286 25EOPR2 EQ 0.0 0.0 1287 25EOCP3 EQ 0.0 0.0 1288 25WGPR1 EQ 4.460999D 00 0.0 1289 25WGPR2 EQ 0.0 0.0 1290 25WGPR3 EQ 0.0 0.0 1291 25WGPR4 EQ 0.0 0.0 1292 25WGCP5 EQ 0.0 0.0 1293 25WGCP6 EQ 0.0 0.0 1294 25EGPR1 EQ 9.999999D- 05 0.0 1295 25EGPR2 EQ 0.0 0. 0 1296 25EGCP3 EQ 0.0 0.0 1297 25WECP1 EQ 5.900000D- 01 0.0 1298 25WECP2 EQ 1.600000D- 02 0.0 1299 25WECP3 EQ 4.719999D- 01 0.0 1300 25WECP4 EQ 0.0 0.0 1301 25WECP5 EQ 1. 870000D- 01 0.0 130 2 25WECP6 EQ 3.999997D- 03 0.0 1303 25EECP1 EQ 1.301000D 00 0.0 1304 25EECP2 EQ 7.900000D-•02 0.0 1305 25EECP3 EQ 3.329999D-•01 0.0 1306 25EECP4 EQ 9.590000D-•02 0.0 1307 25EECP5 EQ 4. 710000D-•01 0.0 1308 25EECP6 EQ 0.0 0.0 1309 25WTCP1 EQ 0.0 0.0 1310 25WTCP2 EQ 0.0 0.0 1311 25ETCP1 EQ 0.0 0.0 1312 25ETCP2 EQ 0.0 0.0 1313 25WDCP1 EQ 0.0 0.0 1314 25WDCP2 EQ 0.0 0.0 1315 25WDCP3 EQ 0.0 0.0 1316 25WDCP4 EQ 0.0 0.0 1317 25WDCP5 EQ 0.0 0.0 1318 25WDCP6 EQ 0.0 0.0 1319 25EDCP1 EQ 0.0 0.0 1320 25EDCP2 EQ 0.0 0.0 1321 25EDCP3 EQ 0.0 0.0 1322 25EDCP4 EQ 0.0 0.0 1323 25EDCP5 EQ 0.0 0.0 1324 25EDCP6 EQ 0.0 0.0 1325 25WCSB EQ 0.0 0.0 1326 25ECSB EQ 0.0 0. 0 1327 25WOSBO EQ 0.0 0.0 1328 25WOSBL EQ 0.0 0.0 1329 25EOSBO EQ 0.0 0.0 1330 25EOSBL EQ 0.0 0.0 1331 25NOMSS BS -7.039652D 00 7.039652D 00 0.0 0.0 2.370238D-03 317 3.131000E- 01 3.131000E- 01 5.176391D-02 318 0.0 0.0 4.072975D-03 319 0.0 0.0 -2.05629 5D-05 320 0.0 0.0 -7.633531D-03 321 1.470000E- 01 1.470000E- 01 -6.468713D-03 322 0.0 0.0 0.0 323 0.0 0.0 1.099286D-02 324 2.000000E- 04 2.000000E- 04 -2. 29 1335D-03 325 0.0 0.0 1.472503D-04 326 0.0 0.0 0.0 327 4.460999E 00 4.460999E 00 9.432895D-03 328 0.0 0.0 -1. 161755D-03 329 0.0 0.0 -8.634918D-04 330 0.0 0.0 -2.913630D-03 331 0.0 0.0 -1.923471D-19 332 0.0 0.0 0.0 333 9.999999E- 05 9.999999E- 05 -4.444399D-03 334 0.0 0.0 -3.218816D-08 335 0.0 0.0 0.0 336 5.900000E-•01 5. 900000E-•01 1. 382504D-03 337 1.600000E-•02 1.600000E-•02 9.501050D-02 338 4.719999E-•01 4.719999E-•01 1.635329D-02 339 0.0 0.0 8.658630D-03 340 1.870000E-•01 1.870000E--01 -6.394757D-03 341 3.999997E-•03 3.999997E-•03 1.716428D-01 342 1.301000E 00 1.301000E 00 1.337175D-02 343 7.900000E-•02 7.900000E--02 1.01009«D-01 344 3.329999E--01 3. 329999E--01 2.251526D-02 345 9.590000E--02 9.590000E--02 1.872463D-02 346 4.710000E--01 ' 4.710000E--01 -5. 3121220-03 347 0.0 0.0 1. 8724630-02 348 0.0 0.0 2.536006D-01 349 0.0 0.0 -1.000050D-07 350 0.0 0.0 2.301138D-01 351 0.0 0.0 -6.854675D-08 352 0.0 0.0 4.718645D-05 353 0.0 0.0 5.234340D-02 354 0.0 0.0 -9.824616D-03 355 0.0 0.0 2.077696D-01 356 0.0 0.0 1. 104317D-02 357 0.0 0.0 1.619689D-02 358 0.0 0.0 -1.032046D-03 359 0.0 0.0 2.480540D-03 360 0.0 0.0 0.0 361 0.0 0.0 -8.630451D-03 362 0.0 0.0 -2. 868524D-03 363 0.0 0.0 4.875548D-03 364 0.0 0.0 2.343537D-03 365 0.0 0.0 1.44 1659D-02 366 0.0 0.0 9.927222D-02 367 0.0 0.0 1.070667D-01 368 0.0 0.0 1.051287D-01 369 0.0 0.0 1.135054D-01 370 -9.999999E 29 0.0 0.0 371 DATA A 05/01/80 13:45:00 UNIVERSITY OF WATERLOO PAGE 008 1332 25NOHEH BS 1333 25WGSB EQ 1334 25EGSB EQ 1335 25WESBE EQ 1336 25WENH UL 1337 25EESBE EQ 1338 25EEHH UL 1339 25WTSBL EQ 1340 25WTSBA EQ 1341 25WTMEA SBS 1342 25ETSBL EQ 1343 25ETSBA EQ 1344 25ETNEA SBS 1345 25WISB EQ 1346 25WISLG BS 1347 25WISLL UL 1348 25WISLC BS 1349 25WISLE UL 1350 25WISUG BS 1351 25WISUL BS 1352 25WISUC LL 1353 25WISUE BS 1354 25EISB EQ 1355 25EISLG UL 1356 25EISLL BS 1357 25EISLC BS 1358 25EISLE SBS 1359 25EISUG BS 1360 25EISUL BS 1361 25EISUC LL 1362 25EISUE BS 1363 25WDSBE ' EQ 1364 25WDSBH EQ 1365 25WDSEO EQ 1366 25WDSUP BS 1367 25WDSUS BS 1368 25WDSUC BS 1369 25WDMCG BS 1370 25EDSBE EQ 1371 25EDSBH EQ 1372 25EDSEO EQ 1373 25EDSUP BS 1371 25EDSUS BS 1375 25EDSUC BS 1376 25EDHCG UL 1377 25NMMEC UL 1378 35WCCP1 EQ 1379 35WCCP2 EQ 1380 35ECCP1 EQ 1381 35ECCP2 EQ 1382 35WOPR1 EQ 1383 35WOPR2 EQ 1384 35WOPR3 EQ 1385 35WOPR1 EQ 1386 35WOCP5 EQ -1.771767D 00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -5.627381D-01 0.0 0.0 -1. 178233D 00 0.0 -2.822719D 00 0.0 -1.881812D 00 0.0 1.881811D 00 4.704530D 00 0.0 2.822718D 00 0.0 0.0 -8.357323D 00 -6.051851D 00 -7. 204573D-01 1.512963D 01 6.772304D 00 0.0 8.357319D 00 0.0 0.0 0.0 -6.197691D 00 -6.504674D-01 -2.788639D 00 -3. 085638D-01 0.0 0.0 0. 0 -2.043285D 01 -2. 144492D 00 -1.226065D 01 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.771767D 00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.627381D-01 0.0 0.0 1.178233D 00 0.0 2.822719D 00 0.0 1.881812D 00 0.0 -1.881811D 00 -4.704530D 00 0.0 -2.822718D 00 0.0 0.0 8.357323D 00 6.051851D 00 7.204573D-01 -1.512963D 01 -6.7723040 00 0.0 -8.357319D 00 0.0 0.0 0.0 6. 197691D 00 6.504674D-01 2.788639D 00 3.085638D-01 0.0 0.0 0.0 2.043285D 01 2.1444920 00 1.226065D 01 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -9.999999E 29 0.0 0.0 372 0.0 0.0 1.954536D-02 373 0.0 0.0 2.578193D-02 374 0.0 0.0 1.075196D-01 375 -9.999999E 29 0.0 -2.890000D-02 376 0.0 0.0 1.0645320-01 377 -9.999999B 29 0.0 -2.403676D-02 378 0.0 0.0 -1.972568D-01 379 0.0 0.0 1.438535D-01 380 -9.999999B 29 0.0 1.155593D-07 381 0.0 0.0 -1.9432510-01 382 0.0 0.0 1. 532424D-01 383 -9.999999E 29 0.0 7.9208180-08 384 0.0 0.0 2.5130450-02 385 -9.999999E 29 0.0 0.0 386 -9.999999E 29 0.0 -1.928124D-03 387 -9.999999E 29 0.0 0.0 388 -9.999999E 29 0.0 -1.256093D-02 389 0.0 9. 999999E 29 0.0 390 0.0 9.999999E 29 0.0 391 0.0 9.999999E 29 1.166615D-02 392 0.0 9.999999E 29 0.0 393 0.0 0.0 2.7766770-02 394 -9.999999E 29 0.0 -3.322813D-03 395 -9.999999E 29 0.0 0.0 396 -9.999999E 29 0.0 0.0 397 -9.999999E 29 . 0.0 -6.855731D-09 398 0.0 9.999999E 29 0.0 399 0.0 9.999999E 29 0.0 400 0.0 9.999999E 29 5.810690D-03 401 0.0 9.999999E 29 0.0 402 0.0 0.0 2.8907100-01 403 0.0 0.0 6.649687D-02 404 0.0 0.0 8.472186D-02 405 -9.999999E 29 0.0 0.0 406 -9.999999E 29 0.0 0.0 407 -9.999999E 29 0.0 0.0 408 -9.999999E 29 0.0 0.0 409 0.0 0.0 2.235832D-01 410 0.0 0.0 7.78 1822D-02 411 0.0 0.0 6.552849D-02 412 -9.999999E 29 0.0 0.0 113 -9.999999E 29 0.0 0.0 111 -9.999999E 29 0.0 0.0 115 -9.999999E 29 0.0 -6.188460D-03 416 c -9.999999E 29 0.0 -1.1713000-