UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A long term energy policy model for Canada 1980

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1980_A1 F94.pdf
UBC_1980_A1 F94.pdf [ 25.41MB ]
Metadata
JSON: 1.0076882.json
JSON-LD: 1.0076882+ld.json
RDF/XML (Pretty): 1.0076882.xml
RDF/JSON: 1.0076882+rdf.json
Turtle: 1.0076882+rdf-turtle.txt
N-Triples: 1.0076882+rdf-ntriples.txt
Citation
1.0076882.ris

Full Text

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 B r i t i s h Columbia, 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (In t e r d i s c i p l i n a r y . S t u d i e s --"Energy Policy"Modelling) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1980 (c) John David F u l l e r , 1980 In present ing t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t ha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r re fe rence and study. I f u r t h e r agree that permiss ion f o r ex tens i ve copying of t h i s t he s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood tha t copying or p u b l i c a t i o n of t h i s t he s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed without my w r i t t e n permi s s ion . >3>gpS>ptKrg£Ptx:scf I n t e r d i s c i p l i n a r y Studies The U n i v e r s i t y of B r i t i s h Columbia 2075 wesbrook P lace Vancouver, Canada V6T 1W5 Date September 15, 1980. ABSTRACT The construction of a dynamic, long term model of the Canadian energy sector i s discussed, with examples of p o l i c y analysis done with the model. A l i n e a r process model of energy supply, conversion, d i s t r i b u t i o n and end- use i s l i n k e d to a model of the demands f o r services provided by energy i n combination with other inputs. Nonlinear programming i s used to f i n d the supply-demand equilibrium by maximizing the discounted sum of consumers' plus producers' surplus over a l l periods — three five-year periods followed by three ten-year periods, from 1975 to 2020. Long-run marginal cost curves for coal, o i l and natural gas are approximated by l i m i t i n g the t o t a l amounts av a i l a b l e at d i f f e r e n t cost l e v e l s . Upper l i m i t s on exports represent current p o l i c i e s and bring about a two p r i c e system (domestic and i n t e r - national) i n the model. Two regions are distinguished throughout the model: the west, ..west of the Ontario-Manitoba border, i s the main producer of coal, o i l and gas; the east, with the larger energy demands, may import coal,, o i l and gas from the west, or coal and o i l from other countries, i f necessary. The model may be used to analyze issues of energy p r i c i n g , the timing of the introduction of f r o n t i e r resources and new technologies, the competitiveness and impacts of some new technologies, the impacts of various l e v e l s of energy exports, and the impacts of various p o t e n t i a l p o l i c y constraints. A base case i s developed, with the best estimates of a l l parameters. In addition, low demand and high demand cases are developed to t e s t the s e n s i t i v i t y of conclusions to base case assumptions about economic and population growth. Some important conclusions are as follows. F r o n t i e r natural gas w i l l not be needed u n t i l a f t e r the year 2000. Coal l i q u e f a c t i o n w i l l probably not be competitive, but coal g a s i f i c a t i o n may play an important r o l e a f t e r the year 2000. Nuclear power w i l l be important i n the east. However, a "no-new-nuclear" p o l i c y a f t e r 1985 would have n e g l i g i b l e cost, but would force a switch i n the east from e l e c t r i c i t y to o i l with the t a r sands playing an important role a f t e r the turn of the century. D i s t r i c t heating by cogeneration with nuclear e l e c t r i c i t y i n the east may increase nuclear safety by reducing r e l i a n c e on nuclear power through the p a r t i a l displacement of e l e c t r i c resistance heating. The e l e c t r i c automobile w i l l probably not be competitive unless there are technical breakthroughs which lower the i n i t i a l cost difference between the conventional and e l e c t r i c automobiles, or the road tax burden i s less f o r e l e c t r i c than f o r con- ventional cars. i v Table of Contents Page Abstract i i L i s t of Tables v i i L i s t of Figures x Acknowledgements x i i i Chapter 1. Introduction 1 Chapter 2. Review of the L i t e r a t u r e 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 f o r the Base Case 42 Chapter 6. Discussion of the Base Case Output 50 6.1 O i l 50 6.2 Natural Gas 63 6.3 Coal 74 6.4 E l e c t r i c i t y 81 6.5 Transportation 92 6.6 Industry 100 6.7 DFC Heating 104 6.8 Sectoral Shares 110 6.9 Fuel Shares 110 6.10 Tot a l Energy 122 Chapter 7. The High Demand and Low Demand Cases 128 7.1 The Assumptions 128 7.2 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 P o l i c y Questions 162 8.1 The Impacts of a No-New-Nuclear P o l i c y , 162 8.2 Allowing Heating by Cogeneration with Nuclear Power. 175 8.3 High O i l Costs ( S e n s i t i v i t y Analysis) 182 8.4 The Impacts of Competitive Coal G a s i f i c a t i o n 190 8.5 The Impacts of the E l e c t r i c Automobile 199 Chapter 9. Summary and Conclusions 209 References 217 Appendix A. Derivation of the Demand Equations 225 Appendix B. Detailed Structure of the Model 234 B . l Coal 235 B.2 O i l 237 B.3 Gas — Natural and Synthetic 240 B.4 E l e c t r i c i t y 242 B.5 Transportation End Use Sectors 244 B.6 I n d u s t r i a l 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 E f f e c t s 253 Appendix C. Data f o r the Base Case 257 C l Data f o r the Coal Sector 257 C. 2 Data f o r the O i l Sector 262 v i Table of Contents (continued) Page Appendix C.3 Data f o r the Gas Sector 269 C.4 Data for the E l e c t r i c i t y Sector 274 C.5 Data for Transportation End Use Sectors 279 C.6 Data f o r I n d u s t r i a l End Use Sector 281 C.7 Data for Domestic, Farm and Commercial (DFC)Sector. 283 C.8 Data f o r the Objective Function 286 C.9 Right-Hand Side Values ( I n i t i a l 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 L i s t i n g s for the Base Case 313 v i i L i s t of Tables gage 1. Units Used i n the Model 36 2. O i l Production, Base Case 51 3. Crude O i l Pr i c e s , Base Case 53 4. National O i l P r i c e , Real and Nominal Dol l a r s , Base Case 59 5. O i l Use, Base Case 61 6. Gas Production, Base Case 65 7. Gas Use, Base Case 67 8. Gas P r i c e s , Base Case 69 9. Gas Prices as Percentages of O i l Pr i c e s , Base Case 73 10. Coal Production, Base Case 75 11. Coal Use, Base Case 77 12. Coal P r i c e s , Base Case 79 13. Western E l e c t r i c i t y Production, Base Case 82 14. Eastern E l e c t r i c i t y Production, Base Case 84 15. E l e c t r i c i t y Use, Base Case 86 16. Western E l e c t r i c i t y P r i c e s , Base Case 88 17. Eastern E l e c t r i c i t y P r i c e s , Base Case 90 18. Transportation, Base Case 93 19. Western Output Energy P r i c e s , Base Case 95 20. Eastern Output Energy Pr i c e s , Base Case 97 21. Road Transportation P r i c e s , Base Case 99 22. I n d u s t r i a l Output Energy, by Fuel, Base Case 101 23. Shares of Fuels i n I n d u s t r i a l Output Energy, Base Case 103 24. DFC Heating, West, Base Case 105 v i i i •List of Tables (continued) Page 25. DFC Heating, East, Base Case 107 26. Heat Pump Costs (in model u n i t s ) , 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. T o t a l Energy, Base Case 123 33. To t a l Energy, Percent Annual Change, Base Case 125 34. Low, Base and High Case Assumptions 129 35. Growth i n To t a l Energy Demands Per Capita, Three Cases 133 36. Crude O i l Production, High Case 134 37. Crude O i l Production, Low Case 136 38. Crude O i l Pr i c e s , High Case 138 39. Crude O i l P r i c e s , Low Case 140 40. Gas Production, High Case 142 41. Gas Production, Low Case 144 42. Gas Pr i c e s , High Case 146 43. Gas P r i c e s , 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 i x L i s t of Tables (continued) Page •49. Total Energy, Low Case 160 50. Crude O i l Production, No-new-nuclear Case 167 51. O i l Use, No-new-nuclear Case 169 52. Eastern E l e c t r i c i t y 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 E l e c t r i c i t y Production, Nuclear Cogeneration Case 178 56. Secondary Energy Fuel Shares, Nuclear Cogeneration Case 180 57. Crude O i l Production, High O i l Costs Case 184 58. Crude O i l Pr i c e s , High O i l Costs Case 186 59. Secondary Energy Fuel Shares, High O i l 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, E l e c t r i c Auto Case 201 65. Crude O i l Production, E l e c t r i c Auto Case 203 66. Secondary Energy Fuel Shares, E l e c t r i c Auto Case 205 67. Primary Energy Fuel Shares, E l e c t r i c Auto Case 207 68. Demand Equations Used i n the Model 233 69. Bounds on I n d u s t r i a l Fuel Shares 283 X L i s t of Figures Page 1. Schematic Diagram of Model i n Each Period 25 2. Energy Flows i n Western Canada 28 3. Energy Flows i n Eastern Canada 29 4. O i l Production, Base Case 52 5. Crude O i l P r i c e s , Base Case 54 6. O i l Use, Base Case 62 7. Gas Production, Base Case 66 8. Gas Use, Base Case 68 9. Gas Pr i c e s , Base Case 70 10. Coal Production, Base Case 76 11. Coal Use, Base Case 78 12. Coal P r i c e s , Base Case 80 13. Western E l e c t r i c i t y Production, Base Case 83 14. Eastern E l e c t r i c i t y Production, Base Case 85 15. E l e c t r i c i t y Use, Base Case 87 16. Western E l e c t r i c i t y P r i c e s , Base Case 89 17. Eastern E l e c t r i c i t y P r i c e s , Base Case 91 18. Transportation, Base Case 94 19. Western Output Energy P r i c e s , Base Case 96 20. Eastern Output Energy Pr i c e s , Base Case 98 21. I n d u s t r i a l Output Energy, by Fuel, Base Case 102 22. DFC Heating, West, Base Case 106 23. DFC Heating, East, Base Case 108 24. Sectoral Output Energy Shares, Base Case 112 x i L i s t 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. To t a l Energy, Base Case 124 30. Total Energy, Percent Annual Change, Base Case 126 31. Crude O i l Production, High Case 135 32. Crude O i l Production, Low Case 137 33. Crude O i l P r i c e s , High Case 139 34. Crude O i l Pr i c e s , Low Case 141 35. Gas Production, High Case 143 36. Gas Production, Low Case 145 37. Gas P r i c e s , High Case 147 38. Gas P r i c e s , 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 O i l Production, No-new-nuclear Case 168 46. O i l Use, No-new-nuclear Case 170 47. Eastern E l e c t r i c i t y Production, No-new-nuclear Case 172 48. Primary Energy Fuel Shares, No-new-nuclear Case 174 x i i L i s t of Figures (continued) Page 49. DFC Heating, East, Nuclear Cogeneration Case 177 50. Eastern E l e c t r i c i t y Production, Nuclear Cogeneration Case 179 51. Secondary Energy Fuel Shares, Nuclear Cogeneration Case 181 52. Crude O i l Production, High O i l Costs Case 185 53. Crude O i l P r i c e s , High O i l Costs Case 187 54. Secondary Energy Fuel Shares, High O i l 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, E l e c t r i c Auto Case 202 60. Crude O i l Production, E l e c t r i c Auto Case 204 61. Secondary Energy Fuel Shares, E l e c t r i c Auto Case 206 62. Primary Energy Fuel Shares, E l e c t r i c Auto Case 208 ACKNOWLEDGEMENTS My thanks go to my supervisor, William Ziemba, for several years of guidance and encouragement i n the work towards t h i s t h e s i s . As well, I would l i k e to thank the other members of my committee for the valuable suggestions and comments which I received at various points i n the work — Ernst Berndt, Alex Meisen, Peter Larkin, Rodrigue Restrepo, James Murray, and U r i Ascher. In addition to the committee members' help, the insigh t s and suggestions from Alan Manne, John H e l l i w e l l , Sandra Schwartz and John Rowse were very u s e f u l . I am g r a t e f u l to Imperial O i l Limited, the Department of Energy, Mines and Resources, and the National Research Council of Canada for f i n a n c i a l support at various times during the thesis work. F i n a l l y , to my wife Jennifer, my daughter Sandra, and, l a t e l y my son Daniel, I extend my deepest appreciation for t h e i r patience and support throughout the course of t h i s work, including Jennifer's assistance with the typing and proofreading. 1 Chapter 1. Introduction Just a few short years ago, i t would have been necessary to introduce a d i s s e r t a t i o n on the analysis of energy p o l i c y with an argument that i t i s a worthwhile t o p i c of i n v e s t i g a t i o n . Today, however, i t i s impossible to read a newspaper without reading several a r t i c l e s on aspects of energy p o l i c y questions. Whether the news features a debate on o i l p r i c i n g , a p i p e l i n e proposal, a report on environmental e f f e c t s i n Ontario from increased use of coal i n the U.S.A., or the promotion of solar energy and the denigration of nuclear power, i t i s clear to anyone that energy p o l i c y i s an important area of i n v e s t i g a t i o n . I t i s perhaps not so c l e a r to everyone why the con- s t r u c t i o n and use of mathematical models of the energy system should form a necessary part of energy p o l i c y analysis, nor why another energy model, the one developed here, should be added to the already long l i s t . The complex r e l a t i o n s h i p s among the demands for and supplies of the d i f f e r e n t energy commodities suggest that a c a r e f u l and systematic analysis must be c a r r i e d out before a decision i s made. "Back of the envelope" c a l - culations cannot begin to come to grips with questions of i n t e r f u e l sub- s t i t u t i o n and changing market shares, e s p e c i a l l y over the longer term. One would expect that c a r e f u l l y constructed mathematical models can do better. However, as Marcuse (1980) points out "... energy models ... cannot be r e l i e d upon f o r p r e d i c t i o n ... models of socioeconomic phenomena unlike those of p h y s i c a l phenomena cannot possibly include a l l of the pertinent v a r i - ables. Even i f they could, the re l a t i o n s h i p s among the vari*. ables are not and perhaps cannot be known." Marcuse argues that an important role of the model i n dec i s i o n support i s i n answering "what i f " questions. That i s , the analyst can compare the values of key variables i n the model s o l u t i o n under d i f f e r e n t scenarios. I f c e r t a i n 2 p o l i c i e s or technologies are preferred i n a reasonable range of scenarios, they are s a i d to be "robust", and some us e f u l information can be given to the decision makers. Furthermore, Marcuse observes that i n s i g h t i s gained i n the very process of modelling, by fo r c i n g the analyst to be systematic and to seek the reasons f o r c o u n t e r - i n t u i t i v e model r e s u l t s . As well, the need f or data f o r the model often forces the analyst to c o l l e c t previously unavailable data, which turns out to be useful information i n i t s e l f . Discussed here i s the construction of a model of the energy sector of the Canadian economy. The model takes i n t o account the i n t e r a c t i o n of energy supplies and demands, but ignores e f f e c t s the energy sector has on the r e s t of the economy. I t i s a long term model, covering the period 1975 to 2020, (three five-year periods, followed by three ten-year periods) a s u f f i c i e n t l y long time f o r the exhaustion of the conventional reserves of crude o i l and natural gas, and for the t r a n s i t i o n to alternate f u e l s . A l i n e a r process model of energy supply, conversion, d i s t r i b u t i o n and end-use i s linked to a model of the demands f o r services provided by energy i n combination with other inputs such as c a p i t a l . Nonlinear programming i s used to f i n d the supply- demand equilibrium by maximizing the discounted sum of consumers 1 plus pro- ducers' surplus. Two regions - east and west, with the d i v i d i n g l i n e at the Ontario-Manitoba border — are distinguished throughout the model, since many important questions centre on the d i f f i c u l t i e s 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 o i l . E l e c t r i c i t y i s exported from both regions. Upper l i m i t s are placed on a l l exports to other countries, to represent n a t i o n a l decision-makers' present risk-averse behaviour. (To examine a p o l i c y of 3' u n r e s t r i c t e d exports, the model would require some a l t e r a t i o n s from i t s present formulation). Linear approximations to long-run marginal cost curves f o r exhaustible hydrocarbon resources (coal, o i l , and gas) are included i n the model. Crude o i l from the t a r sands i s considered separately. Other primary resources include h y d r o e l e c t r i c i t y , nuclear e l e c t r i c i t y , solar heat and biomass. A l l costs of production, conversion, transportation and d i s t r i b u t i o n are u n i t costs which include c a p i t a l components (with a s t i p u l a t e d rate of return). The model represents a network of energy flows from primary production, through secondary conversions (e.g. coal to e l e c t r i c i t y ) , to end-use con- versions i n t o f i n a l demands (e.g. space heating). Linkages among the periods are found i n constraints which require established new capacities of many production and conversion processes to l a s t f o r s t i p u l a t e d l i f e t i m e s . O i l and gas production capacities decline i n the l a t t e r parts of t h e i r l i f e t i m e s . Constraints l i m i t i n g the t o t a l amount of production of exhaustible resources also l i n k d i f f e r e n t periods. The model calculates equilibrium q u a n t i t i e s and many pr i c e s throughout the network of energy sector flows. Because of the export l i m i t s , domestic resource prices are t y p i c a l l y below the i n t e r n a t i o n a l p r i c e s — that i s , the export l i m i t s imply the two-price system presently i n e f f e c t i n Canada.' (To examine the world p r i c i n g a l t e r n a t i v e , the model would have to be a l t e r e d i n the manner required f o r examination of u n r e s t r i c t e d exports.) Prices for exhaustible resources r i s e , over time, to the costs of the "backstop" sources ( i . e . sources which are, for a l l p r a c t i c a l purposes, i n unlimited supply, at a possibly high co s t ) . The model f i l l s a gap i n Canadian energy modelling. I t i s one of only three Canadian energy models ( a l l recently developed) which calculates both 4 equilibrium quantities and p r i c e s i n an integrated supply-demand framework. The process modelling of i n t e r f u e l s u b s t i t u t i o n , including some functional end-use processes, make t h i s 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 s i m p l i c i t y and r e l a t i v e l y small s i z e of the model make i t possible for a si n g l e analyst to update the data and structure. I t may be used to analyze issues of energy p r i c i n g (assuming continuation of the two p r i c e system), the timing of the introduction of f r o n t i e r re- sources and new energy technologies, the competitiveness and impacts of some new energy technologies, the impacts of various l e v e l s of energy exports, and the impacts of various p o t e n t i a l p o l i c y constraints. For example, i t i s shown i n t h i s thesis that f r o n t i e r natural gas i s not needed u n t i l a f t e r the year 2000, according to the model. This i s a robust conclusion under a reasonable range of assumptions about energy demands. Model r e s u l t s suggest that the "appropriate competitive r e l a t i o n s h i p " of gas and o i l p r i c e s (to use the phrase of the Department of Energy, Mines and Resources, 1976a) may be quite d i f f e r e n t i n the west than i n the east: gas should be p r i c e d lower than o i l i n the west, u n t i l 1990, and somewhat higher afterwards; but the eastern gas p r i c e should be about equal to that of o i l u n t i l 1990, and then consider^- ably higher than the o i l p r i c e . I t i s found that the e l e c t r i c automobile w i l l not be competitive unless there i s a breakthrough lowering the d i f f e r e n c e i n i n i t i a l cost between e l e c t r i c and conventional automobiles, or unless the government subsidizes the e l e c t r i c auto by lessening the road tax on e l e c t r i c auto users. Analysis of a moratorium on new nuclear power plants a f t e r 1985 suggests that the economic e f f e c t s would be n e g l i g i b l e , that t o t a l eastern e l e c t r i c i t y production and use would be much lower, and that o i l from the tar sands would be the main a l t e r n a t i v e to nuclear e l e c t r i c i t y i n the east a f t e r the turn of the century. 5 Chapter 2 reviews some rela t e d energy sector models and indicates the niche f i l l e d by this-model. A d e t a i l e d l i s t i n g of model v a r i a b l e s , parameters and equations appears i n Appendix B. An overview of the structure i s contained i n Chapter 3. Appendix A contains the explanation of the der i v a t i o n of the demand functions. The method used to f i n d the equilibrium quantities and p r i c e s (the maximization of consumers' plus producers' surplus) i s given i n Chapter 4, together with a discussion of the s i z e of the nonlinear program and the t y p i c a l computing time required to f i n d the s o l u t i o n . L i s t i n g s of data and program f i l e s f o r the base case, and an explanation of the tech- n i c a l i t i e s of the computing procedure are presented i n Appendix F. C o l l e c t i o n of the data was a major part of the e f f o r t , as i t i s with most large energy modelling p r o j e c t s . The d e t a i l s of sources and calcu- l a t i o n s f o r a l l parameters f o r the base case (the most l i k e l y values) are i n Appendix C, except f o r e l a s t i c i t i e s of demand, which are discussed i n Appendix A. An overview of important (and sometimes controversial) data assumptions f o r the base case i s presented i n Chapter 5. The base case r e s u l t s are analyzed i n Chapter 6. The s e n s i t i v i t y of the r e s u l t s to a l t e r n a t i v e assumptions about energy demands i s investigated i n Chapter 7, focusing on the high and low demand cases. Observations on key energy p o l i c y issues are drawn from comparisons of the high, base and low cases. Detailed l i s t i n g s of the calculated values of a l l variables of these three cases are found i n Appendices D and E. Some energy p o l i c y questions are analyzed i n Chapter 8 with the a i d 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 d i s t r i c t heating by cogeneration with nuclear generated e l e c t r i c i t y . The p o s s i b i l i t y that the r e a l costs of producing crude o i l may have recently escalated above the estimates used i s examined next. F i n a l l y , the e f f e c t s of the a v a i l a b i l i t y of coal g a s i f i c a t i o n and e l e c t r i c automobiles at competitive costs are examined. (Under the base case cost assumptions, these two technologies do not enter the s o l u t i o n ) . Conclusions and suggestions for further research are found i n Chapter •Chapter 2. A Review of the L i t e r a t u r e on Energy Modelling Since the early 1970s, and e s p e c i a l l y since the dramatic increase i n the i n t e r n a t i o n a l p r i c e of o i l i n 1973, hundreds of energy models have been developed i n North America and Europe with the aim of aiding the analysis of energy p o l i c i e s . This review i s a p a r t i a l survey, covering those models whose elements were used i n the development of the model discussed here, or may be used i n future research stemming from the present modelling work. Several important Canadian models are also out- l i n e d . More thorough surveys may be found i n F u l l e r and Ziemba (1980), and i n Manne et a l . (1979). A r t i c l e s , on many energy models i n the United States and Canada may be found i n the c o l l e c t i o n s edited by Ziemba, Schwartz and Koenigsberg (1980), and by Ziemba and Schwartz (1980). The models discussed i n t h i s review t r e a t the en t i r e energy sector of a country (or larger region) as a system, to represent the c r u c i a l l y important behaviour of i n t e r f u e l s u b s t i t u t i o n . The current state of national energy modelling i n Canada i s discussed, with an i n d i c a t i o n of the niche f i l l e d by the model developed here. Some comments on d i r e c t i o n s for future research follow, with reference to some models which are re- viewed. (A more complete discussion of future research may be found i n Chapter 9). Nordhaus (1973) introduced an important methodology and several concepts which are ce n t r a l to much of the l a t e r a n a l ysis. The extraction, transportation and processing of energy to meet f i n a l demands i s represent ed i n a l i n e a r programming (LP) framework. He considers f i v e regions i n the non-Communist world: the United States, Western Europe, Japan, the Persian Gulf and North A f r i c a , and the r e s t of the world. There are f i v e demand categories f o r energy products: e l e c t r i c i t y , i n d u s t r i a l n o n e l e c t r i •8 energy uses, r e s i d e n t i a l n o nelectric uses, substitutable transportation ( i . e . e l e c t r i c i t y could conceivably supply the necessary energy), and nonsubstitutable transportation ( i . e . a i r t r a f f i c and long-distance auto- mobile t r a f f i c , neither of which can be run on e l e c t r i c i t y ) . Demands are s p e c i f i e d exogenously for each category, on the grounds that p r i c e e l a s t i c i t i e s are quite low, and that the chief response to p r i c e changes i s i n t e r f u e l s u b s t i t u t i o n , which i s represented i n the model. The model determines the a l l o c a t i o n of energy resources, oyer several time periods (five ten-year periods, followed by two twenty-five-year periods and two f i f t y - y e a r periods) which minimizes the discounted costs of meeting the s p e c i f i e d f i n a l demands. Nordhaus' primary use of the model i s to discuss the introduction dates of new technologies and primary resources, and to estimate the e f f i c i e n t p r i c e paths for the f u e l s . An important concept introduced by Nordhaus i s the notion of the "backstop" technology. Since the planning problem i s r e a l l y over an i n d e f i n i t e length of time, i t i s necessary, i n p r i n c i p l e , to include at l e a s t one i n f i n i t e l y p l e n t i f u l primary resource and technologies which can transform i t into a l l f i n a l energy demands. Such "backstop" technologies may be much more expensive than today's tech- nologies, but they must be included i n order to ensure f e a s i b i l i t y of the i n f i n i t e - t i m e - h o r i z o n problem. Nordhaus' discussion of resource p r i c e s i s i n s t r u c t i v e f o r under- standing the behaviour of other models, such as the model developed here. Exhaustible resource p r i c e s , taken from the appropriate dual v a r i a b l e s ' values at the optimal s o l u t i o n , have two components. The f i r s t i s the exogenous cost of production. The second component of the p r i c e i s the 9 -"royalty" or economic rent due to the s c a r c i t y of the resource. The p r i c e of a resource gradually r i s e s toward the cost of the backstop technology, as the less c o s t l y but exhaustible sources are used up. As the p r i c e r i s e s to the backstop cost, the royalty component shrinks to zero.• When the backstop technology i s r e l i e d upon, there i s no economic rent, because the p r i c e equals the cost of production. In e a r l i e r periods, p r i o r to re- liance on the backstop technology, the cost of the backstop i s a c e i l i n g on the p r i c e 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 i s a network represent- ation of the energy flows from primary energy commodities through con- version, transportation, d i s t r i b u t i o n and u t i l i z a t i o n a c t i v i t i e s . A l i n e a r programming model i s developed from the Reference Energy System to minimize the cost of meeting s p e c i f i e d end use energy demands. BESOM optimizes over a sin g l e year and one region (usually the U.S.A.). End use demands are defined by function (e.g. space heating) rather than by broad s t a t i s t i c a l categories (e.g. commercial energy demand). There i s extensive d e t a i l i n the energy supply, conversion, transportation, d i s t r i b u t i o n and u t i l i z a t i o n technologies. Environmental emissions are also c a l c u l a t e d . BESOM can be used e i t h e r i n the optimization mode with various objectives, or i n a simulation procedure, as outlined-by Kydes (1980), for the assessment of energy technologies, or to study the impacts of various possible energy p o l i c i e s . The Hudson and Jorgenson (H-J) (1974) model t i e s together a macro- economic growth model, an in t e r i n d u s t r y model with energy sector d e t a i l and a model of consumer demand. There are four non-energy sectors and f i v e energy sectors i n the in t e r i n d u s t r y model, whose input-output co- e f f i c i e n t s are determined endogenously and are p r i c e responsive. Trans- log p r i c e p o s s i b i l i t y f r o n t i e r s r e l a t e the pr i c e s of inputs to the pr i c e s of outputs, and provide f l e x i b i l i t y i n the representation of sub- s t i t u t i o n 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 d e t a i l , l i k e BESOM. Another important d i s t i n c t i o n i s the H-J model's e x p l i c i t representation of the in t e r a c t i o n s between the energy sector and the whole economy. The H-J model has been used extensively to examine a l t e r n a t i v e U.S. tax p o l i c i e s f o r stimulating energy conservation and reducing dependence on energy imports. The H-J and BESOM models have been combined, using a procedure de- scribed i n Hoffman and Jorgenson (1977). (The int e g r a t i o n of dynamic versions of both models i s discussed i n Hudson and Jorgenson, 1978.) The combined model i s a single period model, l i k e BESOM, having the ad- vantages of both the H-J and BESOM models. The in t e g r a t i o n of the models i s based on an in t e r i n d u s t r y accounts system which i s an expansion of the H-J system. The s o l u t i o n procedure involves an i t e r a t i v e method. The combined model can provide assessments of the impacts of research, de- velopment and demonstration p o l i c i e s on the energy sector ( t y p i c a l of BESOM analyses), as we l l as impacts of these p o l i c i e s on the whole economy ( t y p i c a l of H-J analyses). The model can be used to evaluate the impacts of energy tax p o l i c i e s on the economy ( t y p i c a l of H-J Analyses) and i n p a r t i c u l a r on the d e t a i l e d energy sector, including impacts on the i n t r o - duction of new technology, v i a the BESOM component. The PILOT modelling project at Stanford University has developed the Welfare Equilibrium Model (WEM) of energy - economic i n t e r a c t i o n s i n the U.S.A. (Parikh, 1980). WEM i s an intertemporal l i n e a r programming model, with many l i n e a r approximations to nonlinear r e l a t i o n s , maximizing a household welfare function that characterizes a sta n d a r d - o f - l i v i n g measure. An input-output model of the economy i s linked to a d e t a i l e d energy submodel which e x p l i c i t l y includes resource depletion and many energy technologies. The usual unresponsiveness of input-output co*- e f f i c i e n t s i s modified i n WEM by the use of m u l t i l e v e l hierarchy of p a i r - wise s u b s t i t u t i o n s , represented by l i n e a r approximations to nonlinear homothetic functions. WEM i s a "clairvoyant" model, solving f o r a l l time periods simultaneously as i f a l l decision makers i n the economy have per- fe c t f o r e s i g h t for a l l future p r i c e s , i n contrast to the H-J model, which i s "myopic", sol v i n g f o r one period at a time, as i f a l l decision makers make t h e i r decisions based s t r i c t l y on present economic conditions. WEM has been used to explore the long term e f f e c t s on the U.S. economy of r i s i n g energy import p r i c e s . I t has also been used to a i d the planning s t a f f of the E l e c t r i c Power Research I n s t i t u t e with pre- paration of t h e i r research and development plan i n v o l v i n g new energy technologies (Parikh et a l . , 1978). Long range energy projections have been developed f o r the U.S. Department of Energy with the a i d of WEM. Generally, i t can be used f o r d e t a i l e d s e c t o r a l assessments of the impacts on the economy of various energy supply, p r i c e and tax scenarios. The Energy Technology Assessment (ETA) model (Manne, 1976) i s a' 12 •nonlinear programming model which maximizes consumers' plus producers' surplus i n the U.S. energy sector. The constraints are l i n e a r , as i n a conventional LP process a n a l y s i s . ETA has a seventy-five-year planning horizon ( f i f t e e n five-year i n t e r v a l s ) , from 1970 to 2045, but r e s u l t s are presented only to 2030, to avoid "horizon" e f f e c t s . See Grinold (1980) f o r an analysis of "horizon" e f f e c t s i n the ETA model. Like WEM, ETA i s a c l a i r - voyant model. The exogenous GNP trend i s the p r i n c i p a l d r i v i n g force for ex- pansion of energy demands over time. In addition, ETA demand i s p r i c e - responsive, incorporating own- and cross-price e l a s t i c i t i e s of demand between e l e c t r i c and n o n - e l e c t r i c energy. Unitary e l a s t i c i t y of sub- s t i t u t i o n between e l e c t r i c and n o n - e l e c t r i c energy i s assumed. Prices for e l e c t r i c and n o n - e l e c t r i c energy are equal to t h e i r marginal costs of supply, at optimal production and d i s t r i b u t i o n l e v e l s . Energy supply p o s s i b i l i t i e s have t h e i r own cost parameters, and future technologies have t h e i r own introduction dates ( i . e . when they are a v a i l a b l e , although they may not be part of the optimal mix). In ETA, many scenarios are p o s s i b l e , according to input data on costs, introduction dates, and a v a i l a b i l i t y of new technologies. The benefits of d i f f e r e n t technologies can be evaluated by running ETA with and without the a v a i l a b i l i t y of the technology i n question; the difference i n the optimal value of the objective function i s a measure of the benefits of the technology. Manne (1977) describes a modification of the ETA energy sector model, c a l l e d ETA-MACRO, which involves the replacement of the ETA objective function with an aggregated macroeconomic growth model. E l e c t r i c and non- e l e c t r i c energy are supplied by the energy sector to the r e s t of the economy (represented by the macro growth model). Aggregate economic output i s a l l o c a t e d between i n t e r i n d u s t r y payments f o r energy costs and f i n a l demands of current consumption and investment. I t i s assumed that gross output depends upon four inputs: c a p i t a l , labor, e l e c t r i c energy and non- e l e c t r i c energy. The objective function f o r the optimization runs i s the discounted sum of the logarithms of future consumption. The macro model i s driven by three exogenous parameters: the d i s - count rate i n the objective function (the main determinant of the savings- investment accumulation process), the labor force growth index, and the e l a s t i c i t y of s u b s t i t u t i o n between energy and non-energy (the p r i n c i p a l factor governing the economy's a b i l i t y to cope with higher energy prices) ETA-MACRO i s used to examine the two-way linkage between energy and the r e s t of the economy. A base case i s developed i n v o l v i n g the best estimates of a l l parameters. The model i s small enough (350 rows, 600 columns i n the matrix of l i n e a r constraints, and 80 variables entering nonlinearly into the objective function) that numerous a l t e r n a t i v e cases can be run quickly, at low cost. Manne (1977) finds that a "no-nuclear" p o l i c y would have n e g l i g i b l e macroeconomic e f f e c t s , unless the e l a s t i c i t y of s u b s t i t u t i o n i s quite low and there are serious r e s t r i c t i o n s on non- nuclear energy resources. A f t e r the dramatic r i s e i n o i l p r i c e s i n 1973, the U.S. federal gover: ment required not j u s t energy trend forecasts, but a d e s c r i p t i o n of the i n t e r a c t i o n of the supply and demand of many energy products, over time, with a v a r i e t y of geographical c h a r a c t e r i s t i c s . Since there was l i t t l e agreement i n defining desirable f e a s i b l e futures, a d e s c r i p t i v e rather than a normative modelling approach was needed to c a l c u l a t e the .lo g i c a l implications of a consistent set of assumptions or p o l i c i e s . The Project Independence Evaluation System (PIES) i s one such forecasting t o o l (Eynon et a l . 1975, Hogan 1975, 1977 and Greenberg 1980a). (PIES has recently been renamed as the Medium Term Energy Forecasting System). PIES i s used fo r p o l i c y analysis f o r f i v e to f i f t e e n year planning horizons. I t i s a regional model, and forecasts p r i c e s and quantities of energy goods pro- duced, consumed, or converted, f a c i l i t y construction requirements and operational modes, transportation a c t i v i t i e s and associated resource requirements. PIES i s composed of a demand model, a c o l l e c t i o n of supply models, and an in t e g r a t i n g model. There i s a separate model at each supply region, f o r each product (coal, o i l , natural gas, shale o i l ) , to characterize the price-quantity r e l a t i o n s h i p f o r that product. The pro- ducts are moved through a transportation, conversion, and d i s t r i b u t i o n system to the demand regions. A separate model, incorporating cross-price e l a s t i c i t i e s of energy demand, characterizes the price-quantity r e l a t i o n - ship determining the demand for energy products. I f the demand vector i s known, the s e l e c t i o n of supply a l t e r n a t i v e s i s made by a l i n e a r programming, minimum t o t a l cost c a l c u l a t i o n . The dual variables are the supply p r i c e s , f o r the given demand vector. In t h i s way, i m p l i c i t supply curves are generated. The system i s brought into equilibrium by the in t e g r a t i n g mechanism when supply equals demand, and the supply p r i c e s equal the p r i c e s c a l - culated by the demand model f or the equilibrium demand. The i n t e g r a t i n g mechanism involves i t e r a t i o n s of a l i n e a r programming approximation to a f i x e d point algorithm. Eynon et a l . (1975) give the following examples of exogenous inputs which have been introduced i n t o the PIES system f o r p o l i c y analysis: p r i c e changes i n imports; import t a r i f f s ; import quotas; domestic f u e l taxes, accelerated new material supply; conservation measures; demand management; o i l to coal conversion i n e l e c t r i c u t i l i t i e s ; various coal and nuclear construction l i m i t s ; and e l e c t r i c i t y load management. Green- berg (1980a) discusses the p o l i t i c a l background to use of the model for the U.S. National Energy Plan i n 1977. The SRI-Gulf model was o r i g i n a l l y developed by the Stanford Re- search I n s t i t u t e (SRI) i n 19 73 to analyze a synthetic fuels strategy f o r Gulf O i l Corporation. Versions of the model have been used f o r other purposes, such as a study of the economic forces i n f l u e n c i n g the develop- ment of western U.S. energy resources such as coal and o i l shale (SRI, 1976). The model i s regional, dynamic, and contains a great deal of d e t a i l on energy technology and market behavior (including market imperfections). In construction of the model, described by Cazalet (1977, 1978), perfect competition i s not assumed/ the market adjustment process i s de- scribed, and process technologies are e x p l i c i t l y represented. The de- c i s i o n problem to be analyzed i s decomposed i n t o d i f f e r e n t sub-models, which are connected by a network. At the bottom of the network are processes describing long run r e - source supply curves and depletion.of reserves in.the various supply regions. Later stages i n the network involve transportation and con- version processes. When a need can be f i l l e d from several d i f f e r e n t sources, a l l o c a t i o n processes describe the sharing of the market among competing f u e l s . At the top of the network are processes describing the regional end-use demands for energy (not f o r f u e l s , but f o r r e s i d e n t i a l / commercail space heat, i n d u s t r i a l steam, e t c . ) , as functions of end use energy p r i c e s , demographic fac t o r s , economic f a c t o r s , weather, etc. The model also includes s i m p l i f i e d models of the U.S. economy and population growth, and processes describing the p r i c e changes of materials used i n the construction of energy f a c i l i t i e s due to energy industry demands. Each of these processes i n the network consists of p h y s i c a l r e l a t i o n s de- s c r i b i n g flows, e f f i c i e n c i e s , etc., and behavioral r e l a t i o n s describing the decision making behavior which sets p r i c e s and q u a n t i t i e s . An i t e r a t i v e algorithm computes tentative p r i c e s of process outputs for a l l time periods, s t a r t i n g from the resource supply p r i c e s and moving up through the network, using the behavioural r e l a t i o n s , with q u a n t i t i e s estimated at the l a s t i t e r a t i o n . At the second step of an i t e r a t i o n , the quantities of inputs to processes are computed by working downward through the network, using the p h y s i c a l r e l a t i o n s . The algorithm terminates when a l l p r i c e s and quantities are unchanged on successive i t e r a t i o n s . The method used i n the SRI-Gulf model can account f o r market im- perfections and human behaviour,such as p r i c e controls, r a t i o n i n g , learning curves f o r new technology, and the determination of economic rents on primary resources from estimates of future p r i c e s . Applications and ex- tensions of the modelling approach are described i n Cazalet (1979). Debanne" (1975, 1980) has developed a series of network based energy sector models. The version described i n Debanne (1975) deals with a net- work of o i l , gas, nuclear, hydro, coal, geothermal and s o l a r energy flows i n ten U.S. and nine Canadian regions. The model minimizes the t o t a l cost of meeting exogenous energy demands, i n i n t e r a c t i o n with submodels of i n - vestment i n capacity expansion and of exploration and reserves accumulation. With the model, one can examine, from a continental p o i n t of view, the economic advantages of a l t e r n a t i v e p i p e l i n e p r o j e c t s , and the e f f e c t on f o s s i l f u e l market shares of various new energy technologies. Debanne' (1980) discusses methods for incorporating price-responsive demand and supply functions i n the network minimization framework. The National Energy Board (NEB) and the fed e r a l Department of Energy, Mines and Resources (EMR) use two s i m i l a r versions of a model f or making energy demand projections i n Canada. The EMR version i s discussed i n de- t a i l i n a p u b l i c a t i o n by EMR (1977a). Sahi and Erdmann (1980) discuss an important development i n the EMR model — an i n t e r f u e l s u b s t i t u t i o n component. CANDIDE, a large econometric model of the Canadian economy, discussed i n McCracken (1973), supplies consistent, projected values f o r a majority of the independent variables of the EMR model. These are d i s - aggregated, by assumed r a t i o s , over the f i v e s t a t i s t i c a l regions of Canada — A t l a n t i c , Quebec, Ontario, the P r a i r i e s , B.C. and Yukon. End-use energy requirements f o r r e s i d e n t i a l , commercial and i n d u s t r i a l sectors are projected using double-log equations i n v o l v i n g lagged demand, weather variable s , and economic and demographic projections, some of which come from CANDIDE. E l a s t i c i t i e s of energy demand with respect to r e l a t i v e f u e l p r i c e s , r e a l disposable income, volume of r e t a i l trade, and r e a l domestic product and other variables are incorporated i n the projections, allowing for periods of adjustment to the r e l a t i v e p r i c e changes by means of the lagged demand terms. Energy p r i c e s are supplied exogenously by the model user. Input energy required f o r projected end-use (output) energy i s estimated i n the EMR model, using energy conversion e f f i c i e n c y data. The' model user can i n s e r t hypothetical future improvements i n energy use e f f i c i e n c i e s . The market shares of the d i f f e r e n t fuels i n the input energy requirements are calculated by means of semi-log market share equations depending on r e l a t i v e f u e l p r i c e s , described i n Sahi and Erdmann (1980). The econometric model discussed i n H e l l i w e l l e t a l . (1976), H e l l i w e l l (1979) and i n H e l l i w e l l et a l . (1980) w i l l eventually be a t o o l f o r assess- ing a great number of current and future energy sources and p o l i c y options, but presently, the model emphasizes questions concerning f r o n t i e r and non- f r o n t i e r natural gas, non-frontier crude o i l , and synthetic o i l from the Athabaska o i l sands. The H e l l i w e l l model pays close attention to energy trade and trans- portation, and to domestic o i l and natural gas p r i c e s . World crude o i l pr i c e s are determined outside Canada and are exogenous to the model. Domestic o i l and natural gas p r i c e s are determined by a p o l i c y r u l e . A f t e r allowing f o r transport costs to S t a t i s t i c s Canada's f i v e major consuming regions, the r e s u l t i n g p r i c e s are used i n a consistent set of estimated demand equations f o r a l l end-use sectors aggregated together i n each region to forecast demand for o i l , gas, coal and e l e c t r i c i t y . The demand equations, which e x p l i c i t l y account f o r regional p e c u l i a r i t i e s such as u n a v a i l a b i l i t y of natural gas i n the A t l a n t i c provinces, are composed of f u e l cost share equations and equations determining the aggregate ex- penditure on t o t a l energy i n each region. To account f o r delays i n the adjustments (to changing prices) of t o t a l energy consumption and i n f u e l s ubstitutions due to energy use being associated with c a p i t a l stocks, the f u e l p r i c e s used i n the cost share equations are weighted averages of the current p r i c e and previous three years' p r i c e s . Apart from o i l and gas p r i c e s , other exogenous variables are the gross national expenditure (GNE), the GNE p r i c e index, the p r i c e of e l e c t r i c i t y , the growth of hydro- e l e c t r i c i t y supply, and the growth of natural gas d i s t r i b u t i o n p i p e l i n e s . Production sectors f o r non-frontier and f r o n t i e r natural gas, non- f r o n t i e r conventional crude o i l , and o i l sands, and o i l imports meet the calculated demands. Costs of discovery, development and production, production income taxes and r o y a l t i e s , and economic rents are computed. The model hooks up needed reserves, and additions of new reserves are fore- cast exogenously (an attempt i s being made to make the exploration pro- cess endogenous). There i s considerable d e t a i l i n tax and royalty arrangements. There are two types of l i n k s between the energy model and the agg- regate economy. Quarterly versions of the annual models of a r c t i c and o i l sands development, linked with RDX2, a quarterly econometric model of the Canadian economy, allow assessments of the macroeconomic impact of large energy pr o j e c t s . H e l l i w e l l et a l . (1976) achieve consistency between the en t i r e energy model and RDX2 by using output from the energy model as input f o r a new so l u t i o n of RDX2, and vice versa, u n t i l a sol u t i o n which s a t i s f i e s both models i s achieved. An example of the second type of l i n k would be an energy trade surplus flowing into RDX2, where i t influences the exchange rate (and other things), which, when fed back to the energy model, a f f e c t s the Canadian d o l l a r p r i c e of world o i l and hence a l l Canadian energy p r i c e s . Daniel and Goldberg (1980) report on work towards in t e g r a t i n g the EMR demand model with a model of Canadian energy supply, using the l i n e a r programming procedure developed f o r s o l v i n g the PIES model. When t h i s work i s complete, a major t h e o r e t i c a l deficiency i n the EMR demand model w i l l 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 i s to be modified from work by McConaghy and Quon (1980) on an energy supply model f o r Alberta. The model developed here i s s i m i l a r i n s p i r i t to the Daniel and Goldberg model, namely to integrate the EMR demand work with a model of energy supply, conversion and d i s t r i b u t i o n i n Canada. However, here, i n t e r f u e l s u b s t i t u t i o n i s handled by a supply side l i n e a r process sub- model rather than v i a the EMR econometric i n t e r f u e l s u b s t i t u t i o n com- ponent. In the model developed here, i n t e r f u e l s u b s t i t u t i o n i s handled i n the manner developed by Hoffman for BESOM. Another feature of BESOM which has been used, as f a r as the e x i s t i n g data w i l l allow, i s the s p e c i f i c a t i o n of energy demands by functional end uses. In the domestic, farm and commercial sector, heating (space and water) i s distinguished from other energy demands, and the road transportation demands may be met by e i t h e r gasoline or e l e c t r i c automobiles. However, i n contrast to the s t a t i c model BESOM, which i s solved one period at a time ( i . e . the solutions are "myopic", and represent the behaviour of d e c i s i o n makers whose expectations are that future p r i c e s w i l l be the same as present p r i c e s ) , the model described here i s solved for a l l time periods at once ( i . e . the solutions are "clairvoyant", as i f a l l decision makers' expect- ations of future p r i c e s turn out to be exactly c o r r e c t ) . In t h i s respect, t h i s model i s s i m i l a r to Manne's ETA model. Other points of s i m i l a r i t y with the ETA model are: - both are small enough for a si n g l e analyst to manage (updating the data base, modifying the structure, making and i n t e r p r e t i n g runs); - both are small enough that the computing expense i s small, allowing f or the development of many scenarios; - both f i n d the market equilibrium by maximizing consumers' plus producers' surplus; and - both are formulated as nonlinear programming problems with nonlinear objectives but l i n e a r constraints, using the MINOS code (described i n Murtagh and Saunders, 1977) to f i n d the so l u t i o n . Some major points of d i s s i m i l a r i t y between ETA and the model described here are: - t h i s model c a r r i e s the process analysis through to the end uses, i n the cases of space heating and automobile use, while i n ETA the demand i s f o r secondary energy, which i s categorized into e l e c t r i c and nonelectric energy; and - there are two regions, west and east i n the model discussed here, but ETA i s a one-region model. An examination of energy-economy in t e r a c t i o n s i s one possible area of future research stemming from the work discussed here. The work could proceed by l i n k i n g the present model to an e x i s t i n g macroeconomic model, as i n the combination of the H-J and BESOM models. A l t e r n a t i v e l y , the approach of the PILOT p r o j e c t with the WEM model -- a sing l e optimizing model containing an economic model and energy sector d e t a i l -- might be adopted. In the early development of the model discussed here, an attempt was made to represent energy-economy i n t e r a c t i o n s by the method of ETA-MACRO. Although t h i s approach i s appealing since i t keeps the model small and manageable, i t had to be abandoned to keep the process d e t a i l i n the end use sectors because there was no apparent way to make each end use sector's share of t o t a l output energy endogenous. Another possible d i r e c t i o n f o r future work i s i n increasing the number of regions distinguished i n the model. Computational f e a s i b i l i t y •of such a larger model may require decomposition methods, perhaps along the l i n e s of the s o l u t i o n method used by the SRI-Gulf model. A complete discussion of future research p o s s i b i l i t i e s may be found i n Chapter 9. The model discussed here f i l l s a gap i n the energy modelling e f f o r t s i n 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 ca l c u l a t e both p r i c e s and q u a n t i t i e s , given price-respons- ive representations of supply and demand. Other models ca l c u l a t e demands i f the p r i c e s are given (e.g. the EMR model), supplies i f the demands are s p e c i f i e d (e.g. McConaghy and Quon), or both supplies and demands i f the pr i c e s are given (e.g. H e l l i w e l l ) . The model developed here d i f f e r s from the Daniel-Goldberg model mainly i n i t s handling of i n t e r f u e l s u b s t i t u t i o n by the supply side l i n e a r process submodel, which has advantages over an econo- metric approach f o r long range pro j e c t i o n s . Another difference i s i n the computational methods — t h i s model i s solved by a s i n g l e optimization, while the Daniel-Goldberg model i s solved by the complex i t e r a t i v e method o r i g i n - ated for the PIES work. This model i s distinguished from both the Daniel- Goldberg and Debanne''models i n i t s e x p l i c i t process modelling of some end- use demands, by function. The Debanne' model also uses a complex i t e r a t i v e s o l u t i o n 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 i n t e r f u e l s u b s t i t u t i o n , including some functional end-use s p e c i f i c a t i o n s , and computational s i m p l i c i t y . This model w i l l hopefully be useful i n making a contribution to the debate i n the areas of Canadian energy p o l i c y f o r which i t seems wel l - s u i t e d , namely energy p r i c i n g , the timing of the introduction of f r o n t i e r energy resources and new energy technologies, the competitiveness and impacts of some new energy technologies, the impacts of various l e v e l s of energy exports, and the impacts of various p o t e n t i a l p o l i c y constraints (e.g. a nuclear moratorium). Examples of several such analyses are presented i n Chapters 6, 7 and 8. Chapter 3. An Overview of the Structure of the Model The model i s composed of a l i n e a r process submodel of energy supply, d i s t r i b u t i o n and use, coupled with a model of the demands for the ser- vices provided by the energy. The complete•specification of a l l v a r i - ables and r e l a t i o n s may be found i n Appendix B. The model equilibrates energy supplies and demands by maximizing consumers' plus producers' surplus (the procedure i s described i n chapter 4). There are two regions — west and east, with the d i v i d i n g l i n e at the Ontario-Manitoba border. This d i v i s i o n represents the most important regional aspect of Canadian energy p o l i c y questions — f o s s i l f u e l supplies are l a r g e s t i n the west, while the main markets are i n the east. Figure 1 i l l u s t r a t e s the general structure of the model. The west exports energy to other countries and to the east. The east i s an energy importer, taking supplies of f o s s i l fuels from the west and from other countries, but a r e l a t i v e l y small amount of e l e c t r i c i t y i s exported from the east to the U.S.A. In each region, the energy commodities undergo various conversion processes and are d i s t r i b u t e d to the four end-use sectors within the l i n e a r process model 1. the domestic, farm and commercial sector, 2. the i n d u s t r i a l sector, 3. the road transportation sector, and 4. the "other" transportation sector. In the end-use sectors are the f i n a l conversions to output energy (which may be viewed as an index of the useful services provided by energy i n com- bination with other inputs such as c a p i t a l - e.g. space heat, transport- ation, e t c . ) , s t i l l within the l i n e a r process model of supply. For each end-use sector of each region, output energy demand i s s p e c i f i e d as a S U P P L Y 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) e n e r g y ^ 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 v a r i a b l e s , and of the endogenous p r i c e of the output energy. Output, rather than secondary energy i s used i n the demand functions because the demand f o r secondary energy i s 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 c a p i t a l . The use of output energy i n the demand functions allows a process representation of present and possible future devices f o r supplying the services represented by output energy. In t h i s way, the secondary energy f u e l shares may be de- termined endogenously, with e x p l i c i t consideration of future technologies which w i l l use secondary energy. The two data which represent an end-use conversion process are the conversion f a c t o r (the r a t i o of output energy to secondary f u e l input) and the non-fuel conversion cost (representing the other inputs). I t should be noted that i n r e a l i t y the conversion factors and non-fuel costs are price-responsive, but i n the model, they are f i x e d exo- genously. However, t h i s t h e o r e t i c a l d e f i c i e n c y i s l i k e l y minor i n the case of space heating, since i n t e r f u e l s u b s t i t u t i o n (which i s represented i n the model) w i l l probably dominate the e f f e c t of f u e l p r i c e on the conversion c o e f f i c i e n t s and costs. For o i l used i n the two transportation sectors, the conversion c o e f f i c e n t s are varied over time, exogenously, to indi c a t e expected increases i n f u e l e f f i c i e n c i e s . This t h e o r e t i c a l d eficiency may have a s i g n i f i c a n t e f f e c t i n the i n d u s t r i a l sector. There are s i x time periods - three of length f i v e years, followed by three of length ten years, f o r a t o t a l span of 45 years, from 1975 to 2020. A seventh "period" represents the time from 2020 to i n f i n i t y , i n a procedure to mitigate end e f f e c t s , described l a t e r i n t h i s chapter. The l a t e r periods are longer p r i m a r i l y f o r computational e f f i c i e n c y , but the decreased accuracy i s not very important since there i s much larger uncertainty i n these l a t e r periods. The production l e v e l s i n a period are influenced by l e v e l s i n e a r l i e r periods, as described l a t e r . In each time period, the l i n e a r process submodel is. represented as a network of flows of energy commodities. Figures 2 and 3 i l l u s t r a t e , i n complete d e t a i l , the networks for the west and the east, r e s p e c t i v e l y . Primary energy i n i t s various forms ( i . e . crude o i l , natural gas, coal, hydro- e l e c t r i c i t y , nuclear e l e c t r i c i t y , biomass energy products, and s o l a r space heat) i s converted i n t o secondary energy ( o i l products, gas, coal and coke, e l e c t r i c i t y , space heat from cogeneration, and sol a r space heat), which i s converted to output energy i n the four end use sectors. The aggregation chosen f o r the model l i m i t s the user's a b i l i t y to ex- amine c e r t a i n questions e a s i l y with the model. For example, since coal i s treated as a sing l e commodity, separate consideration of d i f f e r e n t grades of coal i s impossible. S i m i l a r l y , there i s no separate treatment of the d i f f e r e n t r e f i n e d o i l products. The upgrading of heavy o i l and i t s separate treatment for the purposes of export may not e a s i l y be considered i n the model. The modeller must make decisions on the degree of aggregation, to make the model a manageable s i z e . The proper examination of c e r t a i n questions may require a r e s t r u c t u r i n g of the model. In some cases, an element may be l e f t out of the model because the decisions associated with i t are separable from the other energy p o l i c y questions. For example, nuclear power enters the model as a primary energy source, without reference to uranium, since i t appears that uranium resources i n Canada are so huge that t h e i r exhaustion i s not a l i m i t i n g factor over the time span of the model (see Energy, Mines and Resources, 1976c, 1978d). Furthermore the p o s s i b i l i t i e s of the thorium near-breeder reactor and the fusion reactor replacing uranium-based plants make consideration of PRIMARY ENERGY SECONDARY ENERGY OUTPUT ENERGY [ O I L ] l O T H E R T R A N S P O R T A T I O N ! conventional, low cosl conventional, high cosl frontier, low cosl frontier high cost tor sands s o l a r h e a t H E A T I N G h e a t b y c o g e n e r a t i o n T ~ | wi th c o a l or n u c l e a r Li e l e c t r i c i t y c o g e n e r a t i o n S Y M B O L D E F I N I T I O N S : X>~ n o < l e^ t o w i n :v f' Q W o u* n o d e ' b u t e n e r q y i n d u s t r y u 5 e i < ^ n o d e with f i n e d i npu t p r o p o r t i o n s ; - Q - c o n v e r s i o n p r o c e s s FIGURE 2 ENERGY FLOWS IN WESTERN CANADA PRIMARY ENERGY SECONDARY ENERGY OUTPUT ENERGY OIL OTHER TRANSPORTATION | S O L A R | solor heat from west heat by cogeneration with coal or nuclear electricity ROAD T R A N S P O R T A T I O N ! DOMEST IC , F A R M 6Y COMMERC IAL HEATING SYMBOL DEFINITIONS : )X)-node-flow in = flow out ; node, but energy industry use ; <̂ >- node with fixed input proportions ; -Q- conversion process FIGURE 3 E N E R G Y FLOWS IN E A S T E R N CANADA a single "nuclear" backstop e l e c t r i c i t y source quite reasonable. For most depletable primary energy resources there are simple approximations to long run marginal cost curves, represented by two cost l e v e l s (low and high), with l i m i t s on the t o t a l resources a v a i l - able at each cost l e v e l . For crude o i l from the t a r sands, there i s only one cost l e v e l . These cost l e v e l s are intended to cover the c a p i t a l costs (with a s t i p u l a t e d rate of return) and the operating costs of f i n d i n g and ext r a c t i n g the resource. Economic rents (e.g. r o y a l t i e s ) can be ca l c u l a t e d a f t e r the so l u t i o n of the model as the differences between the equilibrium p r i c e s (derived from the dual variables) and costs of production. Non-depletable primary resources (hydro, nuclear, solar and biomass), are each a v a i l a b l e at u n i t costs covering operating and c a p i t a l expenses, with a rate of return. Apart from the costs of primary energy production, the other com- ponents of the t o t a l cost of meeting a given set of output energy de- mands are the costs of secondary conversion (coal g a s i f i c a t i o n and l i q u e - f a c t i o n , and the conversion of o i l , gas and coal to e l e c t r i c i t y ) , of non- f u e l heating i n the domestic, farm and commercial sector, of transporting o i l , gas and coal from west to east, of d i s t r i b u t i o n of secondary energy to the end use sectors, and the extra cost of e l e c t r i c automobiles over conventional ones. These u n i t costs also incorporate both operating and c a p i t a l expenses, at a s t i p u l a t e d rate of return. A r e f i n i n g cost i s i n - cluded i n the d i s t r i b u t i o n cost of each o i l flow to the end-use sectors. Revenues from exports of o i l , gas, coal and e l e c t r i c i t y are included i n the t o t a l energy cost c a l c u l a t i o n as negative amounts, since they are ben e f i t s . Many constraints i n the model are p h y s i c a l balance constraints which account for a l l flows i n the network, using exogenous factors to account for energy losses due to i n e f f i c i e n c i e s of conversion and the energy i n d u s t r i e s ' uses of energy (e.g. transmission losses i n e l e c t r i c i t y d i s - t r i b u t i o n , r e f i n e r y use of s t i l l gas, energy losses i n conversion of coal to e l e c t r i c i t y , e t c . ) . Linkages between d i f f e r e n t time periods are found i n the capacity expansion and retirement constraints, i n the o i l : and gas production de- c l i n e constraints, i n the constraints l i m i t i n g the t o t a l a v a i l a b i l i t y of depletable resources, and i n the objective function (the maximization of the discounted sum of consumers' plus producers' surpluses, which i s d i s - cussed more f u l l y i n chapter 4). The capacity expansion and retirement constraint for nuclear e l e c t r i c i t y production, for example, s p e c i f i e s that new capacity (productions and capacities are taken to be i d e n t i c a l i n the model) established i n one period must carry on at the same l e v e l for a t o t a l of 30 years. Many primary and secondary processes also have 30 year l i f e t i m e s , but most heating processes (except cogeneration) have 15 year l i f e t i m e s , and automobiles are taken to have 10 year l i f e t i m e s . Through the o i l and gas production decline constraints, t y p i c a l production t i m e - p r o f i l e s are represented by i n s i s t i n g that new capacities established i n one period l a s t at non-zero l e v e l s f o r a t o t a l of 25 and 30 years f o r o i l and gas, r e s p e c t i v e l y , but at d e c l i n i n g l e v e l s i n l a t e r periods. The demand functions are derived from work done at the Department of Energy, Mines and Resources, described i n Sahi and Erdmann (1980), except f o r the road transportation sector. In the l a t t e r case, the demand function i s 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 i n Appendix A. From a t h e o r e t i c a l point of view, the aggregation of output energy should be i n categories distinguished by end-use functions which are performed with the a i d of secondary energy inputs. For example, i t would be preferable to d i s t i n g u i s h , say, high, medium and low temperature requirements i n the i n d u s t r i a l sector, and a separate category f o r mechanical drive requirements, rather than the aggregate " i n d u s t r i a l output energy" presently i n the model. This would be preferable because each functional end use category could i n p r i n c i p l e be supplied by several possible f u e l inputs, and i f end-use conversion e f f i c i e n c i e s and costs were known, a t o t a l cost minimization c a l c u l a t i o n would s e l e c t the fuels f o r each functional end use. In t h i s way, the market shares of each f u e l input to the i n d u s t r i a l sector could be determined endogenously. However, t h i s approach cannot be f u l l y adopted yet. In the i n d u s t r i a l sector, demand functions would need to be estimated f o r each functional end use, but there are no such estimations f o r Canada, l i k e l y because there i s not a good data base on the e x i s t i n g l e v e l s of the functional end uses of energy (and t h e i r fuels) i n Canada, p a r t i c u l a r l y i n industry. The approach adopted i n t h i s model, f o r the i n d u s t r i a l sector's f u e l shares, has been to put upper and lower l i m i t s on the shares of the input fuels i n i n d u s t r i a l output energy. In the domestic, farm and commercial sector, the f u n c t i o n a l end use approach has been adopted i n a l i m i t e d way, with space/water heating distinguished as a demand which can be supplied by s i x possible processes (see Figures 2 and 3). However, other non-heating demand i s a f i x e d proportion of the t o t a l s e c t o r a l output demand, and i s supplied only by e l e c t r i c i t y . In the road transportation sector, output energy demand ( i . e . road transportation services) can be met by ei t h e r conventional, o i l - f u e l e d v e h i c l e s , or by e l e c t r i c v e h i c l e s . (It has been suggested that automobiles could be converted to running on natural gas. This p o s s i b i l i t y i s not included i n the model since the present natural gas surplus i s only temporary. I t i s therefore u n l i k e l y that great changes w i l l be made i n the service stations and automobile engine design f o r a s h o r t - l i v e d innovation.) O i l i s the only f u e l which can supply the other transportation sector i n the model. I t i s assumed that the use of coal on railways and i n ships w i l l be n e g l i g i b l e , and that there are no technical a l t e r n a t i v e s to o i l fuels i n a v i a t i o n . In order to represent factors i n v o l v i n g geography, climate, the i n - troduction dates and rates of new technologies, etc., there are upper l i m i t s on some shares - the shares- of hydro i n e l e c t r i c i t y generation i n each region, the share of e l e c t r i c automobiles i n road transportation services, and the shares of so l a r heat, the heat pump and d i s t r i c t heating by co- generation i n the supply of heating i n 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 p r i o r to the e a r l i e s t date of introduction. There i s a const r a i n t which places an upper l i m i t on the f r a c t i o n of eastern crude o i l demand which can be met from western Canadian sources. This constraint represents the ph y s i c a l extent of the p i p e l i n e which c a r r i e s western o i l to eastern markets. I f the upper l i m i t on the f r a c t i o n i s l e s s than one i n any period, then the eastern region i s forced to r e l y on im- ported o i l or eastern offshore supplies, i f the l a t t e r are available i n s u f f i c i e n t q u a n t i t i e s . 34 The access of western coal and gas to eastern markets i s modelled by upper bounds on the flows of these commodities from west to east. In the case of coal, the p o t e n t i a l capacity l i m i t a t i o n i s taken to be i n the coal-handling f a c i l i t i e s at Thunder Bay. The bounds on the flow of gas from west to east are intended to represent the lack of a p i p e l i n e east of Montreal (or, i f the modeller wishes, the e l i m i n a t i o n of the upper bound represents the existence of a p i p e l i n e to Quebec and the Maritimes). Coal, o i l and gas may be exported from the west, and e l e c t r i c i t y may be exported from e i t h e r region. Since the assumed export p r i c e s are usually mugh higher than domestic p r i c e s , and since export revenues are benefits i n the model, upper l i m i t s are imposed on a l l exports, consistent with reasonable pr o j e c t i o n s . Without such upper l i m i t s , the model tends to set exports at absurdly high l e v e l s . (In an early stage of model de- velopment, the model was mistakenly run with no export l i m i t s , and with the highest cost source of " o i l " , methanol from biomass, av a i l a b l e i n unlimited q u a n t i t i e s at a cost lower than the export p r i c e . The problem was, of course, unbounded, since even a f t e r the r a p i d exhaustion of con- ventional o i l and t a r sands, the objective function could always be improved by producing and exporting more methanol from biomass). One reason f o r the need f o r export l i m i t s i s that the model i s determ i n i s t i c , viewing a l l re- sources and future conditions as known with c e r t a i n t y . I f t h i s were true, i t would make sense to export cheap supplies as quickly as possible to reap the large benefits of export revenues very e a r l y . In such a s i t u a t i o n , domestic energy p r i c e s would r i s e to the export prices and the "backstop" energy supplies would more quickly become the chief domestic energy sources. However, i n r e a l i t y , resources and a l l future conditions (e.g. the a v a i l - a b i l i t y of the backstop supplies) are uncertain, which has l e d p o l i c y makers to place r e s t r i c t i o n s on exports. Therefore, upper l i m i t s on ex- ports i n the model are r e a l i s t i c representations of decision-makers' risk-averse, somewhat n a t i o n a l i s t i c , behaviour. However, an examination of the opposite p o l i c y — u n r e s t r i c t e d exports -- would require a l t e r - ations to the model. I f i t i s assumed that Canada i s a price-taker, then energy exports would increase to the point where the marginal cost of production equals the export p r i c e , under an u n r e s t r i c t e d export p o l i c y . To represent t h i s behaviour, a model would need increasing marginal costs of labour, c a p i t a l , and possibly other inputs to the production of the commodities f o r export. The present formulation of the model has simply a single unit cost of production f o r each resource, which i s acceptable- i f exports are r e s t r i c t e d . In summary, the present formulation of the model i s as a r e s t r i c t e d - e x p o r t model, which represents the present r i s k - averse behaviour of national policy-makers. However, t h i s formulation has important implications for model behaviour: domestic energy p r i c e s w i l l not r i s e to world p r i c e s , but w i l l r i s e at the most to the backstop costs; the introduction of new, more c o s t l y technologies may be much l a t e r than i n an unrestricted-export model; and of course, resources w i l l be depleted much less quickly than i n an unrestricted-export model. In short, the l i m i t a t i o n of exports, with the implied two-price system (domestic and i n t e r n a t i o n a l ) , i s a key assumption. Except for coal, a l l energy flows are i n natural units i n the model. Coal i s i n units of l O 1 ^ BTU rather than i n tons because the si n g l e commodity, coal, i n the model represents a l l of the grades of coal, of d i f f e r e n t thermal contents. The units used i n the model are l i s t e d i n Table 1. Monetary values are expressed i n units of IO"1"0 d o l l a r s to avoid s c a l i n g d i f f i c u l t i e s i n the s o l u t i o n of the model. Table 1: Units Used i n the Model Coal i o 1 5 BTU O i l i o 9 b b l Gas i o 1 2 cubic feet (Tcf) E l e c t r i c i t y i o 1 2 kwh Solar Heat i o 1 5 BTU Heat by Cogeneration i o 1 5 BTU output energy i o 1 5 BTU monetary values i o 1 0 Canadian d o l l a r s In the reporting procedure a f t e r the model has been solved, coal quantities are expressed i n short tons, using the conversion factor, 1 short ton = 21 x lO^BTU, which i s midway between the factors for bituminous and sub-bituminous co a l . As w e l l , decimal points are s h i f t e d i n some pr i c e s to report them i n t h e i r most f a m i l i a r u n i t s . , The model i s a multi-stage nonlinear programming problem, with decisions i n one period a f f e c t i n g decisions i n future periods through the various constraints r e l a t i n g q u a n t i t i e s i n d i f f e r e n t time periods. To solve the problem, only a f i n i t e number of periods may be considered, i n - troducing possible end e f f e c t s , or d i s t o r t i o n s i n the f i n a l periods. For example, i f there i s no p r o v i s i o n i n the model for times beyond the end of the l a s t period, the production capacities of some depletable resources may be increased too r a p i d l y i n the l a s t few periods, exhausting the re- sources by the l a s t period and ignoring the usual constraints that o r d i n a r i would make new capacity l a s t a c e r t a i n length of time, beyond the l a s t period. Grinold (1980) describes various methods f o r mitigating end e f f e c t s . The most promising i s the dual equilibrium method. This pro- cedure has been adopted i n the l i n e a r process model of energy supply, and extended to the demand model. The e s s e n t i a l assumption i s that undiscounted pr i c e s are constant a f t e r the l a s t period ( i . e . a l l dual variables are con- stant, i f they are converted to undiscounted, actual values i n each period; and undiscounted output energy p r i c e s are constant). This i s c e r t a i n l y j u s t i f i e d i f p r i c e s reach the backstop costs by the l a s t period. Using t h i s basic assumption, extra variables and constraints are derived, along with a s p e c i a l weight f o r the nonlinear expression i n the objective function i n v o l v i n g the extra v a r i a b l e s . See Appendix B f o r d e t a i l s . Chapter 4. The Solution Method The equilibrium p r i c e s and energy quantities are calculated to maximize consumers' plus producers' surplus. In the l i n e a r process model of energy supply and d i s t r i b u t i o n , the t o t a l cost i n each period of supply- ing and d i s t r i b u t i n g a given mix of energy quantities i s 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 i n each time period. The difference between consumers' benefits and t o t a l cost for a given mix of energy supplies i s the consumers' plus producers' sur- plus i n a time period. Maximizing the consumers' plus producers' surplus i s equivalent to f i n d i n g the eight output energy demands f o r which the p r i c e paid by the consumer i s equal to the marginal cost - i . e . f i n d i n g the i n t e r s e c t i o n points of the demand and supply curves. This i s done i n a single maximization c a l c u l a t i o n f o r a l l time periods by maximizing the discounted sum of the consumers' plus producers' surpluses i n each time period. If E. = output energy i n an end-use sector i n period t 1, t ( i = 1,2, ...,8), P. = r e a l p r i c e output energy i n the end-use sector i,., I , t i n period t, and e i = p r i c e e l a s t i c i t y of demand i n the end-use sector i (ei > 0), then the demand curves are: E i , t = A i , t • P i , t " e i ' i = i ' 2 ' - - - ' 8 ' where A j _ t = t* i e P r°duct of the factors independent of P^ fc The consumers 1 benefits from using E. , are 1, t r E i , t r E i , t \P. , dE. = A Vf .U: 1/ 6 1 dE. t\ l , t l , t l , t \ l , t l , t • v0 0 0 • ,, • •, s , 1/ei 1-1/ei = e i / ( e i - l ) A. , . E. , + constant. 1, t l , t I f the lower l i m i t of i n t e g r a t i o n i s zero as above, then the constant term i s f i n i t e only i f 1-1/ei > 0 ( i . e . e i > 1). However, since the con- stant term i s independent of E. , the lower l i m i t of in t e g r a t i o n may be I , t s t r i c t l y p o s i t i v e (making the constant term f i n i t e without r e s t r i c t i n g ei) and the constant term may be dropped from the objective function. F i n a l l y , i f EĈ _ = t o t a l cost of the energy supply mix i n period t, and d = the r e a l s o c i a l 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 . E 1 " ^ 1 - EC ). t i = l l r t l f t t The whole optimization i s a nonlinear prograinming problem, with the above nonlinear objective function and the l i n e a r constraints of the l i n e a r process model of energy supply and d i s t r i b u t i o n . I t should be noted that i t i s assumed that there are no cross p r i c e e l a s t i c i t i e s among demands f o r output energy. Some such assumption i s necessary to make the matrix of p a r t i a l d e r ivatives of demands with re- spect to p r i c e s symmetric. This ensures that the demand functions are integrable (see, e.g., I n t r i l i g a t o r , 1971, p. 165) so that a u t i l i t y 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 i t i s here. I t does seem reasonable, however, to assume that demands f o r output energy i n the four sectors and two regions are independent to a great extent, that i s , that the cross p r i c e e l a s t i c i t i e s are zero. Solutions to the model have been obtained using the MINOS nonlinear programming algorithm, described i n Murtagh and Saunders (1977). This algorithm i s w e l l - s u i t e d to sol v i n g t h i s model, since i t i s designed for large-scale problems with l i n e a r constraints and nonlinear objective functions. MINOS i s a reduced gradient algorithm employing sparse LU f a c t o r i z a t i o n . A stable quasi-Newton method for optimizing the objective function within a given subspace i s used as long as storage requirements are not excessive. Otherwise, MINOS uses a conjugate-gradient method, which requires l i t t l e storage but which converges slowly. The model has 746 rows, 960 columns, 3423 non-zero matrix elements, and 56 variables entering nonlinearly i n t o the objective function. Solution of the model requires about 700 K bytes of storage. Usually the model i s solved by s t a r t i n g from a basis for a s i m i l a r problem, i n order to save computing time. In order to gain an appreciation of how e f f i c i e n t the model would be as a frequently-used t o o l i n energy p o l i c y a n alysis, the model was solved with high-case data (see Chapter 7), from a "cold s t a r t " , without s p e c i f y i n g an i n i t i a l basis near the optimal s o l u t i o n . (However, the INITIAL f a c i l i t y i n MINOS was used, with which the optimal s o l u t i o n to a r e l a t e d LP problem i s f i r s t found, with the nonlinear variables f i x e d at reasonable guesses, followed by the so l u t i o n of the NLP problem s t a r t i n g from the basis of the LP optimal s o l u t i o n ) . The s o l u t i o n of t h i s problem required 2 742 i t e r a t i o n s , and 301 CPU seconds on the IBM 3031 at the University of Waterloo. The CPU time includes both the MINOS ca l c u l a t i o n s of the optimal s o l u t i o n , and ca l c u l a t i o n s to produce more readable p r i n t e d output and p l o t f i l e s to be sent to the CALCOMP p l o t t e r (there are 27 p l o t s produced). •Chapter 5. An Overview of the Assumptions f o r the Base Case The data for the "base case" are the best estimates of a l l the model parameters, and the most l i k e l y projections of a l l exogenous variables and l i m i t s . The d e t a i l s of a l l derivations and sources may be found i n appendix C, "Data f o r 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 c a p i t a l and operating costs. In a l l such cases, a r e a l s o c i a l rate of return on c a p i t a l of 8% per annum was used to amortize the c a p i t a l costs over assumed f i x e d l i f e t i m e s of the processes' equipment. The choice of 8% was based on work by Jenkins (1977), who estimated r e a l s o c i a l rates of return on a l l p h y s i c a l c a p i t a l i n Canada for the period 1965-1974. Jenkins ad- justed reported rates of return by r e v i s i n g depreciation estimates to correspond to actual service l i v e s , and by removing the spurious e f f e c t s of i n f l a t i o n on c a p i t a l stock valuation (he estimates the current replacement value of the c a p i t a l stock) and on income (he makes an inventory valuation adjustment). The return on c a p i t a l includes a l l taxes a t t r i b u t a b l e to the c a p i t a l investment, i n order to derive a s o c i a l rate of return. The r e a l s o c i a l rate of return averaged over a l l i n d u s t r i e s ( i n c l u d i n g housing and a g r i c u l t u r e ) , weighting each industry's rate by the f r a c t i o n of t o t a l 1970 c a p i t a l stock found i n that industry, and averaged over 1965-1974, was approximately 8%. The r e a l s o c i a l discount rate, used i n the objective function, i s taken to be 10%, based on a r e s u l t of the study by Jenkins (1977). Jenkins calculated the s o c i a l opportunity cost of government expenditures. He assumed that i f government funds f o r expenditures are borrowed, then these funds are not a v a i l a b l e for the p r i v a t e sector to make the usual rate of 43- return. Furthermore, Jenkins assumes that even i f the funds were r a i s e d through taxes, they could a l t e r n a t i v e l y be used to lessen government debt, making more funds a v a i l a b l e to the p r i v a t e sector. In e i t h e r case, the p r i v a t e sector's usual rate of return enters i n t o the c a l c u l a t i o n of the s o c i a l opportunity cost of government expenditures. Other factors are the after-tax (Canadian taxes) rate of return earned by foreign investors i n Canadian assets, the decrease i n consumption due to increases i n personal savings when i n t e r e s t rates r i s e because of government borrowing, a "foregone foreign exchange premium", and the difference between the s o c i a l opportunity cost of labour and the wage rate which would be paid i f the investment funds were available to the p r i v a t e sector. Jenkins finds that "the s o c i a l opportunity cost of government funds i s at l e a s t 10 percent per year on the t o t a l amount invested i n p u b l i c p r o j e c t s . " - In the energy sector model d i s - cussed here, one of the key intertemporal elements i s the c a l c u l a t i o n of the p r i c e s of exhaustible resources. Since these p r i c e s include large r o y a l t y components, and since the r o y a l t i e s , or economic rents, accrue l a r g e l y to governments, i t i s sensible to use the s o c i a l opportunity cost of government . funds, 10 percent per year, as the discount rate. The National Energy Board (1979) has also used a 10% r e a l s o c i a l discount rate i n a cost-benefit analysis of new natural gas exports. A l l costs and p r i c e s i n the input data and i n the output are expressed i n r e a l terms, i n 1975 d o l l a r s . The Consumer Price Index has been used f o r a l l conversions to 1975 d o l l a r s , i n c l u d i n g conversions i n energy production sectors. The "low cost" l e v e l s , i n the approximations to the long-run supply curves for coal, crude o i l and natural gas production from sources important before 1975, are taken to be the average p r i c e s , at the point of extraction (after natural gas plant processing, i n the case of gas), j u s t p r i o r to the rapid r i s e i n p r i c e s i n the early 1970s. This procedure avoids the i n c l u s i o n of "windfall p r o f i t s " and v a s t l y increased r o y a l t i e s which are c h a r a c t e r i s t i c of the mid and l a t e 1970s. These estimates of production costs are on the high side, since r o y a l t i e s are included i n the prices which are used, although the r o y a l t i e s are at the r e l a t i v e l y low l e v e l s of the early 1970s. These low costs f o r e x i s t i n g sources are $0.20 per m i l l i o n BTUs f o r western coal, $0.80 per m i l l i o n BTUs f o r eastern coal, $4 per b a r r e l for western conventional o i l , and $0.30 per thousand cubic feet f o r western natural gas. The "high cost" l e v e l s f o r e x i s t i n g production, and the cost of l e v e l s f o r o i l and gas production not yet important i n the early 1970s, are based on estimates by other researchers, as explained i n appendix C. In p a r t i c u l a r , synthetic crude o i l from the t a r sands i s assumed to be a v a i l - able at a cost of $12 per b a r r e l , using estimates of c a p i t a l and operating costs by Energy, Mines and Resources (1977c), and a r e a l rate of return of 8% per annum, over 30 years. The non-fuel costs of f o s s i l - f u e l e l e c t r i c i t y generation are based on figures presented by Hedlin, Menzies and Associates (1976), using an 8% r e a l rate of return, over 30 years. The generation cost of h y d r o e l e c t r i c i t y i s assumed to be 7.7 m i l l s per kilowatt-hour, based on the c a p i t a l cost of a recent, large project i n Manitoba (see P r o t t i , 1978), using an 8% rate of return over 30 years, and assuming that non-fuel operating costs are the : same as f o r c o a l - f i r e d e l e c t r i c i t y . This i s i n l i n e with costs of projected new hydro s i t e s f o r several p r o v i n c i a l u t i l i t i e s (also i n P r o t t i , 1978). Nuclear e l e c t r i c i t y i s assumed to have a generation cost of 10 m i l l s per kilowatt-hour, using c a p i t a l and non-fuel operating costs i n Hedlin, Menzies and Associates (1976), and f u e l l i n g costs i n Kee and Woodhead (1977). The c a p i t a l and non-fuel operating cost estimates are higher than f o r e x i s t - ing .reactors, since they are based on Bruce units 5-8 which w i l l be oper- a t i o n a l i n 1983. The older Pickering reactor recorded a generation cost of l e s s than 8 m i l l s per kilowatt-hour i n 1976, according to Dalrymple and Anderson (1978). Except f o r d i s t r i c t heating by cogeneration, the non-fuel costs of heating i n the DFC sector are based on estimates presented by the Stanford Research I n s t i t u t e (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 i s based on work by Berthin (1980), using an 8% rate of return, over 30 years. The cogeneration cost i s mainly the d i s t r i b u t i o n cost — i . e . the cost of the network of pipes to the customers. The margins f o r d i s t r i b u t i o n , r e f i n i n g (in the case of o i l ) , and taxes, for coal, o i l , gas and e l e c t r i c i t y , , have been estimated by subtracting pro- duction costs from p r i c e s paid i n 1970 or 1971 (before the sharp increase i n energy prices) by customers i n the end use sectors. These margins are assumed to be constant i n a l l time periods. The extra cost of the e l e c t r i c automobile i s based on the estimate by Wayne (1979) of a $1500 p r i c e d i f f e r e n c e between the e l e c t r i c and con- ventional automobiles, i n Canadian, 1975 d o l l a r s . I t i s further assumed that cars l a s t 10 years and t r a v e l 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 m i l l i o n BTUs f or coal, $0.50 per b a r r e l f o r o i l (from Edmonton to Port C r e d i t ) , and $0.44 per thousand cubic feet for gas. The p r i c e e l a s t i c i t i e s of demand for output energy i n each end use sector are based mainly on work by Energy, Mines and Resources, and i n the case of road transportation, on Dewees, Hyndman and Waverman (1975) . The e l a s t i c i t i e s are 0.81 for the DFC sector (this would be 0.39 i f the output energy p r i c e d i d not include the non-fuel costs of heating), 0.48 f o r the i n d u s t r i a l sector, and 0.36 f o r both transportation sectors (see appendix A f o r d e t a i l s ) . The demand functions have been c a l i b r a t e d using p r i c e and quantity data from 1970 and 1971, and 1970 values of the indices f o r pop- u l a t i o n and f o r the exogenous economic parameters. The projections of the indices of the exogenous variables (eastern and western population, eastern and western r e a l domestic product, income per capita, and i n d u s t r i a l 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 r a t i o p r o j e c t i o n which i s based on the p r o j e c t i o n by Energy, Mines and Resources (1977a), u n t i l 1990. The growth rate of the c a p i t a l output r a t i o i s assumed to decrease to zero by the period a f t e r 2010. Population a f t e r 2000 i s assumed to grow at the rate of the mean of the S t a t i s t i c s Canada (cat. no. 91-520) pr o j e c t i o n s . Other economic variables a f t e r 2000 are t i e d to population growth, assuming approximately a 2% per annum rate of increase of output per worker, due to technological change. Conversion e f f i c i e n c i e s f o r coal g a s i f i c a t i o n and l i q u e f a c t i o n , and for heating i n the DFC sectors are based on estimates by the Stanford Re- search I n s t i t u t e (1976). End use conversion e f f i c i e n c i e s i n industry, road transportation and other transportation are based on estimates presented by Energy, Mines and Resources (1977a), with improvements i n the transportation sectors i n l a t e r periods. Conversion e f f i c i e n c i e s f o r e l e c t r i c i t y from f o s s i l f uels have been calculated from data for 1971-1975 compiled by S t a t i s t i c s Canada (cat. no. 57-207), with improvements assumed i n l a t e r time periods. The parameters representing energy industry use of the energy commodities are also based on S t a t i s t i c s Canada data f o r 1971-1975, with improvements assumed i n the case of e l e c t r i c i t y . The remaining reserves of o i l and natural gas are based on the 40% p r o b a b i l i t y l e v e l s of the resource estimates by Energy, Mines and Resources (1977b)(because the d i s t r i b u t i o n s are skewed, the 40% l e v e l i s closer to the mean value of the estimates than the 50% l e v e l ) . I t i s assumed that 9 there are 200 x 10 ba r r e l s of recoverable synthetic crude o i l from the t a r i-5 sands. Coal reserves are assumed to be very large i n the west — 1,587 x 10 BTUs at the low cost l e v e l — but very l i m i t e d i n the east — 22 x 10 "*"5 BTUs at the low cost l e v e l . The prices of coal imports and exports are assumed to increase at the r e a l rate of 2.5% per year u n t i l 2000, from t h e i r l e v e l s i n 1975. The r e a l p r ices of natural gas and crude o i l exports are assumed to increase at the rate of 4% per year u n t i l 2000. The o i l import p r i c e i s assumed to be lower than the export (international) p r i c e , i n the f i r s t three periods, because of the import subsidy. The subsidy i s reduced gradually to zero by the fourth period, 1991-2000. The upper l i m i t s on o i l and gas exports have been set at the currently approved export l e v e l s . Western coal exports are allowed to reach a maximum which increases at the rate of 5% per year. The maximum l e v e l s of e l e c t r i c i t y exports increase at the rate of 1% per year i n the two regions. Production from the tar sands i s f i x e d at the "base case" l e v e l of the National Energy Board (1978) f o r the f i r s t four periods. This i s necessary because the cost of syncrude from the t a r sands i s higher than most other sources of o i l , which would o r d i n a r i l y cause the t a r sands to be l e f t out of the model's s o l u t i o n u n t i l w e ll a f t e r the turn of the century. In r e a l i t y , though, t a r sands production i s an a t t r a c t i v e , immediate a l t e r n a t i v e , since i t i s c e r t a i n and accessible, while f r o n t i e r sources are not. F i x i n g pro- duction at the most l i k e l y l e v e l i s therefore a r e a l i s t i c approach. To ensure a reasonable t r a n s i t i o n to the use of eastern offshore o i l and gas, there are bounds on several variables i n the f i r s t few periods. Production of o i l from southeast offshore sources i s assumed to be ava i l a b l e i n large q u a n t i t i e s f o r the f i r s t time i n the 1986-1990 period, at a maximum l e v e l of 50 m i l l i o n b a r r e l s per year, with a buildup i n the previous period. There are no upper l i m i t s i n l a t e r periods. O i l production from northeast offshore sources i s allowed i n the model f o r the f i r s t time i n the period 1991-2000, at a maximum rate of 50 m i l l i o n b a r r e l s per year, with a buildup i n the previous period, and no l i m i t s i n l a t e r periods. Southeast offshore 12 gas i s ava i l a b l e i n the model s t a r t i n g i n 1988, at a maximum of 0.8 x 10 cubic feet per year, and- no upper l i m i t a f t e r 1990. Reasonable t r a n s i t i o n behaviour of energy flows from west to east are brought about by a constraint on o i l and upper bounds on coal and gas i n the f i r s t few periods. Western o i l i s allowed f u l l a c c e s s i b i l i t y to eastern markets f o r the f i r s t time i n the period 1986-1990. Upper l i m i t s on the transportation of western gas to the east, i n the f i r s t three periods, are intended to represent the possible i n s t a l l a t i o n of a Quebec and Maritimes p i p e l i n e i n 1985, and a five-year buildup to the f u l l p o t e n t i a l of gas i n the energy markets east of Montreal. The transportation of coal from west to east i s bounded above i n the f i r s t three periods, to represent l i k e l y l i m i t s on the coal-handling f a c i l i t i e s at Thunder Bay. The maximum production rate allowed from eastern coal reserves i s increased at the rate of 15% per year f o r the f i r s t three periods. Without such l i m i t s , the model tends to expand production u n r e a l i s t i c a l l y quickly, 'because the cost of eastern coal i s so low, compared to the a l t e r n a t i v e coal sources a v a i l a b l e to the eastern region. Chapter 6. Discussion of the Base Case Output. Throughout t h i s chapter and the two following chapters, there are many figures which present p l o t t e d output of the model. Since the p l o t t e d points (which are connected by s t r a i g h t l i n e s ) are the average values for the periods i n which they occur, the points have been p l o t t e d at the mid- points of the periods. Thus, the l a s t p l o t t e d point i n each graph i s for the year 2015, representing the average annual value i n the period 2011-2020. 6.1. O i l Production from conventional areas i n the west (Figure 4, 'western'), including Lloydminster heavy o i l s , continues at an almost steady l e v e l u n t i l 1990, then declines r a p i d l y . Northern f r o n t i e r o i l , both western A r c t i c and offshore Labrador, i s not used u n t i l a f t e r 2000, even though there are no exogenous assumptions which d i r e c t l y force such a l a t e entry. Southeastern offshore o i l becomes important a f t e r 1985, when exogenous upper l i m i t s i n the model f i r s t allow high production l e v e l s . This source i s depleted by 2020. O i l production from the-tar sands i s f i x e d at the National Energy Board (1978) base case l e v e l u n t i l 2000. A f t e r 2000, ta r sands production drops s l i g h t l y since there i s no new capacity added during 2001-2010, but o l d capacity i s r e t i r e d . I t then increases, to become the predominant o i l source (49% of t o t a l supply) i n the l a s t period (2011-2020). Imports cease a f t e r 1985, when i t i s assumed that the en t i r e eastern o i l market f i r s t becomes f u l l y accessible to western o i l . There i s no o i l pro- duced from coal and none from biomass. The t o t a l of o i l production plus imports drops from the f i r s t period to the second, and then l e v e l s o f f . Crude o i l p r i c e s (Figure 5) i n the east are $0.50 per b a r r e l higher than i n the west, a f t e r 1985, when there are no more imports. The $0.50 difference i s the transportation cost from west to east. Apart from t h i s 51 Table 2. O i l Production, Base Case. BASE CASE; OIL PRODUCTION: IN DNITS OF 10**9 BBL PEE YEAR AVERAGE VALUES FOR THE PERIOD ENDING IN 1980 1985 1990 2000 2010 2020 IMPORTS; FROM BIOMASS; FROM COAL; EASTERN; TAR SANDS; WEST ARCTIC; WESTERN; 0.2786 0.0000 0.0000 0.0008 0.0362 0.0000 0.5567 0.1109 0.0000 0.0000 0.0100 0.0744 0.0000 0.4956 0.0000 0.0000 0.0000 0.0500 0. 1534 0.0000 0.5010 0.0000 0.0000 0.0000 0.1772 0.2756 0.0000 0.2512 0.0000 0.0000 0.0000 0.2058 0.2516 0.0635 0.1319 0.0000 0.0000 0.0000 0.0740 0.3442 0.2554 0.0332 {N.B. The series i n th i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 4. Thus, the differences between the plotted l i n e s are the entries i n Table 2.) 52 1.60 I-.UO H BASE CRSE OIL PRODUCTION: IMPORTS X FROM BIOMflSS • FROM COAL <!> EASTERN X TAR SANDS + WEST ARCTIC * WESTERN © 1.20 H c r l . o o H LU LU Q_ 0.80 CO CD CD X X o 0.60 H 0.40 H 0.20 0.0 1975 1985 1995 2005 2015 2025 Figure 4. O i l Production, Base Case. 53 Table 3- Crude O i l Prices, Base Case. BASE CASE; CEODE OIL PBICES: IN UNITS OF 1975$ 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 L O r ~ CD 15.00 H IO.OO H 5.00 H 0.0 1975 1985 3  lSi 20LT5 2015 2025 Figure 5. Crude O i l Pri c e s , Base Case. 55 difference, p r i c e s (in 1975 $) i n both regions move gradually upward to the cost of synthetic crude o i l from the t a r sands ($12 per barrel) as the less costly o i l i s depleted. This $12 c e i l i n g i s to be expected, since the tar sands production i s e f f e c t i v e l y a "backstop" source of o i l over the timespan considered i n the model. (An examination of the value of the t a r sands reserves l i m i t constraint shows that the t a r sands are f a r from depletion, even inc l u d i n g the production for the extra "end e f f e c t s " period which i s an approximation of the remainder of the i n f i n i t e problem beyond 2020. See Appendix B, section 10 f o r d e t a i l s of the approximation.) However, p r i c e s are below the $12 c e i l i n g u n t i l a f t e r 2010, even though ta r sands production i s used, because t h i s o i l source i s forced i n t o the sol u t i o n exogenously i n the f i r s t four periods. The model brings new t a r sands capacity i n t o the s o l u t i o n without exogenously f o r c i n g i t only i n the s i x t h period, when the o i l p r i c e therefore reaches the t a r sands cost. The difference between the cost of o i l from the t a r sands ($12/bbl) and the western o i l p r i c e i n the s o l u t i o n of the model may be int e r p r e t e d as an upper l i m i t on the subsidy to be paid to t a r sands producers f o r the "insurance" of production from the c e r t a i n t a r sands resource, i n the face of uncertainties about the existence and costs of the other o i l resources. The o i l p r i c e s should therefore be viewed as lower l i m i t s (under the r e - s t r i c t e d trade, two-price assumption), except f o r the l a s t period. A de- t a i l e d , s t o c h a s t i c model of the o i l sector may be needed to examine more c a r e f u l l y the problem of the subsidy f o r t a r sands "insurance". In the f i r s t two periods,the eastern o i l p r i c e i s more than $0.50 above the western p r i c e because the east i s forced to r e l y to some extent on c o s t l y imported o i l . The eastern p r i c e i s the average of the western pri c e (plus the transportation cost) and the p r i c e of imported o i l , weighted by the two corresponding q u a n t i t i e s . The exogenous p r i c e s of o i l imports and exports are included i n Figure 5 f o r comparison with the endogenous domestic p r i c e s . The export p r i c e i s assumed to increase at the rate of 4 percent per year u n t i l the year 2000, and the import subsidy i s assumed to shrink to zero a f t e r the period ending i n 1990. The reader f a m i l i a r with the dictum that p r i c e must be equal to marginal cost may be puzzled by the f a c t that i n the f i r s t two periods the eastern p r i c e i s not as high as the p r i c e of imported o i l , which i s the highest cost source of supply i n those periods. The reason i s r e l a t e d to the form of the constraint l i m i t i n g the a c c e s s i b i l i t y of western o i l to the eastern region: NOMEM: WOE < opipe-E0G, where opipe = 0.54 and 0.77 i n the f i r s t and second periods, r e s p e c t i v e l y . In words, the constraint says that the amount of western o i l flowing east (WOE) must be less than or equal to a f r a c t i o n (opipe) of eastern o i l de- mand (EOG). In the t h i r d and l a t e r periods, opipe = 1.0, giving western o i l f u l l access to eastern markets. Because of exogenous l i m i t s on eastern production i n the f i r s t two periods, the constraint i s ..binding then, be- cause western o i l i s much cheaper than imported o i l . However, the marginal cost of o i l to the east i s not the p r i c e of imported o i l i n the model. A f r a c t i o n (opipe) of the l a s t b a r r e l of o i l demanded comes from the west, and the remaining f r a c t i o n (1-opipe) comes from imports. Therefore, the cost of the " l a s t b a r r e l " demanded i s the average of the p r i c e s of the two sources, weighted by t h e i r f r a c t i o n a l contributions to the " l a s t b a r r e l . " I f the constraint l i m i t i n g the flow of o i l from west to east had been a binding, absolute upper l i m i t rather than a " r e l a t i v e " upper l i m i t , then the marginal cost of eastern o i l would have been the p r i c e of imported o i l , since the " l a s t b a r r e l " of o i l would have come e n t i r e l y from imports. Of the two types of upper l i m i t - r e l a t i v e or absolute - which i s the more r e a l i s t i c ? An absolute upper l i m i t would c o r r e c t l y represent a sharply defined p h y s i c a l l i m i t on p i p e l i n e capacity, but i t may be argued that no such l i m i t e x i s t s . The v e l o c i t y of the f l u i d i n the pipe, and therefore the flow rate, can usually be increased, perhaps with a d d i t i o n a l pumping capacity, up to a point. A f t e r that point, capacity can be increased quickly (compared to the five-year length of the f i r s t two periods), by looping. Quick increases i n capacity may also be achieved by o i l "swap" agreements with the United States, whereby o i l i s shipped from western Canada to the United States and an equal amount i s shipped from the eastern United States to eastern Canada. However, i f there are i n f a c t constraints on western o i l production i n addition to those i n the model, then r e a l be- haviour may be more l i k e a model with an absolute upper l i m i t on o i l ship- ments from west to east. (The only l i m i t a t i o n s on western o i l production i n t h i s version of the model are the reserves l i m i t s , and the o i l production decline constraints by which new capacity i s forced to continue for ten years, then decline at 10% per year f o r 15 years, and then cease.) The present formulation, with the " r e l a t i v e " upper limit,-may therefore be viewed at l e a s t as a very p l a u s i b l e representation. The gradual t r a n s i t i o n to f u l l access to eastern markets for western o i l could be made f i r s t by supplying a l l Montreal r e f i n e r s 1 needs from the Sarnia to Montreal p i p e l i n e and secondly by e i t h e r constructing an extension of the p i p e l i n e to the east coast or constructing f a c i l i t i e s at Montreal for loading o i l onto tankers which would unload at points east of Montreal. The s o l u t i o n of the model, with the " r e l a t i v e " l i m i t on o i l shipments from west to east, i n e f f e c t indicates a s u b s i d i z a t i o n of the 58 portion of the east not served by western o i l , during the f i r s t two periods. Since the import p r i c e i n the model i s subsidized exogenously i n the f i r s t two periods (to represent behaviour i f the subsidy cost i s not borne by the energy sector, which appears to be the case), the r e s u l t s i n d i c a t e an ex- tension of the present p o l i c y of s u b s i d i z a t i o n out of concern by national p o l i c y makers for economic conditions i n the A t l a n t i c region and part of Quebec, which must r e l y on imported o i l . In the model, the further subsidy comes from an extra charge f o r o i l i n the portion of the east served by western o i l , making the calculated eastern p r i c e an average p r i c e . The other major o i l subsidy indicated by the model — that on t a r sands pro- duction — i s not included i n any s o r t of average. As discussed above, i t may be calculated a f t e r s o l u t i o n of the model as the difference between the cost of o i l from the t a r sands, and the western p r i c e calculated by the model. The difference i n p r i c e , above the transportation cost, between east and west i n the f i r s t two periods i s u n r e a l i s t i c (although not large - $2.37/bbl and $1.40/bbl i n the f i r s t two periods), given the federal govern- ment's determination to pursue a p o l i c y of a s i n g l e , national p r i c e . Since i t would be d i f f i c u l t to put a constraint i n t o t h i s model, representing a single, national p r i c e , i t i s probably best to assume that the calculated eastern p r i c e f o r crude o i l , adjusted f o r the west-to-east transportation cost, should be interpreted as the national o i l p r i c e , since eastern o i l demand i s much larger than western demand. Under t h i s i n t e r p r e t a t i o n , the calculated national o i l p r i c e i s shown below i n Table 4. Also included i n Table 4 i s the national o i l p r i c e i n nominal d o l l a r s , adjusted by the i n - crease i n the Consumer P r i c e 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 r e - maining periods. For reference, the c e i l i n g p r i c e of $12/bbl — the cost of o i l from the t a r sands — i s converted to nominal d o l l a r s i n the t h i r d l i n e of Table 4. . _ Table 4. National O i l Pric e , Real and Nominal D o l l a r s , 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 f i r s t period's p r i c e compare with the actual p r i c e levels? According to H e l l i w e l l (1979), the actual wellhead p r i c e s i n 1978, the re- presentative year of the f i r s t period, were $11.75/bbl a f t e r January 1, and $12.75 a f t e r July 1. The nominal p r i c e c alculated by the model, $9.48/bbl, i s lower than the actual p r i c e . This may ind i c a t e that the o i l production costs perceived by the o i l industry have been higher than has been assumed i n t h i s study. The p o s s i b i l i t y that o i l costs are higher than those assumed f o r the base case i s examined i n Chapter 8. 1 Such uncertainties i n key data indicate the need f o r continually updating a model such as t h i s one. An e a r l i e r discussion indicated that the assumption of o i l export l i m i t s implies a two-price system for o i l — the domestic p r i c e i s lower than the i n t e r n a t i o n a l p r i c e , and i t has a c e i l i n g equal to the domestic backstop cost (as long as the o i l export l i m i t s are not so great that the tar sands are exhausted i n the model). A r e l a t e d observation may be made: i f the p r i c e paid to o i l producers i s r a i s e d much higher than the domestic equilibrium p r i c e (allowing f o r r o y a l t i e s to the owners, p r o v i n c i a l govern- ments), there would be very strong pressure to r a i s e export l i m i t s , as pro- ducers would bring i n higher cost supplies too quickly to be absorbed i n the domestic market. This has happened recently i n the Canadian natural gas industry. The p r i c e paid to producers (the "netback", not including r o y a l t i e s ) was increased dramatically a f t e r 1974, leading to vast new additions to reserves and tremendous industry pressure to export more natural gas. The same phenomenon could be observed i n the case of o i l i f the domestic p r i c e i s r a i s e d much above the domestic equilibrium p r i c e and i f the producing companies receive some of t h i s extra economic rent. I t i s now c l e a r why there i s no o i l produced from coal, and none from biomass. With the p r i c e of coal i n the model output, the d i s t r i b u t i o n margin applied to coal f o r o i l production, the assumed fa c t o r for conversion of coal to o i l , and the assumed conversion cost, the cost of o i l from coal i s $17.23/bbl i n a l l periods (1975 $). Therefore, as long as the t a r sands can produce, with no binding upper l i m i t s , at $12.00/bbl, coal from o i l w i l l be uneconomic. I t should be noted that one key assumption i n t h i s matter i s that the same d i s t r i b u t i o n margin for coal to western industry applies to coal for l i q u e f a c t i o n . This margin amounts to $7.46 of the $17.23/bbl. I t i s conceivable that t h i s d i s t r i b u t i o n margin could be lower, since coal l i q u e f a c t i o n plants could be located close to the mine. Even with no d i s - t r i b u t i o n margin, coal l i q u e f a c t i o n would not be economic u n t i l a f t e r 2000, given the p r i c e s i n the base case s o l u t i o n . O i l products from biomass, assumed to cost $25/bbl, are also uneconomic as long as o i l i s a v a i l a b l e from the t a r sands or from coal l i q u e f a c t i o n . Of course, i f i t turns out that there are unavoidable environmental or other l i m i t s on t a r sands production, or i f the o i l p r i c e i s set above the optimal p r i c e , we could see o i l from biomass or c o a l . An examination of the d e t a i l e d output of the base case reveals that the rate of transport of western o i l to the east decreases as eastern offshore o i l 61 Table 5. O i l 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 6. Thus, the differences between the plotted l i n e s are the entries i n 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. O i l Use, Base Case. ' i s exploited, beginning mainly a f t e r 1990, but i t r i s e s again a f t e r 2010 when the main o i l source f o r the east i s from the west (mainly from the tar sands, but also from the western a r c t i c ) . O i l i s used i n the DFC sector for heating (Figure 6) i n the early periods, but i s phased out r a p i d l y to zero i n the west a f t e r 1985, and i n the east a f t e r 1990. O i l ceases to be used f o r e l e c t r i c i t y i n the west and east a f t e r 2000. The use of o i l i n industry peaks i n the period ending i n the year 2000. (For a complete discussion of f u e l use i n industry, see section 6.6 below, i n t h i s chapter.) O i l remains the sole f u e l used i n road transportation (the e l e c t r i c automobile i s not i n the optimal s o l u t i o n ) . Because of assumptions about early, rapid improvements i n the e f f i c i e n c y of automobiles, the use of o i l i n road transportation stays nearly constant u n t i l a f t e r 2000, then begins to r i s e , since e f f i c i e n c y improvements are not assumed to be as rapid then. The use of o i l i n "other" transportation increases gradually, and exports of crude o i l and o i l products are at the exogenously assumed upper l i m i t s . Total o i l use drops by a large amount between the f i r s t and second periods, f o r several reasons — the o i l export l i m i t i s lower, the eastern o i l p r i c e r i s e s to a temporary peak i n the east i n the second period ( i t f a l l s i n the t h i r d ) , and o i l i s phased r a p i d l y out of use i n several areas, as discussed above. 6.2. Natural Gas Natural gas production (Figure 7) -is almost e n t i r e l y from the con- ventional western areas u n t i l a f t e r 1985, when s i g n i f i c a n t q u a n t i t i e s of southeast offshore gas are allowed to enter the model s o l u t i o n . Western conventional gas production peaks i n the period 1981-1985. This i s roughly i n agreement with the National Energy Board (1979), which projects a peak i n 1985. Overa l l production, including eastern production peaks i n the period 1986-1990. Eastern production by i t s e l f peaks i n the period 1991-2000. Natural gas from northeast offshore sources i s not needed u n t i l a f t e r 2000, and gas from the northwest a r c t i c i s not used u n t i l a f t e r 2010. This conclusion c l e a r l y contradicts the conclusions reached by the National Energy Board (NEB) and the Department of Energy, Mines and Resources i n the mid- 1970s, reported i n H e l l i w e l l (1979, Table 7). The "date of estimated need for f r o n t i e r gas" made by the NEB i n 1969, according to H e l l i w e l l (1979, Table 7) was a f t e r 2000, as t h i s present model p r e d i c t s . As H e l l i w e l l (1979) discusses, the reasons f o r the mid-1970s pessimism about conventional natural gas supplies, at l e a s t i n the case of the NEB, included the NEB's acceptance of the arguments by the Mackenzie'Valley p i p e l i n e groups, the major pro- ducing companies, and some Canadian n a t i o n a l i s t groups and i n d i v i d u a l s . According to H e l l i w e l l (1979), the p i p e l i n e r s were t r y i n g to j u s t i f y t h e i r northern gas p i p e l i n e a p p l i c a t i o n s , the producers were attempting to show the need for higher p r i c e s and lower taxes, using the argument that the ex- pensive northern gas must soon be tapped, and the n a t i o n a l i s t s argued that the need for expensive northern gas proved that o i l and gas exports should be reduced immediately. There i s a t i n y amount of gas produced from biomass a f t e r 2000 i n the east, at the upper l i m i t s allowed i n the base case. There i s no gas produced from coal. The use of natural gas (Figure 8) f o r e l e c t r i c i t y declines to zero a f t e r the turn of the century. However, the use of gas i n both the DFC and i n - d u s t r i a l sectors grows u n t i l 2000. Gas use i n western industry f a l l s to i t s lower l i m i t (in share terms) i n the next period, producing a dip i n the t o t a l of i n d u s t r i a l gas use i n both regions. (See section 6.6 below f o r a discussion 65 Table 6. Gas P r o d u c t i o n , 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom entry o f the t a b l e , t o a r r i v e at the values o f the p l o t t e d l i n e s i n F i g u r e 7. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n 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 B A S E C A S E GPS PRODUCTION: FROM BIOMflSS FROM CORL ERSTERN WEST ARCTIC WESTERN 19̂ 5 <!> X + © 1995 SiJ 2005 2015̂  20̂ 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 i n this table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 8. Thus, the differences between the plotted l i n e s are the entries i n 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 P r i c e s , 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 C o r r e c t e d , 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 19̂ 5 l S 2005 2015 20^5 Figure 9. Gas Pr i c e s , Base Case. 71 "of f u e l shares i n industry.) Exports continue to be very large i n the f i r s t two periods, but decline to zero by the turn of the century. Exports are at the exogenous upper l i m i t s , which represent e x i s t i n g approved exports, as reported by the NEB (1979). Wellhead p r i c e s f o r gas i n the west (Figure 9) r i s e quite smoothly from $.92/mcf i n the f i r s t period to $2.50/mcf a f t e r 2010. The l a t t e r p r i c e i s the cost of "low cost" gas from the western a r c t i c , which comes in t o use a f t e r 2010 f o r the f i r s t time. Toronto city-gate prices are more v o l a t i l e than western p r i c e s , with quite high p r i c e s i n the f i r s t two periods, followed by a drop,- then a r i s e to $3.00/mcf a f t e r 2000, when northeastern offshore gas (costing $3.00/mcf) f i r s t comes in t o use. A large component of the eastern p r i c e i n the f i r s t three periods i s due to the binding upper l i m i t on WGE, gas transported from west to east, i n these periods. This l i m i t , which i s increased at the rate of 3.5% per year i n the f i r s t two periods (from i t s l e v e l i n 1971-1975) and by a larger amount i n the t h i r d period, i s intended to represent the i n i t i a l i n a c c e s s i b i l i t y of gas to points east of Montreal, followed by an extension of the p i p e l i n e to Quebec and the Maritimes during the t h i r d period, from 1986-1990. There i s no upper l i m i t on WGE a f t e r the t h i r d period. This method of representing the i n a c c e s s i b i l i t y of gas to part of the east has the drawbacks that the model behaves as i f consumers i n a l l of the eastern region have access to gas d i s t r i b u t i o n l i n e s and as i f equipment that uses gas i s spread evenly over the e n t i r e region. The imposed supply shortage forces the p r i c e up and drives some gas "users" to alternate f u e l s . Of course, there w i l l be no gas d i s t r i b u t i o n l i n e s i n the region i n question f o r several years, at l e a s t , and there w i l l be no gas- using equipment there u n t i l then. A more t h e o r e t i c a l l y pleasing procedure to represent the s i t u a t i o n would involve the d i s t i n c t i o n of a t h i r d region which has no gas-using equipment i n the end-use sectors and secondary e l e c t r i c i t y , and which shrinks i n some way to represent the extension of the gas p i p e l i n e and gradual market penetration of gas. However, such a procedure would introdue great complexities. A simpler procedure i s the present model formulation, together with the recognition that the com- ponent of the eastern p r i c e which i s due to the upper l i m i t on WGE i s a r t i f i c i a l and should be removed. This p r i c e component r e f l e c t s an a r t i f i c i a l , u n s a t i s f i e d demand for gas i n the model from points east of Montreal. The corrected Toronto city-gate gas p r i c e i s given i n Table 8, according to t h i s approximation to the more t h e o r e t i c a l l y exact type of model discussed above. The corrected p r i c e f o r gas at Toronto i n the f i r s t period (whose re- presentative year i s 1978) agrees well with the Toronto city-gate p r i c e s i n 1978 reported by H e l l i w e l l (1979). I f the corrected p r i c e i s i n f l a t e d by the increase i n the Consumer Price Index between 1975 and 1978 (26%), reported by the Economic Council of Canada (1979), the pr i c e i n 1978, i n 1978$, i s $1.87/mcf. The actual Toronto city-gate p r i c e s i n 1978, reported by H e l l i w e l l (1979) were $1.68/mcf during January, $1.85/mcf beginning on February 1, and $2.00/mcf beginning on August 1. The Department of Energy, Mines and Resources (1976a) has stated a p o l i c y of moving domestic natural gas pr i c e s to an "appropriate competitive r e l a t i o n s h i p with o i l " . What i s t h i s r e l a t i o n s h i p , according to the base case r e s u l t s of t h i s model? The following table shows the p r i c e s of natural gas i n the west and east (corrected as above), as percentages of the pri c e s of crude o i l , where p r i c e s are i n i t i a l l y expressed i n d o l l a r s per m i l l i o n BTUs, using the conversion fa c t o r s : 1 oncf gas = 1.04 MMBTU, and 1 bb l o i l = 5.8 MMBTU. The crude o i l p r i c e s were taken to be the national 73 •wellhead p r i c e s calculated i n section 6.1 of t h i s chapter, f o r the west, and the same prices f o r the east, adjusted upward by the cost of trans- porting o i l from west to east ($.50/bbl). Table 9. Gas Prices as Percentages of O i l 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 r e l a t i o n s h i p " should be d i f f e r e n t i n the two regions. According to t h i s a n a l y s i s , gas i n the east should be p r i c e d about equivalently with o i l u n t i l 1990 but s i g n i f i c a n t l y higher than o i l a f t e r 1990. However, i n the west, gas should be p r i c e d considerably below the equivalent o i l p r i c e u n t i l 1990 (perhaps 2/3 of the o i l p r i c e , roughly), but the p r i c e should move to somewhat higher than the o i l p r i c e a f t e r the year 2000. The higher p r i c e r a t i o i n the east may be l a r g e l y explained by the f a c t that the west-to-east transport cost i s a much greater f r a c t i o n of the eastern gas p r i c e than of the eastern o i l p r i c e (the transport costs are $.44/mcf and $.50/bbl). Thus, the conclusion that the "appropriate competitive r e l a t i o n s h i p " should be d i f f e r e n t i n the two regions i s simple to understand, but i t may not have been obvious without the "prompting" of the model r e s u l t s . I t i s now apparent why there i s no gas from coal i n the base case s o l u t i o n . Using the p r i c e of coal i n the s o l u t i o n , the assumed d i s t r i b u t i o n margin for coal used i n g a s i f i c a t i o n , and the assumed conversion e f f i c i e n c y and cost, the cost of gas from coal would be $3.00/mcf. Since the p r i c e of gas i n the west (the only region i n which g a s i f i c a t i o n i s allowed) only reaches $2.50/mcf over the time span of the model, coal g a s i f i c a t i o n i s uneconomic. Coal g a s i f i c a t i o n could therefore be introduced some time a f t e r 2020, when the western a r c t i c gas costing $2.50/mcf nears depletion. Note that $1.41/mcf of the $3.00/mcf cost i s due to the.assumed margin f o r the d i s t r i b u t i o n of coal to industry, which i s also applied to coal f o r g a s i f i c a t i o n . However, even i f t h i s margin were zero (for a mine-mouth plant, say), coal g a s i f i c a t i o n would not be economic u n t i l a f t e r 2000, given the western gas p r i c e s from the base case s o l u t i o n . In the long run, though, coal g a s i f i c a t i o n could play the r o l e of a backstop technology for gas, be- cause of the huge siz e of the coal reserves. 6.3. Coal Coal production (Figure 10) r i s e s quite s i g n i f i c a n t l y over the time span of the model. Eastern coal imports decline to zero a f t e r 1985, when a combination of eastern coal production and shipments from the west be- comes s u f f i c i e n t to meet eastern demand. There i s a strong and growing demand i n the east for western coal, through a l l time periods. Eastern "low-cost" coal i s depleted by 2020, but western "low-cost" coal i s f a r from depletion. Eastern use of coal (Figure 11) f o r e l e c t r i c i t y drops to zero a f t e r 2000, but i n the west, coal used f o r e l e c t r i c i t y production grows gradually u n t i l 2010, and sharply a f t e r that. The combined e f f e c t on t o t a l use of coal for e l e c t r i c i t y i n both regions i s a temporary drop i n the period ending i n 2010, followed by an increase. A f t e r 2000, there i s cogeneration of heat for space heating from c o a l - f i r e d e l e c t r i c i t y production i n the west. The sharp increase, a f t e r 2010, i n coal used for e l e c t r i c i t y i n the west i s re l a t e d to the s u b s t i t u t i o n of cogeneration for gas heating i n the DFC sector (Figure 2 3 ) T h e r e i s no coal used for l i q u e f a c t i o n or g a s i f a c t i o n . In l a t e r periods, a f t e r 1990, industry i s the biggest coal user, i n both regions. Exports increase at the rate of 5% per year, which i s 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 10. Thus, the differences between the plotted l i n e s are the entries i n 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 i i 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 11. Thus, the differences between the plotted l i n e s are the entries i n 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 P r i c e s , 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 L U ° - 28.00 H L O CD 21.00 H 14.00 H 7.00 H © © © ©- -©- -© 0.0 1975 1985 35 19̂ 5 2005 . 2015 "2025 Figure 12. Coal Prices, Base Case. -upper l i m i t . Coal p r i c e s (Figure 12) i n the west are at the "low-cost" i n a l l time periods, because the "low-cost" coal i s not depleted, even inc l u d i n g pro- duction i n the extra period which mitigates end e f f e c t s . A f t e r 1990, eastern coal p r i c e s are equal to the "low-cost" of western coal, plus the cost of transporting coal from west to east. Before 1990, there i s a bulge i n eastern coal p r i c e s due to the (binding) upper l i m i t placed on WCE, the quantity of coal shipped from west to east, i n the f i r s t three periods. These upper l i m i t s are intended to represent the capacity of the coal-handling f a c i l i t i e s at Thunder Bay on Lake Superior. 6.4. E l e c t r i c i t y Production of e l e c t r i c i t y (Figures 13,14) from o i l and gas i s phased out by the turn of the century i n both regions. The bulk of e l e c t r i c i t y i n the west i s produced from hydro power, with the remainder (except'for e l e c t r i c i t y from o i l and gas i n the f i r s t four periods) produced from co a l . The production of h y d r o e l e c t r i c i t y never reaches i t s exogenous maximum be- fore 2020 i n the west, but the eastern maximum i s reached a f t e r 1990, f o r c i n g an increasingly heavy r e l i a n c e on nuclear power a f t e r the turn of the century. This may be interpreted to mean that a f t e r the turn of the century, Quebec and Newfoundland, with t h e i r James Bay and Labrador s i t e s f u l l y developed, w i l l be forced to adopt a nuclear future, as Ontario has done. The rapid r i s e i n generation i n the west during the period a f t e r 2010 — at the rate of 9.8% per year — corresponds to a s u b s t i t u t i o n of e l e c t r i c i t y f o r o i l i n western industry. The large increase i n the east a f t e r 2000 — at the rate of 8% per year i n the period 2001-2010 — corresponds to a switch from o i l to e l e c t r i c i t y i n eastern industry, and to a switch from gas heat to e l e c t r i c resistance i n the eastern DFC sector. (See section 6.6 below f o r 82 Table 13. Western E l e c t r i c i t y 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 13 . Thus, the differences between the plotted l i n e s are the entries i n 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 O J .—I X D 0.30 H 0.20 H o.io H © — © — © 0.0 1975 1985 3 19&5 2005 20*15 2025 Figure 13. Western E l e c t r i c i t y Production, Base Case. 84 Table 14. Eastern E l e c t r i c i t y P r o d u c t i o n , 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y o f the t a b l e , t o a r r i v e at the valu e s of the p l o t t e d l i n e s i n F i g u r e 14. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n 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 E l e c t r i c i t y Production, Base Case. 86 Table 15. E l e c t r i c i t y 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 15. Thus, the differences between the plotted l i n e s are the entries i n Table 15.) 87 BASE CASE ELECTRICITY USE: EXPORTS ELECTRIC AUTO INDUSTRY OFC 2.40 H Figure 15. E l e c t r i c i t y Use, Base Case. 88 Table 16. Western E l e c t r i c i t y P r i c e s , 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 19̂ 5 2005 2015 20̂ 5 Figure 16. Western E l e c t r i c i t y P r i c e s , Base Case. 90 Table 17. Eastern E l e c t r i c i t y P r i c e s , 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 E l e c t r i c i t y P r i c e s , Base Case. a discussion of i n d u s t r i a l f u e l use i n the model.) The use of e l e c t r i c i t y (Figure 15), except for exports, grows at an average rate of 5.2% per year between 1978 and 1995 (the representative years of the f i r s t and fourth periods, r e s p e c t i v e l y ) , and at 5.1% per year between 1995 and 2015. E l e c t r i c i t y exports from the two regions are at the exogenously s p e c i f i e d l e v e l s , increasing at the rate of 1% per year. There i s a quickly growing demand f o r e l e c t r i c i t y i n industry. The growth i n e l e c t r i c i t y demand from the DFC sector i s quite strong a f t e r 2000, when there i s a switch from gas heat to e l e c t r i c resistance and s o l a r i n the east. The growth i n DFC demand slackens somewhat a f t e r 2010, when s o l a r heating becomes quite important i n the east. I t might be noted that s e l f - generation of e l e c t r i c i t y by industry i s not e x p l i c i t l y allowed i n the structure of the model. However, the margins allowed i n the model f o r the d i s t r i b u t i o n of e l e c t r i c i t y to the i n d u s t r i a l sectors are very small (1.8 mills/kwh i n the west, and -1.0 mills/kwh i n the east) compared to the generation costs and to the margins for d i s t r i b u t i o n to the other sectors. Therefore, to minimize the s i z e of the model, the p o s s i b i l i t i e s of i n d u s t r i a l self-generation of, s a y , h y d r o e l e c t r i c i t y or e l e c t r i c i t y from wood waste, were included i n the appropriate e l e c t r i c i t y variables as_ if_ such e l e c t r i c i t y o riginated from the u t i l i t i e s . E l e c t r i c i t y p r i c e s (Figures 16,17) are stable i n both regions. The cost of nuclear power (1 cent per kwh) becomes the determining element of eastern e l e c t r i c i t y p r i c e s a f t e r 2000, when hyd r o e l e c t r i c production i s at i t s 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 18. Thus, the differences between the plotted l i n e s are the entries i n 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 3  19&5 2005 2015 20^5 Figure 19. Western Output Energy .Prices, Base Case. 97 Table 20. E a s t e r n output Energy P r i c e s , 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 L U Q 1.50 l . o o H 0.50 H •—f- 0.0 1975 1985 3 19̂ 5 2005 i o ^ 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 i n the face of r i s i n g o i l prices can be explained by a look at the p r i c e s of energy i n the road transportation sectors (Figures 19,20). Apparently the assumed rate of increase of automobile e f f i c i e n c y i s more than enough to o f f s e t the e f f e c t of r i s i n g o i l prices on the p r i c e of output energy (except for the l a s t period). Although motorists w i l l be paying more and more per gallon f o r f u e l , they w i l l be spending le s s and less per mile f o r f u e l , according to the base case s o l u t i o n . Thus, even though population growth slows, the d e c l i n i n g cost of road transportation encourages rapid growth i n the t o t a l amount of d r i v i n g which people do. The e l e c t r i c automobile i s not introduced i n e i t h e r region. The following chart shows the p r i c e s of output energy, i n model u n i t s , i n road transportation, using the conventional and the e l e c t r i c automobile. (The p r i c e for conventional i s from the gradient of the objective function, with the discounting removed, while the e l e c t r i c p r i c e i s derived from the e l e c t r i c i t y generation p r i c e , plus the d i s t r i b u t i o n margin, converted to an output p r i c e , and added to the d i f f e r e n t i a l cost of the e l e c t r i c car.) Table 21. Road Transportation P r i c e s , 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, e l e c t r i c 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, e l e c t r i c n.a. n.a. 2.1376 2.1319 2.2043 2.2043 Two major elements i n the p r i c e of road transportation by e l e c t r i c 100 "car are the road tax assumed to be placed on e l e c t r i c i t y f o r e l e c t r i c autos (equal to 0.4313 i n the units of the above chart), and the extra i n i t i a l cost of the e l e c t r i c automobile versus a conventional one (equal to 1.32 i n the above u n i t s ) . According to the base case r e s u l t s , then, a s u b s t a n t i a l narrowing of the difference i n the prices ($1,500 f o r sub- compacts i s assumed here) of the e l e c t r i c and conventional autos w i l l be necessary, perhaps i n combination with a lessening of the road tax for the e l e c t r i c a l t e r n a t i v e , i f the e l e c t r i c auto i s to be competitive. I t i s worth noting, too that the increasing e f f i c i e n c y of the conventional auto makes the e l e c t r i c auto (assumed to have a constant e f f i c i e n c y ) less com- p e t i t i v e . 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 i n other transportation compared to road transportation i s l i k e l y due to an assumed slower growth i n e f f i c i e n c y , which o f f s e t s r i s i n g o i l p r i c e s less than i n road transportation. This i s apparent from a glance at the p r i c e indices f o r other transportation (in Figures 19, 20). 6.6. Industry The use of o i l and gas i n industry (Figure 21) peaks i n the period 1991-2000. A f t e r 1990, coal becomes a very important source for industry, and a f t e r 2000, e l e c t r i c i t y plays the l a r g e s t role of a l l the four f u e l s . Total output energy used i n 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 p r i c e s for industry (Figures 19,20) are somewhat e r r a t i c , p a r t i c u l a r l y i n the east, i n part because any e f f i c i e n c y changes are due 101 Table 22. I n d u s t r i a l 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 i n th i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 21. Thus, the differences between the plotted l i n e s are the entries i n 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 L O 6.00 5 4.50 3.00 1.50 H 0.0 1975 1985 3  l S 2005 2015 20^5 Figure 21. I n d u s t r i a l Output Energy, by Fuel, Base Case. s o l e l y to the changing f u e l mix, and because of the bulges i n o i l and gas prices i n the f i r s t two periods i n the east. The somewhat e r r a t i c behaviour (ups and downs) of e l e c t r i c i t y , gas and o i l use i n industry i s due to the model structure. There are upper and lower bounds on the shares of i n d u s t r i a l output energy i n the model. A lower bound indicates non-substitutable uses of the f u e l . Above the lower bound, there i s p e r f e c t i n t e r - f u e l s u b s t i t u t a b i l i t y , up to a point (the upper bound). These share bounds spread apart u n t i l 2000 and are constant a f t e r that. At the optimal s o l u t i o n , the i n d u s t r i a l f u e l mix i n a period i s the l e a s t cost mix, given a l l the optimal f u e l p r i c e s . I t i s therefore not s u r p r i s i n g to see the e r r a t i c behaviour of some f u e l s . Table 23 gives the calculated shares of the four fuels i n i n d u s t r i a l output energy, at the optimal s o l u t i o n of the base case. Table 23. Shares of Fuels i n I n d u s t r i a l Output Energy, Base Case. (Note: The symbols " which are at (L)" and "(u)" indi c a t e the t h e i r lower or upper bounds, shares resp e c t i v e l y .) Period Ending Fuel Region 1980 1985 1990 2000 2010 2020 E l e c t r i c i t y 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 • K L ) • K L ) • K L ) -KL) • K L ) O i l West East .24(L) .40(U) .21(L) .25(L) •17(L) .28 . 1 (L) .38 .4 • K L ) • K L ) • K L ) The upper and lower bounds were taken from estimates by Hedlin, Menzies and Associates (1976) of future t e c h n i c a l p o s s i b i l i t i e s i n the i n d u s t r i a l sector. An a l t e r n a t i v e method of modelling f u e l shares might involve- econometric estimation of s u b s t i t u t i o n parameters i n a function g i v i n g i n - d u s t r i a l output energy for d i f f e r e n t f u e l inputs. Although such an approach would l i k e l y produce smoother projections of f u e l shares, i t would be based on past t e c h n i c a l p o s s i b i l i t i e s , a serious drawback when making projections into the d i s t a n t future. The best approach t h e o r e t i c a l l y , would be to d i s - t inguish i n d u s t r i a l 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 i n the model's structure can l i k e l y be corrected only by a large e f f o r t i n the categorization of i n d u s t r i a l uses of energy, together with estimates of demand curves for these categories. Since there i s apparently no r e l i a b l e data i n t h i s area, the present form- u l a t i o n of the i n d u s t r i a l sector of the model i s the best possible now. 6.7. DFC Heating O i l heating (Figures 22,23) i s phased out as r a p i d l y as possible i n the west (zero a f t e r 1985). However i n the east, there i s new o i l heating capacity i n s t a l l e d i n the f i r s t period, and o i l heating i s consequently phased out l a t e r i n the east than i n the west (zero a f t e r 1990). Gas heating plays a b i g r o l e i n the west u n t i l 2010, and i n the east u n t i l 2000. Depletion of the low cost reserves, and the r i s i n g gas p r i c e s make al t e r n a t i v e fuels more economical a f t e r these dates. E l e c t r i c resistance heating i s phased out quickly i n the west (zero a f t e r 1985), i n favour of gas, and l a t e r cogeneration and solar, but i t plays an increasingly important role i n the east, becoming the si n g l e most important heating source i n the east a f t e r 2000, when gas becomes too expensive. Heating by cogeneration with c o a l - f i r e d e l e c t r i c i t y production i s used i n the west a f t e r 2000 (the model allows i t a f t e r 1980), but not at a l l i n the east because cogeneration with nuclear e l e c t r i c i t y production i s not allowed i n the base case, and because there i s no new c o a l - f i r e d e l e c t r i c i t y 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , to a r r i v e a t the valu e s of the p l o t t e d l i n e s i n F i g u r e 22. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a r e the e n t r i e s i n 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 5 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 23. Thus, the differences between the plotted l i n e s are the entries i n 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 i n the east. The heat pump i s not i n the solu t i o n i n ei t h e r region. Solar heating i s used i n the west to i t s maximum allowed share a f t e r 2010, but i s at the zero l e v e l before 2010. Solar i s at i t s maximum share a f t e r 2000 i n the east (when e l e c t r i c i t y p r ices increase s i g n i f i c a n t l y ) , and zero before then. In both the west and east, solar heating i s allowed by the model constraints a f t e r 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 i n the west and east, given the e l e c t r i c i t y p r i c e s calculated i n the base case, and a l l of the assumed conversion e f f i c i e n c i e s and costs. Table 26. Heat Pump Costs (in model u n i t s ) , 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 i s 0.706, i n model units, i t i s cl e a r from the above figures why sol a r heating i s the preferred new technology. I t was assumed f o r both regions that the non-fuel cost of the heat pump for heating purposes was 5/6 of the t o t a l cost, since 1/2 of the users would have a i r conditioning with or without a heat pump, and that the a i r con- d i t i o n i n g function of a heat pump would be used i n 1/3 of the year, f or a t o t a l , average c r e d i t of 1/6 of the non-fuel cost. I t may be argued that f o r the h a l f of the users who would have a i r conditioning i n any case, there should be a c r e d i t of the f u l l 1/3 of the non-fuel cost of the heat pump. However, t h i s further reduction i n the cost would only be 0.0932, i n model units, s t i l l leaving solar heating le s s c o s t l y , according to the above 110 'figures. I f the "thermal e f f i c i e n c y " 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 c o i l s of the heat pump i n a device which i s warmed by trapping so l a r r a d i a t i o n ) , then the heat pump could be competitive. 6.8. Sectoral Shares The shares of t o t a l output energy (Figure 24) al l o c a t e d to the two transportation sectors stay approximately constant over a l l periods, i n - di c a t i n g that the growth rates of transportation services are about the same as the growth rate of t o t a l output energy. However, since the i n - d u s t r i a l share increases and the DFC share decreases, we may conclude that the energy services provided i n the former sector increase f a s t e r than t o t a l output energy, and i n the l a t t e r , slower than t o t a l output energy. The rates of growth of output energy are determined by the exogenous assumptions about rates of growth of population and some economic va r i a b l e s , by p r i c e and other e l a s t i c i t i e s , and by pri c e s determined i n the so l u t i o n of the model. The shares of t o t a l secondary energy, the energy inputs to the end use sectors, are shown i n Figure 25 . The share consumed i n road transportation decreases i n the f i r s t three periods, r e f l e c t i n g the large e f f i c i e n c y im- provements assumed i n conventional automobiles. The increasing share of industry and the decreasing share of the DFC sector i n t o t a l secondary energy consumption follow the pattern observed i n the s e c t o r a l shares of output energy. 6.9. Fuel Shares The shares of t o t a l output energy (Figure 26) provided by e l e c t r i c i t y and coal both increase f a i r l y s t e a d i l y , except f o r a l u l l i n the t h i r d period corresponding to temporary drops i n eastern i n d u s t r i a l coal use 111 Table 27. S e c t o r a l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y o f the t a b l e , to a r r i v e at the values of the p l o t t e d l i n e s i n F i g u r e 24. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n 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 3  19^5 2005 2015 20^5 Figure 24. Sectoral Output Energy Shares, Base Case. 113 Table 28. S e c t o r a l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , t o a r r i v e at the valu e s of the p l o t t e d l i n e s i n F i g u r e 25. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n 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 -© © 3  I9S5 2005 " 20*15 2025 Figure 25. Sectoral Secondary Energy Shares, Base Case. 115 Table 29. Output Energy F u e l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom entry o f the t a b l e , to a r r i v e at the valu e s o f the p l o t t e d l i n e s i n F i g u r e 26. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n Table 29.) 116 Figure 26. Output Energy Fuel Shares, Base Case. 117 and i n eastern e l e c t r i c resistance heating. The large increase i n e l e c t r i c i t y ' s share a f t e r 2000 corresponds to a switch from o i l to e l e c t r i c i t y i n eastern industry, and from gas to e l e c t r i c resistance heating i n the east. The share of gas peaks i n the period 1986-1990, while o i l ' s share of output energy s t e a d i l y decreases. The share of e l e c t r i c i t y i n secondary energy inputs to the end-use sectors (Figure 27) increases s t e a d i l y , except for a l u l l i n the t h i r d period, to 38% i n the l a s t period, 2011-2020. Coal's share increases to 15% by the l a s t period. The share of gas peaks at 34% i n the period 1986-1990, and o i l ' s share declines s t e a d i l y from 61% i n the f i r s t period to 26% i n the l a s t period. The shares of cogeneration and s o l a r i n second- ary energy are less than t h e i r shares i n 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 i n conversion from secondary to output energy. Primary f u e l shares (Figure 28) change i n a way s i m i l a r to the changes observed i n secondary and output energy f u e l shares i n the cases of coal, gas and o i l . Hydro's share of primary energy increases to about 15% by 2000, and nuclear's share takes a sharp jump a f t e r 2000, when eastern hydro has been expanded to i t s maximum. The t i n y share of "biomass" (this category i n - cludes energy production from garbage, wind, t i d a l power) comes mainly from western e l e c t r i c i t y production. Solar's share of primary energy i s even smaller than i t s share of secondary energy because the quantities of primary and secondary s o l a r energy (and output, too) are taken to be the same. In summary, o i l becomes less important but remains s i g n i f i c a n t as an energy source; coal increases i n importance; there i s a major s h i f t to greater re l i a n c e on e l e c t r i c i t y , with nuclear power playing an important part, 118 Table 30. Secondary Energy F u e l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , t o a r r i v e at the v a l u e s of the p l o t t e d l i n e s i n F i g u r e 27. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n Table 30.) Figure 27. Secondary Energy Fuel Shares, Base Case. 120 Table 31. Primary Energy F u e l 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; o i l ; 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom entry o f the t a b l e , t o a r r i v e at the v a l u e s of the p l o t t e d l i n e s i n F i g u r e 28. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n Table 31.) 121 1.60 - i 1.40 H B R S E C A S E 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 ^ i S 2005 2015 20̂ 5 Figure 28. Primary Energy Fuel Shares, Base Case. 122 e s p e c i a l l y a f t e r the turn of the century; gas peaks i n importance i n the period 1986-1990 and declines r a p i d l y a f t e r 2000; and so l a r energy becomes s i g n i f i c a n t only a f t e r the turn of the century. 6.10. Total Energy To t a l 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 e l e c t r i c i t y are evaluated at 3,412 BTUs per kilowatt-hour, which i s the amount of usable energy i n one kilowatt-hour. Other authors (e.g. Energy, Mines and Resources, 1977a) have used a d i f f e r e n t accounting convention — 10,000 BTUs per kilowatt- hour -- for the reason that approximately 10,000 BTUs of f o s s i l f u e l input i s necessary to produce one kilowatt-hour of e l e c t r i c i t y . Thus, the generation of one kilowatt-hour of e l e c t r i c i t y by hydro or nuclear would have required 10,000 BTUs of f o s s i l f u e l s i f - f o s s i l f u e l s had been used. The "10,000" con- vention f a c i l i t a t e s i n t e r n a t i o n a l comparisons of primary energy use, when the focus i s on exhaustible, f o s s i l f u e l s . However, the "10,000" convention masks changes i n the o v e r a l l e f f i c i e n c y of primary energy use by obscuring the e f f e c t s of f o s s i l f u e l use to generate e l e c t r i c i t y . I t should be noted that the adoption of one convention or another has no e f f e c t on the so l u t i o n of the model — the only e f f e c t i s on the c a l c u l a t i o n of t o t a l primary energy for the report on the r e s u l t s of the model. The rates of change of primary, secondary and output energy, (Figure 30) are the average annual rates obtained by comparing t o t a l energy i n each period 123 Table 32. T o t a l 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 B A S E C A S E 32.00 TOTAL ENERGY: PRIMARY SECONDARY OUTPUT + © 28.00 H 2U.00 H 0.0 1975 19£ 19̂ 5 2005 2015 20^5 Figure 29. Total Energy, Base Case. 125 Table 33. T o t a l 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 - \ B A S E C A S E 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 3  2005 2LY15 20^5 Figure 30. Total Energy, Percent Annual Change, Base Case. 127 to the previous period. The drop i n rates of change i n the second period coincides with higher coal, o i l and gas p r i c e s i n the east, as well as the slower economic growth which i s assumed for t h i s period. The r i s e i n rates of change i n the t h i r d period coincides with a drop i n coal, o i l and gas p r i c e s i n the east, and higher assumed economic growth rates. The temporary drop i n rates of increase i n the period ending i n 2010 i s apparently due to a large jump i n o i l and gas p r i c e s (especially gas) and i n the eastern e l e c t r i c i t y p r i c e . The eastern gas and e l e c t r i c i t y p r i c e s reach a plateau and do not change i n the f i n a l period, which means that only the economic and demographic factors i n the demand function can have an e f f e c t on the rate of increase of demand f o r output energy between the l a s t two periods. The rate of growth of secondary energy i s l e s s , i n a l l periods, than the rate of growth of output energy, and the rate of growth of primary energy i s even less than that of secondary energy i n most periods. These observations in d i c a t e an increasing, o v e r a l l energy system e f f i c i e n c y i n the base case, both i n the end-use sectors and at the intermediate l e v e l of secondary energy. The increasing e f f i c i e n c y r e f l e c t s such things as the rapid growth i n hydro- e l e c t r i c i t y and nuclear power (rather than t o t a l r e l i a n c e on f o s s i l f uels f o r e l e c t r i c i t y ) , the introduction of cogeneration i n the west, the switch to e f f i c i e n t e l e c t r i c resistance heating i n the east (away from o i l and gas heat), the use of s o l a r heat (whose energy content i s evaluated at the same amount at the primary, secondary and output stages), and the assumed improving e f f i c i e n c i e s i n transportation. 128 Chapter 7. The High Demand and Low Demand Cases 7.1. The Assumptions The base case assumptions are the best estimates of a l l parameters. One key element of uncertainty i s the exogenous p r o j e c t i o n of the economic and demographic variables which, along with p r i c e s , determine demands for output energy. In order to t e s t the s e n s i t i v i t y of some conclusions to the assumptions about these exogenous demand-related v a r i a b l e s , the model has been solved f or high and low estimates of the future l e v e l s of the economic and demographic va r i a b l e s . The assumptions on the supply side are the same as i n the base case (since the s e n s i t i v i t y analysis here i s f o r demand-related v a r i a b l e s ) , except for some d i f f e r e n t exogenous projections of production from the t a r sands. (The l i n e a r process model of supply adjusts to the a l t e r e d demand conditions, except for the exogenously-projected t a r sands production. Thus, to be consistent, the t a r sands projections must be a l t e r e d i n a reason- able way.) The assumptions for the low, base and high'cases are presented i n 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 i n Douglas and Nichols (1979), which i s 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 i n t e r n a l l y 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 t h i s author's judgement, since there were no low projections of these variables prepared f o r the National Energy Board. (Their approach to t h e i r low demand case was to take the base case estimates of demographic and economic v a r i a b l e s , 129 and project high energy p r i c e s , which are exogenous i n t h e i r model.) The National Energy Board (1978) base case p r o j e c t i o n of t a r sands production to 1995 i s used as the base case exogenous p r o j e c t i o n here, and as the lower l i m i t from 1980 to 2000 f o r p r o j e c t i o n i n the high case. The low case p r o j e c t i o n of the National Energy Board (1978) i s the basis f o r the values assumed f or t a r sands production i n t h i s low case. Table 34. Low,Base and High Case Assumptions. (for end Period Ending 1980 1985 1990 2000 2010 2020 effects i 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 10 9 bbl/yr Low =.0362 >.0706 >.1380 y.2205 130 7.2. The Results of the High Case Generally speaking, production and use l e v e l s are higher i n the high case than i n the base case, but the o v e r a l l patterns (peaks, introduction of new sources, etc.) are the same as i n the base case. Some noteworthy exceptions to these general observations are: - some o i l and coal sources are exhausted sooner i n the high case; - gas production and use are at roughly the same l e v e l s i n the high case as i n the base case, except f o r the l a s t period; - s o l a r heat i s introduced one period e a r l i e r i n each region (after 1990 i n the east, and a f t e r 2000 i n the west, i n the high case); and - o i l and gas pr i c e s r i s e s l i g h t l y f a s t e r i n the medium term (1985 to 2000) than i n the base case. Some conclusions drawn from an examination of the base case s o l u t i o n are strengthened by the r e s u l t s of the high case. As i n the base case, northwestern a r c t i c o i l i s not used u n t i l a f t e r 2000 i n the high case i n spite of the higher demand (but northeastern offshore o i l i s used one period sooner, 1991-2000, i n the high case). Imports of o i l and coal cease a f t e r 1985 i n the high case, as i n the base case. The crude o i l p r i c e s t i l l does not reach i t s upper l i m i t of $12 per b a r r e l u n t i l the l a s t period, 2011-2020, i n spite of the higher demand. As i n the base case," natural gas from the northeast offshore i s not needed u n t i l a f t e r 2000, and gas from the northwest a r c t i c i s not used u n t i l a f t e r 2010. The two primary fuels which appear to make up the extra supply required to meet the higher demands are nuclear e l e c t r i c i t y and c o a l . A r e l a t e d ob- servation i s that e l e c t r i c i t y p r i c e s are not affected very much by the i n - creased demands i n the high case (compared to the base case), because of the v i r t u a l l y l i m i t l e s s supplies of nuclear power i n the east and coal f o r e l e c t r i c i t y i n the west. Thus, the base case conclusion that e l e c t r i c i t y p r i c e s are stable, i s strengthened. Plots and tables from the high and low cases r e l a t i n g to t h i s d i s - 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 l e v e l s of production and use of energy, and the o v e r a l l pattern i s s i m i l a r . Some exceptions are: - o i l from the northwest a r c t i c i s introduced one period l a t e r (after 2010) than i n the base case; and - western conventional o i l supplies are used les s i n the f i r s t four periods and more i n the l a s t two periods, "stretching out" the cheaper o i l supplies. Solar heating i s introduced i n the same periods as i n the base case i n both regions - 2011-2020 i n the west, and 2001-2010 i n the east. This reinforces the conclusion that s o l a r heat w i l l be a competitive energy source, even i f energy demands grow slowly, although i t w i l l not be com- p e t i t i v e i n the near future. Since nuclear's share of primary energy i s les s than f o r base case demand, i t may be concluded that nuclear power w i l l play a key ro l e i n matching energy supplies and demands. This reinforces the observation made on the high case r e s u l t s , that nuclear made up a good part of the extra energy supply required over the base case requirements. I t i s noteworthy that the periods of introduction of natural gas from the northwest a r c t i c and the northeast offshore areas are the same i n the low case as i n the high case — the periods ending i n 2020 and 2010, resp e c t i v e l y . This puts upper bounds on the introduction dates - before '2020 for northwest a r c t i c gas, and before 2010 for northeast offshore gas. The conclusion that these f r o n t i e r gas sources need not be tapped u n t i l a f t e r the turn of the century, f i r s t discussed with reference to the base case, i s therefore a robust conclusion. An examination of the high, base and low r e s u l t s reveals that eastern gas production (the sum of southeast and northeast offshore production) i s the same i n the f i r s t four periods i n a l l three cases. There are two reasons for t h i s behaviour. F i r s t , southeast offshore gas i s used at the maximum allowable rates i n the f i r s t three periods because i t i s inexpensive, and i n the fourth period, the reserve l i m i t and the production decline constraint combine to make another upper l i m i t on production. Secondly, the other component of eastern gas production, the northeast offshore gas, i s not brought i n t o the so l u t i o n u n t i l the f i f t h period i n a l l three cases. There- fore, differences among the cases i n eastern gas production do not appear u n t i l the f i f t h period. There i s very l i t t l e d i fference i n the p r i c e s e r i e s of the low and base cases. Plots and tables from the high and low cases r e l a t i n g to the above discussion appear on pages 134 to 161. Table 35, below shows the growth rates of t o t a l energy demand per capita fo r the three cases, at the primary, secondary and output energy l e v e l s , using each case's population p r o j e c t i o n . Table 35. Growth i n 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 f o r output energy grows, even on a per capita b a s i s , because the demand i s also r e l a t e d to several economic variabl e s , which grow f a s t e r than population, p a r t l y because of technological change. 134 Table 36. Crude O i l 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 i n this table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to a r r i v e at the values of the plotted l i n e s i n Figure 31. Thus, the differences between the plotted l i n e s are the entries i n 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 O i l Production, High Case. 136 Table 37. Crude O i l Prod u c t i o n , 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , to a r r i v e at the valu e s of the p l o t t e d l i n e s i n F i g u r e 32. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n Table 37.) 1.60 n i o H L O W C A S E OIL PRODUCTION: IMPORTS FROM BIOMASS FROM CORL EASTERN TAR SANDS WEST ARCTIC WESTERN + X + © 1.20 H C C C C 1.00 H C C L U CL. _j 0.80 H CO CO C D X X 2 0.60 H 0.40 H 0.20 H 0.0 1975 1985 1995 2005 2015 2025 Figure 32. Crude O i l Production, Low Case. 138 Table 38. Crude O i l P r i c e s , 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 C A S E CRUDE OIL PRICES: EXPORTS X IMPORTS + ERST A WEST © 30.00 H 25.00 H _ J 0 3 CO QZ U J ° - 20.00 LO r ~ 15.00 -A lo.oo H 5.00 H 0.0 1975 1985 3  19^5 2005 2LT15 20^5 Figure 33. Crude O i l Pr i c e s , High Case. 140 Table 39. Crude O i l P r i c e s , Low Case. LOW CASE; ; CfiUDS OIL PRICES: IH UNITS OF 1975$ PER B B 1 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 L U ° - 20.00 - | if* LO r - CD 15.00 H I O . O O H 5.00 H 0.0 1975 1985 19^ 2005 2S5 2025 Figure 34. Crude O i l Pr i c e s , Low Case. 142 Table 40. Gas Pr o d u c t i o n , 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 s e r i e s i n t h i s t a b l e a re summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y o f the t a b l e , to a r r i v e at the values of the p l o t t e d l i n e s i n F i g u r e 35. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 i i 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to a r r i v e at the values of the plotted l i n e s i n Figure 36. Thus, the differences between the plotted l i n e s are the entries i n 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 . 0 0 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 P r i c e s , 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 C o r r e c t e d , 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 1 9 E 2005 20i5 20^5 Figure 37. Gas Pr i c e s , High Case. 148 Table 43. Gas P r i c e s , 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 C o r r e c t e d , 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 1 9 £ I9B5 2005 2015 20^5 Figure 38. Gas Pri c e s , Low Case. 150 Table 44., Secondary Energy Fue l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , to a r r i v e at the values of the p l o t t e d l i n e s i n F i g u r e 39. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 3 1 9 b 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 i n t h i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 40. Thus, the differences between the plotted l i n e s are the entries i n Table 45.) 1.60 - i 1.140 H L O N C A S E 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 -©- 3 2005 2015 20^5 Figure 40. Secondary Energy Fuel Shares, Low Case. 154 T a b l e 4 6 . Primary Energy F u e l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom entry o f the t a b l e , t o a r r i v e a t the valu e s of the p l o t t e d l i n e s i n F i g u r e 41. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 F u e l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom entry of the t a b l e , t o a r r i v e a t the values of the p l o t t e d l i n e s i n F i g u r e 42. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n Table 47.) 157 1.60 - i 1.140 -A L O N C A S E 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. T o t a l 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 H I G H C A S E 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. T o t a l 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 L O W C A S E 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 3 I965 2005 2015 2025 Figure 44. Total Energy, Low Case. 162 Chapter 8. Analysis of Some Energy P o l i c y Questions 8.1. The Impacts of a No-New-Nuclear P o l i c y To examine the e f f e c t s of a moratorium on the construction of new nuclear power f a c i l i t i e s , the model was solved with a d d i t i o n a l l i m i t s f i x i n g new nuclear e l e c t r i c i t y capacity at zero a f t e r 1985. Upper bounds were placed on new nuclear capacity i n the east i n the f i r s t two periods, at the base case solution's l e v e l i n 1976-1980, and s l i g h t l y below the base case l e v e l i n 1981-1985. For reasons that w i l l become apparent shortly, the f i x i n g of tar sands production u n t i l 2000 was changed to lower bounding, but at the same l e v e l . A l l other assumptions were those of the base case. There were unexpected r e s u l t s . The east, which i n the base case r e l i e s heavily on nuclear power e s p e c i a l l y a f t e r 2000, does not switch mainly to c o a l - f i r e d e l e c t r i c i t y production. Instead, the main change i s a massive switch away from e l e c t r i c i t y production and use a f t e r 1985 i n the east. O i l , notably from the tar sands, l a r g e l y takes the place of e l e c t r i c i t y i n the i n d u s t r i a l sector and i n the domestic, farm and commercial sector. There i s increased use of western conventional o i l i n the early periods, followed by increased use of o i l from the western a r c t i c and e s p e c i a l l y from the t a r sands a f t e r the year 2000. Since western coal, with i t s high trans- portation cost, i s the al t e r n a t i v e source for new e l e c t r i c capacity a f t e r eastern hydro i s used to i t s maximum, e l e c t r i c i t y i s more expensive than o i l i n end uses. O i l heating regains i t s importance i n the east a f t e r 2000, r e - pla c i n g heavy reliance on e l e c t r i c resistance heating. There i s some heating by cogeneration with the small amount of new c o a l - f i r e d e l e c t r i c i t y production, and s o l a r heating i s introduced a f t e r 1990 i n the east, one period e a r l i e r than i n the base case. At the primary energy l e v e l , there i s a b i g switch from nuclear energy to o i l and somewhat to co a l . O i l p r i c e s r i s e more quickly to the backstop p r i c e , $12/bbl, because of the more rapid exhaustion of the cheaper sources than i n the base case. Tables 50 to 53 and Figures 45 to 48 i l l u s t r a t e these trends. There are no s i g n i f i c a n t changes i n the west, compared to the base case, apart from changes i n o i l production discussed above. The economic benefits of allowing nuclear power can be estimated by comparing the values of the objective function i n the solutions of the base case and the no-new-nuclear case. The objective function i s the discounted sum of consumers' plus producers' surplus. (The dual equilibrium method to mitigate end e f f e c t s i s an approximation to the i n f i n i t e horizon problem.) The difference i n the two values of the objective function i s approximately 9 $1.7 x 10 (1975$, discounted to 1975 using a 10% per annum discount r a t e ) . This i s a s u r p r i s i n g l y small value when one considers the importance of nuclear power i n the base case s o l u t i o n . In per capita terms, the cost of following the no-new-nuclear route i s only $77 per person (assuming a popu- l a t i o n of 22 m i l l i o n ) , discounted to 1975, and i n 1975$. Discounting to 1980, and converting to 1980$, t h i s cost i s 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 e f f e c t s of banning a d d i t i o n a l c i v i l i a n nuclear power plants i n the United States a f t e r 1975. The present value of the losses i n aggregate consumption (not of energy, but of a l l non- investment goods and services) from 1975 through 2050, also discounted at 9 10% per year, i s $77 x 10 , i n 1975$. The macroeconomic losses are low i n the early years, but r i s e r a p i d l y a f t e r the year 2000, when there are binding constraints on coal supplies. Manne concludes that "although a 'no-nuclear' p o l i c y would have n e g l i g i b l e macroeconomic e f f e c t s , there would be impacts throughout the energy sector." These general r e s u l t s are the same as the "no-nuclear" r e s u l t s for Canada, discussed above. The estimated value of 9 the losses i n the United States, $77 x 10 , i s higher than the value f o r 9 Canada, $1.7 x 10 , even i f the usual factor of 10 i s applied for rough economic comparisons between the two countries. Reasons f o r the higher figure include Manne's e a r l i e r cutoff of nuclear (after 1975, versus a f t e r 1985 i n the model discussed here), and the existence i n Canada of a r e l a t i v e l y inexpensive alternate f u e l — o i l from the t a r 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 t h i s appears to be the most important consideration i n nuclear safety. A i k i n , Harrison and Hare (1977), made a very rough estimate of the cost of an under- ground nuclear waste repository. The c a p i t a l cost i s i r r e l e v e n t here, since even i n the no-new-nuclear a l t e r n a t i v e , the repository would have to be b u i l t , and operated u n t i l the o l d nuclear stations are shut down. The operating cost estimated by A i k i n , Harrison and Hare (1977), $100 m i l l i o n per year, i s based on a p r o j e c t i o n of nuclear power development i n the year 2000. The operating cost i n the no-new nuclear a l t e r n a t i v e , u n t i l the plants are shut down, would presumably be much less than $100 m i l l i o n per year, since the maximum nuclear l e v e l , i n 1981-1985, i s considerably l e s s than i n 2000. The extra cost of the containment of nuclear wastes i n the nuclear a l t e r - native i s therefore approximately ( ($100xl0 6)/0.10) x (1.10)~ 1 5^= $0.24 x 10 9, discounted to 1975 at the rate of 10% per year, under the assumption that the repository would not begin operation u n t i l 1991. This cost i s small 9 compared to the cost of the no-new-nuclear path, $1.7x10 , calculated above. These cost c a l c u l a t i o n s do not n e c e s s a r i l y suggest that the nuclear path should be favoured as the cheaper a l t e r n a t i v e . Since the estimated costs of safety are quite low i n e i t h e r case, i t may be concluded that the issue should not be decided on economic grounds. Rather, the c l o s e s t attention should be paid to the t e c h n i c a l f e a s i b i l i t y of the nuclear safety proposals by the nuclear advocates, and to the health e f f e c t s of nuclear power production. Some key p l o t s are shown i n 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 a v a i l a b i l i t y of o i l from the t a r sands. I f there are i n f a c t upper l i m i t s on t a r sands production (due to p h y s i c a l and environ- mental l i m i t s such as water shortages, or i n a b i l i t y to t r e a t the waste water) , or i f synthetic crude o i l i s much more expensive than was assumed (due perhaps to cost escalations i n periods of rapid increases i n capacity) , the cost of the no-new-nuclear path would be greater. Inclusion of upper l i m i t s on t a r sands production, or an increasing marginal cost f o r expansion of t a r sands capacity would l i k e l y b ring about a smaller s h i f t to t a r sands, and a greater s h i f t to other f u e l s , such as natural gas (in the medium term, at l e a s t , before supplies are nearly exhausted) and c o a l . As a step i n t h i s d i r e c t i o n , the no-new-nuclear case was solved again, but with o i l from the t a r sands at a cost of $13.50/bbl, rather than $12/bbl. S t i l l the t a r sands play a b i g r o l e i n replacing e l e c t r i c i t y i n general, and nuclear power i n p a r t i c u l a r , but f r o n t i e r natural gas adopts much of the replacement r o l e i n i t i a l l y , before the l a s t period, 2011-2020. Another assumption which influences the no-new-nuclear case, but i n a way which does not a f f e c t the main conclusions above, i s the constraint l i m i t i n g the share of new eastern e l e c t r i c i t y generation which may be met by hydro. In the f i r s t period, t h i s constraint has no e f f e c t d i f f e r e n t from the base case, since there i s no severe r e s t r i c t i o n on nuclear i n t h i s 166 period. In the second period, the upper l i m i t on new nuclear capacity, smaller than the l e v e l c a l c u lated i n the base case, brings about a forced decrease i n hydro, through the hydro share constraint. This i s u n r e a l i s t i c since i n r e a l i t y , r e s t r i c t i o n s on nuclear would l i k e l y increase hydro's share, perhaps by Quebec exporting h y d r o e l e c t r i c i t y to Ontario. S i m i l a r l y , i n the t h i r d period, there i s no new nuclear capacity allowed, and no c o a l - f i r e d e l e c t r i c i t y i s added, which together force zero new hydro capacity, through the share constraint. A f t e r the t h i r d period, there i s some c o a l - f i r e d e l e c t r i c i t y capacity added, which allows new hydro to be added, u n t i l the upper l i m i t on hydro generation i s reached a f t e r the year 2000, one period l a t e r than i n the base case. This deficiency does not a f f e c t the conclusions of the switch from nuclear to t a r sands and from e l e c t r i c i t y i n general to o i l , since the main switch i s a f t e r 2000, when hydro i s at i t s upper l i m i t i n the no-new-nuclear case. Furthermore, the c a l c u l a t i o n of the economic benefits of allowing nuclear power would lead to even lower benefits i f the r e s t r i c t i o n s on hydro were relaxed, since the no-new-nuclear route would be less c o s t l y . Thus, the o v e r l y - r e s t r i c t i v e assumptions about hydro r e i n f o r c e the conclusion that the economic benefits of allowing nuclear power are n e g l i g i b l e . 167 ( Table 50. Crude O i l Prod u c t i o n , 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , to a r r i v e at the v a l u e s o f the p l o t t e d l i n e s i n F i g u r e 45. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 . 0 0 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 O i l Production, No-new-nuclear Case. 169 Table 51. O i l 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 i n this table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to a r r i v e at the values of the plotted l i n e s i n Figure 46. Thus, the differences between the plotted l i n e s are the ent r i e s i n Table 51.) 170 1.60 - i B A S E C A S E 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 19̂ 5 19 CD © - 95 2005 201! 20^5 Figure 46. O i l Use, No-new-nuclear Case. 171 Table 52. E a s t e r n E l e c t r i c i t y P r o d u c t i o n , 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , to a r r i v e a t the valu e s o f the p l o t t e d l i n e s i n F i g u r e 47. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a r e the e n t r i e s i n Table 52.) 172 3.20 - i 2.80 H 2.U0 H CC cr 2 . 0 0 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 E l e c t r i c i t y Production, No-new-nuclear Case. 173 Table 53. Primary Energy F u e l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , t o a r r i v e at the values of the p l o t t e d l i n e s i n F i g u r e 48. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n Table 53.) 174 1.60 - i 1.40 H B A S E C A S E NO NEW NUCLEAR PRIMARY FUEL SHARES: SOLAR X BIOMASS • HYDRO • NUCLEAR 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 I t was assumed i n the base case that heating by cogeneration with nuclear e l e c t r i c i t y i s not allowed, because the p u b l i c might not accept i t . To investigate t h i s , the base case was run again, but allowing co- generation with nuclear power. I t was assumed that the maximum r a t i o of heat to e l e c t r i c a l output i n nuclear cogeneration i s h a l f the maximum r a t i o i n c o a l - f i r e d cogeneration - i . e . for every kilowatt-hour of nuclear e l e c t r i c i t y , up to 2,132.5 BTU of heat can be supplied to the domestic, farm and commercial sector. This lower figure f or nuclear cogeneration was chosen because, according to Berthin (1980), there i s less heat available i n a CANDU generation system f o r t h i s purpose than i n a c o a l - f i r e d e l e c t r i c i t y generation s t a t i o n . The cost of using nuclear cogenerated heat was assumed to be the same as f o r cogeneration using c o a l . As with coal cogeneration,it was assumed that new capacity of heat by cogeneration with nuclear can only be established with new nuclear e l e c t r i c i t y capacity. Judging by Berthin's study, i t i s l i k e l y that nuclear f a c i l i t i e s would have to be closer to population centres than at present, f o r the d i s t r i c t heating scheme to work with the costs Berthin estimates. Under these assumptions, nuclear cogeneration begins i n the east as soon as i t i s allowed (after 1980), and reliance on t h i s heating method becomes quite heavy a f t e r 2000, i n d i c a t i n g that nuclear cogeneration i s competitive i n the east. The main heating method displaced i s e l e c t r i c resistance heating, although i t i s s t i l l very important. Solar heating enters the so l u t i o n one period l a t e r (2011-2020) than i n the base case. One curious consequence of the displacement of e l e c t r i c resistance heating- i s that the generation of e l e c t r i c i t y by nuclear power i s considerably lower than i n 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 i n th i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 49. Thus, the differences between the plotted l i n e s are the entries i n Table 54.) 177 U.00 - i B A S E C A S E 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. E a s t e r n E l e c t r i c i t y p r o d u c t i o n , 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , t o a r r i v e at the valu e s o f the p l o t t e d l i n e s i n F i g u r e 50. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 E l e c t r i c i t y Production, Nuclear Cogeneration Case. 180 Table 56. Secondary Energy Fue l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y o f the t a b l e , to a r r i v e at the v a l u e s of the p l o t t e d l i n e s i n F i g u r e 51. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a r e the e n t r i e s i n Table 56.) 181 1.60 -I B A S E C A S E 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 i n the number of nuclear power st a t i o n s . I f d i s t r i c t 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 i n magnitude by adopting t h i s type of heating on a large scale i n the east, although the l i k e l i h o o d that nuclear stations would have to be closer to population centres may i n - fluence t h i s r e s u l t . The difference i n the value of the objective function between the base case and the nuclear cogeneration case - i . e . the economic b e n e f i t 9 of nuclear cogeneration - i s $0,562 x 10 , i n 1978$, discounted to 1975 at the rate of 10% per year, or about $26 per person i n 1975. Even when t h i s i s converted to 1980$, and discounting i s done to 1980, the b e n e f i t i s only approximately $100 per person, or $10 per person per year. Thus, as with the question of whether to f o r b i d new nuclear power st a t i o n s , the issue of nuclear cogeneration should not be decided on economic grounds. The important questions are the t e c h n i c a l f e a s i b i l i t y and safety of the system. Some key p l o t s f o r t h i s case are shown i n Figures 49, 50 and 51, with the corresponding Tables 54, 55 and 56. 8.3. High O i l Costs ( S e n s i t i v i t y Analysis) There have recently been suggestions that the costs of syncrude from the t a r sands and of conventional o i l have been esc a l a t i n g more ra p i d l y than the general r i s e i n p r i c e s . Quon (1980) suggests that the r e a l costs of o i l production have been increasing as both c a p i t a l and labour have demanded a higher portion of the perceived economic rent (in the ex- pectation of much higher o i l p r i c e s ) . Furthermore, they have a c t u a l l y received higher payments f o r d r i l l i n g r i g r e n t a l s , wages, etc. because 183 of the strong demand for these services (again due to the expectation of much higher o i l p r i c e s ) . To investigate t h i s p o s s i b i l i t y the model was solved with a l l the base case assumptions except the following higher o i l costs: O i l Source Base Case Cost Higher Cost western conventional, "low cost" $ -4/bbl western conventional, "high cost" $ -8/bbl northwest f r o n t i e r , "low cost" $10/bbl northwest f r o n t i e r , "high cost" $14/bbl ta r sands $12/bbl southeast offshore $ 7/bbl northeast offshore $10/bbl $ -4/bbl $10/bbl $12/bbl $16/bbl $15/bbl $ 9/bbl $12/bbl (unchanged) The t a r sands cost has been increased to approximately the 1980 i n t e r - national p r i c e of o i l (in 1975$) since the p a r t i c i p a n t s i n proposed new t a r sands projects claim that the world p r i c e i s needed to make the projects economically v i a b l e . Other costs have been increased by $2 per b a r r e l , except the established, low cost western o i l . The r e s u l t s of t h i s s e n s i t i v i t y analysis were not s u r p r i s i n g , with one exception - sol a r heating i s introduced i n the east a f t e r 1980, although i t remains at a very low l e v e l u n t i l a f t e r 2000, when i t i s f i r s t introduced i n the base case. Apparently the higher o i l costs cause increases i n the p r i c e of heating i n the east j u s t enough to make s o l a r competitive e a r l i e r . Except f o r the l a s t period, there i s lower o i l production and use. Tar sands production i n the f i r s t f i v e periods i s at the same l e v e l as i n the base case because production i n the f i r s t four periods i s f i x e d exogenously, and drops i n the f i f t h to the same l e v e l i n both cases because there i s no capacity added, but o l d capacity i s removed. Production of "low cost" western o i l , the cheapest source, at an unchanged cost, i s delayed, 184 Table 57. Crude O i l Production, High O i l C o s t s 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , t o a r r i v e a t the valu e s of the p l o t t e d l i n e s i n F i g u r e 52. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 D Z CE 1.00 H L U D Z L U 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 O i l Production, High O i l Costs Case. 186 Table 58. Crude O i l P r i c e s , High O i l Cos t s Case. BASE CASE; HIGH O i l 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 O i l Pr i c e s , High O i l Costs Case. 188 Table 59. Secondary Energy F u e l Shares, High O i l C o s t s Case. BASE CASE; HIGH O i l 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 s e r i e s i n t h i s t a b l e a re summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , to a r r i v e at the valu e s of the p l o t t e d l i n e s i n F i g u r e 54. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 -©- -© IB ttbs 2005 20*15 2025 Figure 54. Secondary Energy Fuel Shares, High O i l Costs Case. compared to the base case — i n e f f e c t "saved" for the future, to put o f f the use of the more expensive sources at the increased costs. The i n t r o - duction dates of northwestern a r c t i c and northeastern offshore o i l are de- layed one period due to the assumed higher costs and consequent lower de- mand and production . The p r i c e s of o i l are higher, but the increase over the base case i s les s than the cost increase ($2/bbl f o r a l l except t a r sands) except i n the period 1986-1990. The o i l p r i c e does not reach the backstop cost (tar sands) within the model's time horizon. Gas prices are higher i n the east, u n t i l the l a s t two periods. There i s a small switch from o i l use to greater r e l i a n c e on gas i n the medium term and on e l e c t r i c i t y from coal and nuclear sources, compared to the base case. In the two transportation sectors, which depend on o i l alone, there i s only a s l i g h t l y reduced demand for o i l , due to the quite i n e l a s t i c de- mand s p e c i f i e d i n those sectors. See Figures 52, 53 and 54 f o r p l o t s of t h i s case. 8.4. The Impacts of Competitive Coal G a s i f i c a t i o n As discussed i n chapter 6, coal g a s i f i c a t i o n i s not i n the base case solut i o n , but i s almost competitive i n the l a t e r periods. To examine the impacts of the introduction of coal g a s i f i c a t i o n , the model was solved with the base case assumptions except that the d i s t r i b u t i o n margin for coal to g a s i f i c a t i o n plants was reduced by one h a l f , to $0.40/10^ BTU. This i s equivalent to reducing the p r i c e of gas from coal to $2.30/mcf, from the p r i c e of $3.00/mcf i n the base case, making t h i s gas source cheaper than gas from the northwest a r c t i c . Another change i n the assumptions f o r t h i s 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 i n th i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to arrive at the values of the plotted l i n e s i n Figure 55. Thus, the differences between the plotted l i n e s are the entries i n Table 60.) 192 B A S E C A S E 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 serie s i n th i s table are summed, one l i n e at a time, s t a r t i n g with the bottom entry of the table, to a r r i v e at the values of the plotted l i n e s i n Figure 56. Thus, the differences between the plotted l i n e s are the ent r i e s i n 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 U J 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 F u e l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y o f the t a b l e , to a r r i v e at the valu e s of the p l o t t e d l i n e s i n F i g u r e 57. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 20̂ 5 Figure 57. Secondary Energy Fuel Shares, Coal Gas Case. 197 Table 63. Primary Energy F u e l 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom entry of the t a b l e , t o a r r i v e at the v a l u e s of the p l o t t e d l i n e s i n F i g u r e 58. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n Table 63.) 198 1.60 - i I.UO H B A S E - C A S E 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 3 1955 2005 20*15 2025 Figure 58. Primary Energy Fuel Shares, Coal Gas Case. •case was to make the 1991-2000 t a r sands p r o j e c t i o n into an upper l i m i t on production i n that period, i n order to allow for some switching to gas from o i l . Under these assumptions, coal g a s i f i c a t i o n i s introduced a f t e r 2000, bringing about much higher coal production then. Since t h i s i s a backstop source of gas at $2.30/mcf (as long as the huge coal supplies l a s t ) , the more expensive northern f r o n t i e r sources (in the west and the east) are l e f t out of the s o l u t i o n . Total gas production and use are larger i n the period 2011-2020, with the i n d u s t r i a l and domestic, farm and commercial sectors taking the extra gas. There i s much less e l e c t r i c i t y produced i n 2011-2020 i n the west, with i n d u s t r i a l e l e c t r i c i t y use l a r g e l y switched to gas. Heating by cogeneration and by s o l a r i n the west are l e f t out of the s o l u t i o n , i n favour of gas heating, unlike the base case s o l u t i o n . At the secondary energy l e v e l , a f t e r 2000, there i s a switch away from heat by cogeneration, s o l a r heat and e l e c t r i c i t y , towards the use of gas, compared to the base case. At the primary energy l e v e l , the switch i s away from so l a r , hydro, crude o i l and natural gas, e s p e c i a l l y i n the l a s t period, to c o a l . The share of coal i n t o t a l primary energy r i s e s to 36% i n the l a s t period, compared to 19% i n the base case. Tables 60 to 63 and Figures 55 to 58 give the relevant d e t a i l e d output fo r t h i s case. 8.5. The Impacts of the E l e c t r i c Automobile. The e l e c t r i c auto does not enter the base case s o l u t i o n . To study the impacts of the e l e c t r i c auto on the energy system, the base case was solved with a lower cost associated with the e l e c t r i c auto. The amount of the cost reduction was chosen to be j u s t large enough to make the e l e c t r i c auto 200 competitive, a f t e r examination of the base case output. This lowering of the cost i s equivalent to (a) lowering the i n i t i a l cost difference between the e l e c t r i c and conventional autos from $1500 to $364, but keeping the road tax on e l e c t r i c i t y used by e l e c t r i c cars; (b) lowering the i n i t i a l cost differences from $1500 to $1,127 and eliminating the e l e c t r i c i t y road tax; or (c) combinations of (a) and (b). In addition, the projected value of t a r sands production i n the period 1991-2000 was changed to an upper l i m i t , to allow for the l i k e l i h o o d of lower o i l consumption. There are no surprises i n the s o l u t i o n . O i l production i s lower than i n the base case, e s p e c i a l l y from the t a r sands, a f t e r 1990. Coal pro- duction i s higher i n the l a s t two periods (after 2000) i n the west, f u e l l i n g higher e l e c t r i c i t y production for the e l e c t r i c auto. E l e c t r i c i t y production i s higher i n the east, as well, a f t e r 2000. The share of e l e c t r i c i t y i n secondary energy reaches 45% by the l a s t period, 2011-2020, compared to 38% i n the base case. At the primary energy l e v e l , crude o i l ' s share reaches 18% by the l a s t period, compared to 26% i n the base case, with co a l , nuclear and hydro energy taking o i l ' s place. One small side e f f e c t of the higher e l e c t r i c i t y production i s the p a r t i a l displacement of s o l a r heating i n the west by an increased quantity of heat by co- generation with c o a l - f i r e d e l e c t r i c i t y production, i n the l a s t period. Refer to Tables 64 to 67, and Figures 59 to 62 for s p e c i f i c d e t a i l s of t h i s case. 201 Table 64. T r a n s p o r t a t i o n , E l e c t r i c 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y of the t a b l e , to a r r i v e at the values of the p l o t t e d l i n e s i n F i g u r e 59. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a r e the e n t r i e s i n Table 64.) 202 B A S E C A S E CHEAP ELEC. AUTO TRANSPORTATION: OTHER TRANSPORT + ROAD,ELECTRIC A ROAD. GASOLINE © 1.80 H Figure 59. Transportation, E l e c t r i c Auto Case. 203 Table 65. Crude O i l P r o d u c t i o n , E l e c t r i c 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y o f the t a b l e , t o a r r i v e at the values of the p l o t t e d l i n e s i n F i g u r e 60. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n Table 65.) 204 1.60 - i B A S E C A S E CHEAP ELEC. AUTO OIL PRODUCTION: IMPORTS FROM BIOMRSS FROM COAL EASTERN TAR SANDS WEST ARCTIC WESTERN X X + © Figure 60. Crude O i l Production, E l e c t r i c ' A u t o Case. 205 Table 66. Secondary Energy F u e l Shares, E l e c t r i c 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 s e r i e s i n t h i s t a b l e a re summed, one l i n e a t a time, s t a r t i n g with the bottom e n t r y o f the t a b l e , t o a r r i v e at the v a l u e s of the p l o t t e d l i n e s i n F i g u r e 61. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s a re the e n t r i e s i n 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 C E CC 0.60 H 0.140 0.20 H 0.0 1975 1985 Ei 19̂ 5 2005 20*15 2025 Figure 61. Secondary Energy Fuel Shares, E l e c t r i c Auto Case. 207 Table 67. Primary Energy F u e l Shares, E l e c t r i c 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 s e r i e s i n t h i s t a b l e are summed, one l i n e a t a time, s t a r t i n g '..with the bottom e n t r y of the t a b l e , t o a r r i v e at the v a l u e s o f the p l o t t e d l i n e s i n F i g u r e 62. Thus, the d i f f e r e n c e s between the p l o t t e d l i n e s are the e n t r i e s i n 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 20̂ 5 Figure 62. Primary Energy Fuel Shares, E l e c t r i c Auto Case. 209 Chapter 9. Summary and Conclusions This d i s s e r t a t i o n describes the construction of a model of the energy sector i n the Canadian economy using a nonlinear programming algorithm to e q u i l i b r a t e energy supplies and demands i n three five-year periods and three ten-year periods, from 1975 to 2020. A l i n e a r process model of energy supply, conversion and d i s t r i b u t i o n i s linked to a model of the demands f o r services provided by energy i n combination with other inputs such as c a p i t a l . Upper l i m i t s on energy exports i n the model present current p o l i c i e s and imply a two p r i c e system (domestic and i n t e r n a t i o n a l ) , which also represents current p o l i c i e s . Other important features of the model are the d i s t i n c t i o n of two regions, western and eastern (the main energy producing and consuming regions, r e s p e c t i v e l y ) , and the l i n e a r approximations to long-run marginal cost curves f o r exhaustible hydrocarbon resources. The main e f f o r t s to date have been i n the c o l l e c t i o n of data f o r the "base case", i n the construction of a structure f o r which data e x i s t , i n the computer coding (including routines f o r reporting the r e s u l t s ) , and i n the t e s t i n g and debugging of the model. Apart from the base case, data f o r low demand and high demand cases were used i n other solutions of the model. Examination of the low, base and high cases shed some l i g h t on the dates of introduction of various new tech- nologies and f r o n t i e r petroleum resources, on energy p r i c i n g , and on the competitiveness of c e r t a i n new technologies. As well, some energy p o l i c y questions have been analyzed with the a i d of the model, namely the questions of banning further nuclear power development and of allowing d i s t r i c t heating by cogeneration with nuclear e l e c t r i c i t y , the e f f e c t s of higher o i l costs (a s e n s i t i v i t y a n a l y s i s ) , the impacts of competitive coal g a s i f i c a t i o n , and the impacts of competitive e l e c t r i c automobiles. Some important conclusions drawn 210 from the r e s u l t s of the model are summarized below. I t was found that o i l from the northwest A r c t i c and northeast offshore w i l l not l i k e l y be needed u n t i l a f t e r 2000, although northeast offshore o i l i s required a f t e r 1990 under the high demand assumptions. Coal l i q u e f a c t i o n appears to be uneconomical i n a l l periods i n the base case. Even under the most favourable assumption about the cost of the coal input, the cost of the o i l output would be higher than the p r i c e of o i l u n t i l a f t e r the year 2000. The assumption of r e s t r i c t e d exports, with the r e s u l t i n g two p r i c e system, i s a key assumption i n a l l conclusions. For example, i f u n r e s t r i c t e d exports, or even much higher o i l export r e s t r i c t i o n s were allowed, f r o n t i e r o i l production would begin e a r l i e r and coal l i q u e f a c t i o n may become competitive. O i l production and use were found to be approx- i m a t e l y constant a f t e r 1980, due to increasing f u e l e f f i c i e n c y i n the trans- port a t i o n sectors, and to s u b s t i t u t i o n of other fuels i n the other sectors. F r o n t i e r natural gas sources w i l l not be needed u n t i l a f t e r 2000 under the three demand scenarios (low, base, and high). Gas i s a t r a n s i t i o n a l f u e l , to be used i n place of o i l i n the medium term, but i t w i l l eventually be replaced by other energy sources. Canadian use of natural gas peaks i n the period 1991 to 2000, and production (including f or export) peaks i n the period 1986-to 1990. I t was found that the "competitive r e l a t i o n s h i p " 'of gas and o i l i s quite d i f f e r e n t i n the two regions — the r a t i o of the gas p r i c e to the o i l p r i c e r i s e s over time i n each region, but i t i s higher i n the east. Coal g a s i f i c a t i o n i s nearly competitive i n the base case. S e n s i t i v i t y analysis indicates that g a s i f i c a t i o n of coal may play an important role a f t e r 2000, d i s p l a c i n g some e l e c t r i c i t y , solar heat and heat by cogeneration, compared to the base case. The model indicates strong demands f o r coal i n industry, for the gener- 211 ation of e l e c t r i c i t y and heat by cogeneration i n the west, and possibly, for synthetic f u e l production as discussed above. H y d r o e l e c t r i c i t y i s important i n both regions, since i t i s the l e a s t expensive source of e l e c t r i c i t y . The existence of large supplies of inexpensive coal for e l e c t r i c i t y i n the west and of low cost nuclear e l e c t r i c i t y i n the east ensure f a i r l y stable e l e c t r i c i t y p r i c e s i n both regions. The eastern picture changes dramatically under the assumption of no new nuclear development a f t e r 1985. The alternate source of eastern e l e c t r i c i t y - from coal - i s so expensive that there i s a large switch from e l e c t r i c i t y to o i l i n the no-new-nuclear case, compared to the base case. O i l from the t a r sands i s e s p e c i a l l y important i n t h i s switch a f t e r 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 i s not one of economics, but of the safety of nuclear power. The e l e c t r i c automobile w i l l not l i k e l y be competitive unless there are technical breakthroughs which lower the i n i t i a l cost differences between the e l e c t r i c and conventional cars, or the road tax burden i s less f o r e l e c t r i c cars than f o r conventional ones. Under the assumptions of improvements i n the f u e l e f f i c i e n c y of conventional cars, the p r i c e of transportation (price per mile) decreases u n t i l 2010, even though the f u e l p r i c e (price per gallon) increases. Heating i n the domestic, farm and commercial sector of the west w i l l l i k e l y be done mainly by gas u n t i l 2010, with s o l a r and cogeneration taking the place of gas l a t e r . In the eastern region, o i l and gas are important heating fuels u n t i l 2000 and 2010, r e s p e c t i v e l y . E l e c t r i c resistance and s o l a r heating are the important types of heating i n l a t e r periods. I t appears that the heat pump i s not competitive i n e i t h e r region. I f d i s t r i c t heating by 212 cogeneration with nuclear e l e c t r i c i t y i s allowed ( i t i s not allowed i n the base case), t o t a l e l e c t r i c i t y production i s lower i n the east, p a r t i c u l a r l y nuclear e l e c t r i c i t y , because e l e c t r i c i t y f o r resistance heating i s not r e - quired i n such large amounts. This indicates that one route to improving nuclear safety may be to d i s t r i b u t e the waste heat from nuclear stations for r e s i d e n t i a l and commercial heating, provided, of course, that any new r i s k s from c i r c u l a t i n g radioactive hot water, or from b u i l d i n g nuclear stations c l o s e r to population centres do not outweigh the safety benefits of decreased nuclear power development. There are many possible d i r e c t i o n s f o r future research. A major e f f o r t to construct a data base on the f u n c t i o n a l end uses of energy i n Canada, p a r t i c u l a r l y i n industry, would allow the r e v i s i o n of the structures of models such as t h i s one to a more t h e o r e t i c a l l y s a t i s f y i n g structure. The market shares of fuels i n the end use sectors could be made more endogenous, for example, by a more d e t a i l e d process modelling i n the end use sectors. This data base work can l i k e l y be c a r r i e d out only by a government agency such as S t a t i s t i c s Canada. The e x i s t i n g areas of end use process modelling — DFC heating and road transportation — could b e n e f i t by e x p l i c i t representation of "vintage e f f e c t s " i n the energy-using processes. For example, automobiles might be distinguished by period of production, with a new-car f u e l e f f i c i e n c y f or each period. In the present formulation of the model, average f u e l e f f i c i e n c y i s projected f o r each period f o r a l l cars, regardless of when they were produced. However, t h i s average i n r e a l i t y depends on the rate of introduction of new cars. The vintage approach would avoid t h i s problem. The p o l i c i e s of u n r e s t r i c t e d energy exports and world p r i c i n g could be explored by incorporating increasing, marginal costs of capacity expansion i n 213 key energy sectors (e.g. o i l and gas). Apart from straightforward s t r u c t u r a l changes, the work would involve c a r e f u l estimation of the cost escalations which can occur by a too rapid construction of, say, t a r sands plants. A stochastic model of o i l production might shed l i g h t on the optimal rate of development of t a r sands, given the uncertainties surrounding the a l t e r n a t i v e , less c o s t l y conventional o i l resources. Stochastic modelling may also give i n s i g h t into optimal export p o l i c i e s , without exogenously r e s t r i c t i n g exports. The model discussed here i s a p a r t i a l equilibrium model, viewing the energy - economy linkages as only one-way. I t i s assumed that the various macroeconomic variables used i n the energy demand functions are not them- selves affected by events i n the energy sector. The model would b e n e f i t by an extension to include automatic two-way energy economy i n t e r a c t i o n s . In the early development of t h i s model, a representation of energy economy int e r a c t i o n s was attempted, by the method of ETA-MACRO (Manne, 1977). How- ever, t h i s approach had to be abandoned to keep the process d e t a i l i n the end use sectors because there was no apparent way to make each end-use sector's share of t o t a l output energy endogenous. Probably the most important area of energy-economy int e r a c t i o n s i s the e f f e c t of the demand for investment c a p i t a l by energy investments, p a r t i c u l a r l y the large p r o j e c t s . 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 c a p i t a l needs, t o t a l c a p i t a l investment, and economic growth, and judging whether energy investments w i l l cause any s t r a i n s to develop. Most conclude that there w i l l be no great d i f f i c u l t i e s , provided the federal and p r o v i n c i a l governments adopt c e r t a i n p o l i c i e s . Waddingham (1980), however, 214 i s r e l a t i v e l y p e s s i m i s t i c , forseeing the p o s s i b i l i t y of c a p i t a l supply l i m i t a t i o n s f o r energy investments. A f r u i t f u l area of further research, therefore, would involve the extension of the model to account f o r constraints on c a p i t a l a v a i l a b i l i t y f o r energy investments. Id e a l l y , such an extension should include the feedback e f f e c t of a large energy-related c a p i t a l re- quirement d r i v i n g up the economy-wide cost of c a p i t a l , which i n turn raises the cost of energy, thus dampening the demand f o r energy. As a f i r s t step, a data base on i n i t i a l c a p i t a l 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 f o r the s o l u t i o n i n each period could then be calculated, examined for "bulges", and compared to projections of c a p i t a l a v a i l a b i l i t y to look for c a p i t a l supply constraints, as i n the approach of the other studies mentioned above. However, the base case r e s u l t s i n t h i s d i s s e r t a t i o n are u n l i k e l y to be constrained by c a p i t a l requirements. Total secondary energy i n 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) i n 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 o p t i m i s t i c about financing, the energy projections here should cause even les s concern about financing. Nevertheless, a de t a i l e d , c a r e f u l look at the problem would c e r t a i n l y be worthwhile, p a r t i c u l a r l y i f the u n r e s t r i c t e d trade p o l i c y i s to be investigated thoroughly. A systematic study by Canadian energy analysts of the various Canadian 215 energy models, with a c a r e f u l examination of the s t r u c t u r a l and data assumptions, would be a great help i n 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 a r i s i n g from such a study. Survey papers such as those by F u l l e r and Ziemba (1980), and Manne et a l . (1979) can be u s e f u l steps i n the evaluation process, but the Energy Modeling Forum i n the United States provides an example of the method and bene- f i t s of deeper studies by researchers from industry, government and u n i v e r s i t i e s . I f many new d e t a i l s are incorporated i n t o the model i n future research, closer a t t e n t i o n w i l l have to be paid to computing methods, to minimize computation costs. Decomposition by region might be attempted, p a r t i c u l a r l y i f more than two regions are distinguished (perhaps f o r a better represent- ation of e l e c t r i c i t y generation). Time period decomposition might proceed by so l v i n g a s e r i e s of two-period problems — at each step, one period would be the "present", and the second "period" would represent a l l time beyond the f i r s t period, i n the manner of the dual equilibrium method of Gr i n o l d (1980). I t i s possible that the s o l u t i o n obtained by stepping through the time periods i n t h i s way may be a good, inexpensively-obtained s t a r t i n g basis fo r the f u l l problem, i n which the optimal s o l u t i o n i n a l l time periods i s to be found by a s i n g l e optimization. The interim s o l u t i o n found by t h i s time decomposition may be of i n t e r e s t i t s e l f -- i t might be interpreted as a "myopic" s o l u t i o n , representing the behaviour of d e c i s i o n makers who act on the basis of somewhat vague, average notions about the future. I f t h i s model and i t s variants are to be used continually f o r a n a l y s i s of energy p o l i c i e s , i t w i l l be necessary to revise the data base p e r i o d i c a l l y as new f a c t s come to l i g h t . To cope with the i n e v i t a b l e demands to change the data and the structure of the model, i t w i l l be advantageous to construct improved input software to speed up the process of entering the structure and data base. I f t h i s model and i t s variants are to be used a c t i v e l y i n energy p o l i c y debates, and i f they are to be used by researchers wishing to experiment with d i f f e r e n t aggregations of energy flows, and with d i f f e r e n t scenarios, ease of spe c i f y i n g new data and structures would be a great, although very " p r a c t i c a l " , advantage. This d i s s e r t a t i o n has out l i n e d the construction of a long-term energy p o l i c y model f o r Canada, and has given examples of the use of the model i n the analysis of several energy p o l i c y issues. There remain many opportunities f o r further analysis with t h i s model and f o r advancement of the c a p a b i l i t i e s of models i n energy p o l i c y a n a l y s i s . REFERENCES Ai k i n , A.M.; Harrison, J.M.; and Hare, F.K. August 31, 1977. "The Management of Canada's Nuclear Wastes". Energy, Mines and Resources Canada,. Report EP 77-6, Ottawa. Berkowitz, M.K. 1977. "Implementing Solar Technology i n Canada", Energy, Mines and Resources Canada, Report EI 77-7. Berthin, W. A p r i l 1980. "An Economic and Technical Evaluation of the Use of Waste Heat from E l e c t r i c i t y Generation for Space Heating", fourth-year undergraduate p r o j e c t . Faculty of Engineering, The Uni v e r s i t y of Waterloo, Waterloo, Canada. Canadian Petroleum Association. 1977. S t a t i s t i c a l Handbook. Calgary. Cazalet, E.G. May 1977. "Generalized Equilibrium Modeling: The Method- ology of the SRI-Gulf Energy Model". Decision Focus, Inc., Palo A l t o , C a l i f o r n i a . Cazalet, E.G., et a l . December 1978. The DFI Energy-economy Modeling System. F i n a l Report prepared by Decision Focus Inc., Palo A l t o , C a l i f o r n i a , f o r the U.S. Department of Energy. Cazalet, E.G. November 1979. "A Progress Report on the Development of Generalized Equilibrium Modeling." Decision Focus Inc., Palo A l t o , C a l i f o r n i a . Dalrymple, D.G.; and Anderson, D.R. 1978. " R e l i a b i l i t y and Peformance of CANDU Nuclear Generating Stations". In R e l i a b i l i t y Problems of Reactor Pressure Components, Volume I, International Energy Agency, Vienna. Daniel, T.E.; and Goldberg, H.M. 1980. "An Alberta Energy Planning Model." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Debanne^ J.G. 1975. A Regional Techno-economic Energy Supply-Distribution Model f o r North America. Computers and Operations Research 2:153-193. Debanne'', J.G. 1980. "Network Based Regional Energy Planning Models: An Evolutionary Expose." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Dewees, D.N. ,: Hyndman, R.M.; and Waverman, L. June, 1975. "Gasoline Demand i n Canada 1956-1972". Energy P o l i c y 111:116-123. "Douglas, G.W.,- and Nichols, R.A. December 18, 1979. "The Canadian Economy to the Year 2000: NEB Macroeconomic Forecasts 1979." Prepared f o r Economics Branch, National Energy Board, Ottawa. Downs, J.R. 1977. The A v a i l a b i l i t y of C a p i t a l to Fund the Development of Canadian Energy Supplies. Canadian Energy Research I n s t i t u t e , Calgary. Economic Council of Canada. 1979. "Two Cheers f o r the E i g h t i e s . " Sixteenth Annual Review, Ottawa. E l l i s o n , A.P. A p r i l , 1978. "Past and Future Energy Costs i n the Canadian Economy." Working paper No. 78-3, Canadian Energy Research I n s t i t u t e , Calgary. Energy, Mines and Resources Canada. 1973. An Energy P o l i c y f o r Canada Phase 1: Volume I I . Ottawa. Energy, Mines and Resources Canada. 1976a. An Energy Strategy f o r Canada: P o l i c i e s f o r Self-Reliance. Ottawa. Energy, Mines and Resources Canada. February 25, 1976b. "New Energy Conservation Measures - Fact Sheets." Ottawa. Energy, Mines and Resources Canada. June 1976c. "1975 Assessment of Canada's Uranium Supply and Demand." Ottawa. Energy, Mines and Resources Canada. September 1976d. "Proceedings of the 28th Canadian Conference on Coal." Ottawa. Energy, Mines and Resources Canada. 1976e. " E l e c t r i c Power i n Canada, 1975. Ottawa. Energy, Mines and Resources Canada. A T o t a l Energy Approach. Energy, Mines and Resources Canada. sources of Canada, 1976." June 1977a. Energy Demand Projections- Report ER 77-4, Ottawa. 1977b. " O i l and Natural Gas Re- Report EP 77-1, Ottawa. Energy, Mines and Resources Canada. 1977c. " O i l Sands and Heavy O i l s : The Prospects." Report EP 77-2, Ottawa. Energy, Mines and Resources Canada. 1977d. A d r a f t copy of work on the costs of developing new Canadian o i l and gas reserves. Energy, Mines and Resources Canada. 1977e. "Energy Conservation i n Canada: Programs and Perspectives." Report EP 77-7, Ottawa. Energy, Mines and Resources Canada, January 1977f. "Coal Mines i n Canada." Operators L i s t 4, Ottawa. "Energy, Mines and Resources Canada. 1977g. "1976 Assessment of Canada's Coal Resources and Reserves." Report EP 77-5, Ottawa. Energy, Mines and Resources Canada. 1977h. "Financing Energy Self-Reliance." Report EP 77-8, Ottawa. Energy, Mines and Resources Canada. 1978a. " O i l and Natural Gas Industries i n Canada, 1978." Report ER 78-2, Ottawa. Energy, Mines and Resources Canada. 1978b. Energy Futures for Canadians Report EP 78-1, Ottawa. Energy, Mines and Resources Canada. 1978c. "Energy Update, 1977." Report EI 78-2, Ottawa. Energy, Mines and Resources Canada. 1978d. "1977 Assessment of Canada's Uranium Supply and Demand", Report EP 78-3, Ottawa. Eynon, R.T.; Pearson, J.vD.; Wagner, M.H. November 1975. "Energy Models Available from FEA." Prepared f o r Operations Research Society of America/The I n s t i t u t e of Management Science j o i n t national meeting, Las Vegas, Nevada. . F u l l e r , J.D.; and Ziemba, W.T. 1980. "A Survey of Some Energy P o l i c y Models." In Energy P o l i c y Modeling:. United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Greenberg, H.J. 1980a. "Analyzing Alaskan Gas D i s t r i b u t i o n Options". In Energy P o l i c y Modeling: United States and Canadian Ex- periences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Greenberg, H.J. 1980b. "Crash Mode Modeling: Analyzing the National Energy Plan." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Grinold, R.C. 1980. "Time Horizons i n Energy Planning Models." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Hedley, T.B., et al.. May 1976. "The Conservation of O i l Through the Use of E l e c t r i c Automobiles." Energy Research Group,CCarleton Un i v e r s i t y , Ottawa. Hedlin, Menzies and Associates, Ltd. July 1976. "Energy Scenarios for the Future." Report prepared for the Science Council of Canada, Ottawa. H e l l i w e l l , J.F., et a l . December 1976. "An Integrated Model f o r Energy P o l i c y Analysis." Resources Paper No.7, Department of Economics, The University of B r i t i s h Columbia, Vancouver. H e l l i w e l l , J.F. 1979. "Canadian Energy P o l i c y " , Annual Review of Energy, 4:175-229. H e l l i w e l l , J.F.; Hendricks, K.; and Williams, D.B.C. 1980. "Canadian Perspectives on the Alaska Highway P i p e l i n e : Modeling the A l t e r n a t i v e s . " In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Hoffman, K.C. 1973. "A U n i f i e d Framework f o r Energy System Planning." i n Energy Modeling, ed. M.F. Searl, Resources f o r the Future, Washington, D.C. Hoffman, K.C; and Jorgenson, D.W. 1977. "Economic and Technological Models f o r Evaluation of Energy P o l i c y . " B e l l Journal of Economics 8:444-466. Hogan, W.W. 1975. "Energy Models for Project Independence." Computers and Operations Research 2:251-271. Hogan, W.W. January 1977. "Project Independence Evaluation System: Structure and Algorithms." In Mathematical Aspects of Production and D i s t r i b u t i o n of Energy, v o l . 21 of Proceedings of Symposia i n Applied Mathematics, American Mathematical Society, Providence, R.I. Hudson, E.A.; and Jorgenson, D.W. 1974. "U.S. Energy P o l i c y and Economic Growth, 1975-2000." B e l l Journal of Economics and Management Science 5:461-514. Hudson, E.A.; and Jorgenson, D.W. 1978. "Energy P o l i c y and U.S. Economic Growth." The American Economic Review. Papers and proceedings of the n i n e t i e t h annual meeting of the American Economic Association. I n t r i l i g a t o r , M.D. 1971. Mathematical Optimization and Economic Theory. P r e n t i c e - H a l l , Inc., Englewood C l i f f s , New Jersey. Jenkins, G.P. October 1977. "Capital i n Canada: Its S o c i a l and Private Performance 1965-1974." Discussion Paper 92, Economic Council of Canada. Kalymon, B.A. 1980. "Potential C a p i t a l Cost and Financing Required for Canadian Energy Projects." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. 221 Keairns, D.L., et a l . September 1975. " F l u i d i z e d Bed Combustion Process Evaluation, Phase II - Pressurized F l u i d i z e d Bed Coal Combustion Development." Prepared by Westinghouse Research Laboratories f o r U.S. Environmental Protection Agency, Report EPA - 650/2-75-027-c. Kee, F.J.; and Woodhead, L.W. June 1977. "A Progress Review of Ontario Hydro's Nuclear Generation and Heavy Water Production Programs." Presented to the 17th Annual International Conference of the Canadian Nuclear Association, Montreal. Kydes, A.S. 1980. "The Brookhaven Energy System Optimization Model: I t s Variants and Uses." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Manne, A.S. 1976. "ETA: A Model for Energy Technology Assessment." B e l l Journal of Economics and Management Science 7:379-406. Manne, A.S. 1977. "ETA-MACRO: A Model of Energy-economy Interactions." In Modeling Energy-economy Interactions: Five Approaches, ed. C.J. Hitch, Resources f o r the Future, Washington, D.C. Also i n Advances i n the Economics of Energy and Resources, Volume 2, JAI Press, Inc., 1979. Manne, A.S. November, 1978. "Energy T r a n s i t i o n Strategies f o r the In d u s t r i a l i z e d Nations." Presented at the International S c i e n t i f i c Forum on an Acceptable World Energy Future, Miami. Manne, A.S.; Richels, R.G.; and Weyant, J.P. 1979. "Energy P o l i c y Modeling: A Survey." Operations Research 27:1-36. Marcuse, W. 1980. "Why Should Energy Models Form a S i g n i f i c a n t P o l i c y Input i n an Uncertain P o l i t i c a l World?" In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Middleton Associates. A p r i l 1976. "Canada's Renewable Energy Resources: An Assessment of P o t e n t i a l , " Toronto. M i l l a n , S. February 25, 1980. Quoted from a speech to a seminar i n Toronto. Oilweeky 31, 3:44. Murtagh, B.A.; and M.A. Saunders. February 1977. "MINOS, a Large-Scale Nonlinear Programming System,"- Technical Report SOL 77-9, Systems Optimization Laboratory, Department of Operations Research, Stan- ford U n i v e r s i t y . McConaghy, D.J.; and Quon, D. 1980. "The Al b e r t a Energy Resources A l l o c a t i o n Model." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. McCracken, M.C. February 1973. An Overview of CANDIDE Model 1.0. CANDIDE Project Paper no. 1, Economic Council of Canada. National Energy Board. September 1978. Canadian O i l Supply and Require- ments , Ottawa. National Energy Board, November 1979. "Reasons f o r Decision i n the Matter of Applications under Part VI of the National Energy Board Act," Ottawa. Nordhaus, Wm. D. 1973. "The A l l o c a t i o n of Energy Resources." Brookings Papers on Economic A c t i v i t y , 3:529-576. Oilweek. February 12, 1979, 30_, 1. Parikh, S.C. 1980. "A Dynamic Welfare Equilibrium Framework f o r Projecting Energy Futures." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz Martinus N i j h o f f Publishing, Boston. Parikh, S.C; Braun, C ; and Yu, O.S. 1978. "1978 Overview Planning Scenarios from the Welfare Equilibrium Model of Stanford's PILOT System," E l e c t r i c Power Research I n s t i t u t e , Planning Memorandum 78-2. P r o t t i , G.J. May 1978. "Canadian E l e c t r i c U t i l i t y Industry Costs, 1960-1990," Working Paper No. 78-4, Canadian Energy Research I n s t i t u t e , Calgary. Quon, D. May, 1980. Personal discussion with the author, at the 1980 conference of the Canadian Operations Research Society, Quebec C i t y Rothman, M.P. 1980. "The Demand f o r Funds f o r Energy Investment i n Canada." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Sahi, R.K. February 15, 1979. "Transportation Sector i n the EMR IFSD Model," EMR report, Ottawa. Sahi, R.K. January 15, 1980. Personal communication with the author. Sahi, R.K.; and Erdmann, R.W. 1980. "A P o l i c y Model of Canadian I n t e r f u e l Substitution Demands." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I, eds. W.T. Ziemba, S.L. Schwartz and E. Koenigsbert, Martinus N i j h o f f Publishing, Boston. Schwartz, S.L. 1980a. "The Problems of Financing Energy Development Projects." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Schwartz, S.L. 1980b. "Energy Demand Modeling." In Energy P o l i c y Modeling United States and Canadian Experiences, Volume I, eds. W.T. Ziemba, S.L. Schwartz, and E. Koenigsberg, Martinus N i j h o f f Publishing, Boston. Stanford Research I n s t i t u t e , November 1976." A Western Regional Energy Development Menlo Park, Study: Economics," SRI Decision Analysis Group, C a l i f o r n i a . S t a t i s t i c s Canada. 13-•211. "Fixed C a p i t a l Flows and Stocks," Ottawa. S t a t i s t i c s Canada. Volume 1 13- 11 / •531. Ottawa "National Income and Expenditure Accounts, ., March, 1976. S t a t i s t i c s Canada. 26-•206. "Coal Mines," Ottawa. S t a t i s t i c s Canada. 45-•206. "Petroleum Refineries," Ottawa. S t a t i s t i c s Canada. 57-•202. " E l e c t r i c Power S t a t i s t i c s , Volume I I , " Ottawa. S t a t i s t i c s Canada. 57-•204. " E l e c t r i c Power S t a t i s t i c s , Volume 1," Ottawa. S t a t i s t i c s Canada. 57-•205. "Gas U t i l i t i e s , " Ottawa. S t a t i s t i c s Canada. Canada," 57-207. Ottawa. "Detailed Energy Supply and Demand i n S t a t i s t i c s Canada. 57-•506. "Consumption of Purchased Fuel and E l e c t r i c i t y by the Manufacturing, Mining and E l e c t r i c Power Industries, 1962-1974," Ottawa. S t a t i s t i c s Canada. 68-201. " P r i n c i p a l Taxes and Rates," Ottawa. S t a t i s t i c s Canada. 91-201. "Estimates of Population f o r Canada and the Provinces, June 1, 1979," Ottawa. S t a t i s t i c s Canada. 1978. Canada Yearbook, 1976-77, Ottawa. S t a t i s t i c s Canada. 91-520. "Population Projections f o r Canada and the Provinces, 1976-2001," Ottawa, February, 1979. Swinton, M.C. June 1976.- "Comparison of Primary Energy Requirements f o r the Operation of E l e c t r i c and Conventional Automobiles," Energy Research Group, Carleton University, Ottawa. Waddingham, D.G. 1980. "Financing Canadian Energy to 1990: Some Supply Side Constraints." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Walters, R.M. October 22, 1979. Quoted from a presentation on behalf of Q and M Pi p e l i n e before the National Energy Board. Oilweek, 30, 37:52. 224 Wayne, M. November, 1979. "The Promise and Puzzle of E l e c t r i c Vehicles." EPRI Journal, 4_, 9:6-15, E l e c t r i c Power Research I n s t i t u t e , Palo A l t o , C a l i f o r n i a . Ziemba, W.T. 1980. "The Process of Energy P o l i c y Modeling." In Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , eds. W.T. Ziemba and S.L. Schwartz, Martinus N i j h o f f Publishing, Boston. Ziemba, W.T.; and Schwartz, S.L. (eds.). 1980. Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I I , Martinus N i j h o f f Publishing, Boston. Ziemba, W.T.; Schwartz, S.L.; and Koenigsberg, E. (eds.). 1980. Energy P o l i c y Modeling: United States and Canadian Experiences, Volume I, Martinus N i j h o f f Publishing, Boston. Appendix A. Derivation of the Demand Equations. The model calculates equilibrium p r i c e s and energy quantities i n each region, f o r every time period, f o r four end-use sectors — road transportation, other transportation, i n d u s t r i a l , and DFC (domestic, farm and commercial). The bulk of the model i s a l i n e a r process model of energy supply and d i s t r i b u t i o n . The demands for output energy i n each of the four end use sectors are determined as functions of the respective p r i c e s , and of exogenous economic and demographic v a r i a b l e s . Except f o r 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 c a r r i e d out here. Instead, the work of other researchers, e s p e c i a l l y at EMR, has been used as a guide i n the s e l e c t i o n of independent variables and e l a s t i c i t i e s to derive the demand equations used here. These demand equations have been c a l i b r a t e d with data on demands and independent v a r i a b l e s from 1970 and 1971, which were assumed to be equilibrium years f o r the energy sector. The EMR demand equations, described i n Sahi and Erdmann (1980) and Sahi (1979), a l l incorporate lagged demands as determinants of present demands since the e f f e c t s of changes i n pr i c e s and other variables are not immediate. Long term versions of the EMR demand equations can be e a s i l y derived, with the i n t e r p r e t a t i o n that the calculated demands would be the demands at the given p r i c e s , etc., a f t e r s u f f i c i e n t time has elapsed f o r the f u l l response to be made. The long term versions of the demand equations have been used because 1) the model has f i v e and ten-year periods, but t y p i c a l adjustment times range from 4.6 years to 7.3 years f o r 90% of the adjustment to be made; and, v 2) the l i n e a r process model of energy supply incorporates lag .effects by f o r c i n g the continued use of established capacity of many energy supply and end-use technologies f o r s p e c i f i e d l i f e t i m e s . There i s some evidence (Schwartz, 1980b) that the long term e l a s t i c i t i e s of demand for t o t a l output energy i n each end use sector reported by Sahi and Erdmann are too low, and represent shorter term responses. The problem may be i n the l i t t l e v a r i a t i o n i n time ser i e s used f o r estimation. Cross- country studies, with wider v a r i a t i o n i n the data, generally indicate l a r g e r long term e l a s t i c i t i e s . Sahi and Erdmann (1980) t r e a t r e s i d e n t i a l and commercial demands separately i n the EMR model. The present model combines these two sectors i n the DFC sector. Hence, i t i s necessary to combine the two EMR demand equations i n a reasonable way. The EMR demand equation for the r e s i d e n t i a l sector i s l n (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 f o r output energy i n the r e s i d e n t i a l sector, RQ = a regional constant, H = number of households, IPH = disposable income per household, SDPH = sin g l e dwellings per household, y' = .1276 (for Ontario), .2337 (for Manitoba), 0 (elsewhere), DD = degree days (a weather f a c t o r ) , and P = p r i c e of output energy i n the r e s i d e n t i a l sector. The subscript "-1" i n the above equation indicates that the variable i s 2 lagged one year. Sahi and Erdmann report that R = .998 for t h i s equation. A l l equations were estimated over the period 1963-1974, pooling time series f o r seven regions. The long term version of the above equation may be derived by assuming that lagged variables equal the present year variables i n the long term. I f the weather f a c t o r i s incorporated i n t o the constant (since long range weather forecasting i s impossible), the long term r e s i d e n t i a l demand equation i s 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 t h i s equation i s combined with the EMR long term commercial energy demand equation and used i n the present model, the energy demand and pr i c e variables are endogenous. The EMR equation f o r commercial energy demand, i n long term form, and incorporating the weather f a c t o r into the constant, i s CDEM = C Q X (POP) x ( I P C ) ' 9 0 6 0 x (MDPH) • 1 5 6 5:,.xP " • 3 8 2 3 where, CDEM = demand f o r output energy i n the commercial sector, CQ = a constant POP = population IPC = disposable income per capita MDPH = number of multiple dwellings per household, and, P = p r i c e of output energy. The commercial sector's estimated income and p r i c e e l a s t i c i t i e s were al t e r e d by EMR judgementally to the above more reasonable values, according to Sahi (1980). In combining the r e s i d e n t i a l and commercial sectors f o r the purpose of long-range forecasting, several s i m p l i f y i n g assumptions can be made. The f i r s t i s the elimination of the weather f a c t o r . .Secondly, the MDPH va r i a b l e may be dropped from the combined equation, since i t s p o s i t i v e e l a s t i c i t y suggests that i t i s more a measure of the amount of r e s i d e n t i a l energy f a l l i n g under the s t a t i s t i c a l c l a s s "commercial" than a measure of energy e f f i c i e n c y due to multiple dwellings. T h i r d l y , the SDPH' var i a b l e may be dropped from the combined equation since i t has a non-zero e l a s t i c i t y f o r only two provinces, i n d i c a t i n g that i t s i n c l u s i o n i s p r i m a r i l y to explain the data c l a s s i f i c a t i o n problem associated with large multiple dwellings f a l l i n g under the commercial c l a s s i f i c a t i o n . (This problem should disappear when the two sectors are combined.) Fourthly, the p r i c e e l a s t i c i t i e s f o r the r e s i d e n t i a l and commercial sectors are very close, suggesting a p r i c e e l a s t i c i t y of -.39 for the combined demands would be a good choice. L a s t l y , although there has been a higher rate of growth of the number of households than that of population i n recent decades (due to such factors as increasing divorce rate, the "baby boom" c h i l d r e n growing to adulthood, and a lower b i r t h r a t e ) , i t i s d i f f i c u l t to j u s t i f y making a d i s t i n c t i o n between fore- casts of these two growth rates over the long term of the present model (45 years). Therefore, output energy demand i n the DFC sector i s taken to be proportional to population, and to income per capita r a i s e d to some power z - 39 DFC = A Q x (POP) x (IPC) x P * where DFC = demand f o r output energy i n the DFC sector, and = a constant. The e l a s t i c i t y , z, i s taken to be 0.9060 by EMR f o r the commercial sector. 3407 In the EMR equation for r e s i d e n t i a l demand, the factor H x (IPH)* z corresponds to the f a c t o r (POP) x (IPC) i n the above combined DFC equation. . 3407 If z i s chosen to make the average annual rates of growth of H x (IPH)" and (POP) x (IPC) equal i n the h i s t o r i c a l period 1960-1976, then, using the data f o r these growth rates presented by the National Energy Board (1979 , p.84), z = .58. Thus, i f the above combined equation were to re- present only the r e s i d e n t i a l sector, the e l a s t i c i t y 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 r e s i d e n t i a l and commercialsectors, respect- i v e l y , i s z = .71. .^Indices of -population (pop) and of income per capita (ipc) are used/.with a base year of 1973 i n the : DFC demand equations, giving 71 - 39 DFC = D Q x (pop) x (ipc)* x p- where D Q = a constant, d i f f e r e n t f o r the east and west. The constant factors are chosen using data of 1970, which i s assumed to be an equilibrium year. One further adjustment i s necessary to make the DFC demand equation appropriate f o r the model. In the DFC sector of the l i n e a r process model of energy supply, the non-fuel costs of space heating are taken into account, as well as the f u e l costs. However, i n the demand equation derived above, only the f u e l cost i s represented i n the p r i c e v a r i a b l e . In section 8 of Appendix C, "Data f o r the Base Case", the output energy p r i c e s are derived for the base year, 1970. The weighted average of the western and eastern DFC output p r i c e s (weighted by output energy i n the two DFC sec t o r s ) , i n - cluding non-fuel costs of heating, was 0.5074, i n model u n i t s . The weighted average of the DFC output f u e l p r i c e s , not incl u d i n g non-fuel heating costs, was 0.2431, i n model u n i t s . An e l a s t i c i t y of 0.39 with respect to f u e l p r i c e means that a 1% change i n f u e l p r i c e leads to a 0.39% change i n output energy demand. However, a 1% change i n f u e l p r i c e alone implies a 0.48% '.':•(•= .01 x .2431/.5074 x 100%) change i n t o t a l output energy p r i c e , including non-fuel heating costs. Therefore, since a change of 0.48% i n t o t a l output energy p r i c e leads to a 0.39% change i n output energy demand, the e l a s t i c i t y of demand f o r output energy with respect to t o t a l p r i c e i s - (0.39)/(0.48) = ---.-'81. Therefore, the demand equation f o r the DFC sectors of the present model i s 71 — 81 DFC = D x(pop)x(ipc)" xP ' The EMR i n d u s t r i a l energy demand equation excludes the demands f o r coke, coke oven gas and non-energy use of o i l , but includes the demand fo r natural gas as a petrochemical feedstock. The EMR variables and e l a s t i c i t i e s have been used i n an equation which includes a l l of industry's demands f o r energy commodities, including f o r the above s p e c i a l uses. EMR makes separate projections f o r coke, coke oven gas and petrochemical use of o i l , but here the approach adopted i s that of Hedlin, Menzies and Associates (1976), of pr o j e c t i n g the upper and lower l i m i t s of the f r a c t i o n s of i n d u s t r i a l output energy (including the s p e c i a l uses) supplied by coal, o i l , gas and e l e c t r i c i t y . The EMR equation uses i n d u s t r i a l r e a l domestic product as an explanatory v a r i a b l e , but since i t i s d i f f i c u l t to make a d i s t i n c t i o n between the growth rates of i n d u s t r i a l RDP and t o t a l RDP over the long range of the present model, t o t a l r e a l domestic product has been used here. Using indices (1973 = 1) of r e a l domestic product and c a p i t a l - output r a t i o , and combining the weather factor into the constant, the long term EMR equation i s al t e r e d to the form used here: IND = I x (rdp) x (cor) xP " 4 8 , where,IND = output energy demand of i n d u s t r i a l sector, I = constant, d i f f e r e n t f o r each region rdp = index (1973 = 1) of r e a l domestic product, cor = index (1973 =1) of the capital/output r a t i o (manufacturing c a p i t a l stock divided by i n d u s t r i a l output) , and P = p r i c e of output energy, i n d u s t r i a l sector. Again, the constant factors are chosen using the v a r i a b l e s ' values i n 1970, an equilibrium year. The EMR model of demand f o r motor gasoline, i n Sahi (1979), has been estimated using as data the econometric-judgemental forecasts f o r 1976-1990 prepared by the National Energy Board (NEB) with the a i d of the NEB's complex motor gasoline model. The i n t e r p r e t a t i o n of EMR's long-term income and p r i c e e l a s t i c i t i e s f o r use i n the present model i s complicated because EMR i s estimating input energy requirements, and they use a lagged, new-car f u e l economy standard as an explanatory v a r i a b l e . This model requires an equation of the demand for output energy requirements, where the average f u e l economy of a l l cars i s projected i n the l i n e a r process supply model. Therefore, i n the model discussed here, income and p r i c e e l a s t i c i t i e s are assumed to be i n the ranges found by Dewees, Hyndman, and Waverman (1975), who estimated f i v e d i f f e r e n t models of demand f o r gasoline (input energy) using Canadian data f o r 1956-1972. Although these researchers used an urbanization index and automobile p r i c e as explanatory variables (as w e l l as gasoline p r i c e and income per ca p i t a ) , i t has been assumed here that these two variables w i l l be r e l a t i v e l y constant over the time period covered by the model. In addition, i t has been assumed that average f u e l economy was constant over t h e i r estimation period, so that t h e i r e l a s t i c i t i e s are applicable to the estimation of demand f o r output energy. Since d i e s e l f u e l supplied only about 6% of the input energy to road transportation i n 1973, i t has been assumed here that the same income and p r i c e e l a s t i c i t i e s apply to the demands for both gasoline and road-diesel. The equation f o r the demand for output energy i n the road transport sector i s then: 8 — 36 RTR = R Q x (pop) x (ipc)* x P. where, RTR = demand f o r output energy i n the road transport sector, R Q = a regional constant, pop = an index of population (1973 = 1), ipc = index of disposable income per capita (1973 = 1), and, P = p r i c e of output energy i n the road transport sector. The long term income and p r i c e e l a s t i c i t i e s , .8 and -.36, res p e c t i v e l y , are the midpoints of the ranges reported by Dewees, Hyndman and Waverman (1975) for a l l of Canada —.69 to .91, and -.26 to -.45. -The regional constants are derived from 1970 data. The demands f o r input energy to the r a i l , a v i a t i o n and marine sub- sectors of the transportation sector together accounted f o r 23% of the input energy demands of the whole transportation sector i n 1973. I t i s therefore worthwhile to have a separate demand equation f o r the r a i l - a v i a t i o n - marine sector, which i s l a b e l l e d "other tansportation" i n t h i s model. EMR has estimated demand equations, i n Sahi (1979), f o r each of these three subsectors, using a 1976-1990 p r o j e c t i o n by the NEB. The long term p r i c e e l a s t i c i t i e s f a l l between -.067 and -.71, with an average (weighted by the 1973 input energy to the three subsectors) of -.36. The income variables are e i t h e r r e a l domestic product per capita (aviation) or r e a l domestic product i n industry and a g r i c u l t u r e (the others). Population i s also an explanatory variable i n the av i a t i o n equation. Considering the average p r i c e e l a s t i c i t y above, and the s i m i l a r i t y i n the growth rate of r e a l domestic product (RDP) and RDP i n industry and a g r i c u l t u r e , i t i s reasonable, upon examination of the three EMR equations, to adopt the following demand equation f o r other transportation: 30 OTR = 0 Q x (rdp) x P , where, OTR = output energy demand i n the sector of other transportation, 0 Q = a regional constant rdp = an index of r e a l domestic product (1973 = 1), and, P = p r i c e of output energy, i n the other transportation sector. The regional constants are derived from 1970 data. The following chart summarizes the four long- term,-demand questions used i n the present model. Table 68. Demand Equations Used i n the Model. Sector Equation 71 — 81 1. Domestic, Farm DFC = D Q x (pop) x ( i p c ) " x P and Commercial , -, x -667 -.48 2. I n d u s t r i a l IND = I x (rdp) x (cor) X P 8 — 3 6 3. Road Transportation RTR = R Q x (pop) x (ipc)" x p — 36 4. Other Transportation OTR = 0 Q x (rdp) x P D e f i n i t i o n s of Symbols DFC, IND, RTR, OTR = output energy demands i n the various sectors D , I , RQ, 0 Q = regional (east or west) constants pop = index of population i n each region (1973 = 1) ipc = index of disposable income per capita (1973 = 1) rdp = index of r e a l domestic product i n each region (1973 = 1) cor = index of capital/output r a t i o . (1973 = 1) - i . e . manufacturing c a p i t a l stock divided by i n d u s t r i a l output. Appendix B. Detailed Structure of the Model. In t h i s section, the d e t a i l e d equations of the model are given. Endo- genous variables are represented by upper case l e t t e r s . Exogenous parameters are represented by lower case l e t t e r s or by upper case l e t t e r s with a bar above. There are s i x time periods — three five-year periods, three 10-year periods, a l l l a b e l l e d by the l a s t year. The periods are Tn{l980, 1985, 1990, 2000, 2010, 2020J . In l i s t i n g the model contraints, the time index, t, appears i n the i n t e r - p e r i o d constraints, and i s otherwise suppressed, for the sake of c l a r i t y . Furthermore, because of the complications introduced into i n t e r - p e r i o d constraints by the unequal lengths of the time periods, the constraints are f i r s t presented as i f the time periods are of equal length, i . e . T 1 = {1980, 1985, 1990, 1995, 2005, 2000, 2010, 2015, 2020 } . In a l a t e r section, a l t e r a t i o n s to i n t e r - p e r i o d constraints due to time period aggregation are discussed. The forms of i n t r a - p e r i o d constraints do not change when time periods are aggregated. The names of variables generally obey the following pattern: the f i r s t l e t t e r indicates the region (W f o r west — B.C., the p r a i r i e provinces, and northern t e r r i t o r i e s — E f o r east); the second l e t t e r i ndicates the type of energy commodity or the end-use sector (e.g., 0 for o i l , G f o r gas, T f o r transportation, e t c . ) ; the l e t t e r X i n the t h i r d place indicates a flow and capacity of an energy commodity; and the l e t t e r D i n the t h i r d place indicates an addition to capacity. In addition, there are numerals appearing i n some vari a b l e names, and i n the computer implementation, there are 2 numerals pre- f i x i n g the variable name to indicate the time period. 235 In a d d i t i o n to the parameters l i s t e d i n the following sections, there are exogenously-assigned parameter values f o r pre-1980-period v a r i a b l e s which occur i n i n t e r - p e r i o d constraints. Constraint names obey the following pattern: (1) (2) (3) (4) (5) (6) (7) (1_) (2) - two numerals indi c a t e the time period. (_3) - the l e t t e r s W, E, or N stand for west, east, or non-regional. C4J C5J - two l e t t e r s i n d i c a t e constraint type: PR - production decline ( o i l or gas) CP - capacity expansion and replacement SB - supply-demand balance SE - share eguation SL - share, lower bound SU - share, upper bound • RL - reserves l i m i t M - miscellaneous (.7) - t h i s may be a l e t t e r , numeral, or blank. The constraint names appear to the l e f t of the constraints i n t h i s appendix (without the f i r s t two numerals, i n d i c a t i n g time p e r i o d ) . Constraints which are upper or lower l i m i t s on sing l e v a r i a b l e s are not given names. The l e t t e r s "DFC" stand f o r the Domestic, Farm and Commercial end- use sector. B . l . Coal a) L i s t of Variables western production, low cost western production, high cost coal f o r l i q u e f a c t i o n i n west coal f o r g a s i f i c a t i o n i n west coal f o r e l e c t r i c i t y production i n west coal for i n d u s t r i a l use i n 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 e l e c t r i c i t y production i n east coal for i n d u s t r i a l use i n east capacity increases of low and high cost eastern production coal imports L i s t of Parameters mciw, mcie = cwcl,cwc2 = cecl,cec2 = pcex = pcim = c c t r = WCRi, (i=l,2) = ECRi, (i=l,2) = WCE bwc, bee ECXl d i s t r i b u t i o n margin f o r coal to i n d u s t r i a l sector, l i q u e f a c t i o n and g a s i f i c a t i o n costs of corresponding western coal production costs of corresponding eastern coal production p r i c e of coal exports p r i c e of coal imports cost of transporting coal from west to east reserves of corresponding western production type remaining a f t e r 1975. reserves of corresponding eastern production type remaining a f t e r 1975 maximum capacity of west-to east coal transportation system f r a c t i o n of coal supply remaining a f t e r deduction of coal use by energy supply i n d u s t r i e s , i n the west and east, r e s p e c t i v e l y upper l i m i t 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 ( i i ) Reserve Limits WCRLi: E WCXi(t) <_ WCRi, i = 1,2 t£T' ECRLi: E ECXi(t) . <_ ECRi, i = 1,2 t£T" ( i i i ) 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: b e e ( I ECXi + ECIM + WCE) = i=l Bounds 4 I i=3 ECXi WCE < WCE — west-to-east coal transport l i m i t s ECXl <_ ECXl — l i m i t on r a t e of production of eastern coal O i l L i s t of Variables ("LHF" stands f o r " l i q u i d 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 L i s t of Parameters mltw,mlrw,mldw,"\ = mliw, mite,mire, mlde,mlie J cwoi,(i=l,,.., 6) = poex = cotr = WORi,(i=l,2,.. .5) = conventional production, low cost, west conventional production, high cost, west northwest f r o n t i e r production, low cost northwest f r o n t i e r production, high cost tar sands production western methanol production, from biomass capacity expansions of above o i l exports (to USA) western o i l transported to eastern region o i l to western r e f i n e r y gate eastern production, low cost (mostly southeast offshore) eastern production, high cost (mostly northeast offshore) eastern methanol production, from biomass capacity expansions of above o i l imports o i l to eastern r e f i n e r y gate LHF for e l e c t r i c i t y production i n west & east LHF f o r domestic, farm and commercial use i n west & east LHF for i n d u s t r i a l use i n west & east LHF for transportation use i n west & east capacity expansion of coal l i q u e f a c t i o n , i n west o i l d i s t r i b u t i o n & r e f i n i n g margins to Transporta- t i o n , Road Transportation, DFC and to I n d u s t r i a l sectors, r e s p e c t i v e l y , west and east costs of corresponding western o i l production p r i c e of o i l exports cost of transporting o i l from west to east reserves of corresponding western production type remaining a f t e r 1975. 238 ao (s) opipe WOEX foim ceoi, (i=l,2^3) poim EORi, (i=l,2) c l c bwl,bel a c l WLDC W0X6, E0X3 W0X5 E0X1, E0X2 c) Constraints (i) O i l 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,... ( i i ) 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 o i l production decline curve = f r a c t i o n of capacity established s years ago which i s s t i l l producing now = f r a c t i o n of eastern crude market accessible to western o i l production = upper l i m i t on o i l exports = maximum f r a c t i o n of Canadian crude o i l market served by net imports = costs of corresponding eastern production = p r i c e of o i l imports = reserves of corresponding eastern production type remaining a f t e r 1975 = cost per unit output of coal l i q u e f a c t i o n , not includ i n g cost of the coal = f r a c t i o n of o i l supply remaining a f t e r deduction of o i l use by energy supply i n d u s t r i e s , west and east = o i l output per unit of coal input to coal l i q u e f a c t i o n = upper l i m i t on capacity expansion of western coal l i q u e f a c t i o n = upper l i m i t s on production of methanol from biomass, i n west and east = exogenously f i x e d t a r sands production = upper l i m i t s on eastern o i l production 239 ( i i i ) 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 s e l f - s u f f i c i e n c y for se c u r i t y of o i l supply NOMEM: WOE <_ opipe • EOG — a l l of eastern market i s acc e s s i b l e to western o i l when opipe = 1 (vi) Bounds WLDC < WLDC W0X6 < W0X6 E0X3 < E0X3 WOEX < WOEX W0X5 = WOX5 EOXI <_ EOXI E0X2 < E0X2 Limits on introduction of coal l i q u e f a c t i o n Limits on introduction of methanol from biomass, i n west Limits on introduction of methanol from biomass, i n east Export l i m i t s F i x i n g of tar sands production to 2000 Limits on eastern o i l production 240 B.3. Gas — Natural and Synthetic a) L i s t of Variables WGX1 = western natural gas production, conventional areas, low cost WGX2 = western natural gas production, conventional areas, high cost WGX3 = northwest f r o n t i e r natural gas production, low cost WGX4 = northwest f r o n t i e r natural gas production, high cost WGX5 = synthetic gas (from biomass) production, i n west WGDi, (i=l,2,...,5) = capacity expansions of above WGD6 = capacity expansion of syn. gas production from coal,..west WGX7 = gas f o r e l e c t r i c i t y production i n west WGX8 = gas f o r domestic, farm and commercial use i n west WGX9 = gas f o r i n d u s t r i a l use i n 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, i n east EGDi, (i=l,2,3) = capacity expansions of above EGX4 = gas f o r e l e c t r i c i t y production i n east EGX5 = gas f o r domestic, farm and commercial use i n east EGX6 = gas for i n d u s t r i a l use i n east b) L i s t 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 = p r i c e of gas exports = cost per un i t output of coal g a s i f i c a t i o n , not including cost of the coal = cost of transporting gas from west to east = reserves of corresponding western production type remaining a f t e r 1975 = gas output per unit of coal input to g a s i f i c a t i o n = f r a c t i o n of gas supply remaining a f t e r deduction of gas use by energy supply i n d u s t r i e s , i n the west and east, r e s p e c t i v e l y = upper l i m i t on production of synthetic gas from biomass i n west = upper l i m i t on capacity expansion of western coal gas'n = maximum capacity of west-to-east gas p i p e l i n e = costs of corresponding eastern gas sources = parameters f o r natural gas production decline curve = f r a c t i o n of capacity established s years ago which i s s t i l l producing now = upper l i m i t on gas exports = reserves of corresponding eastern production type remaining a f t e r 1975 = upper l i m i t on production of synthetic gas from biomass i n east = gas d i s t r i b u t i o n margins, to DFC and to I n d u s t r i a l sectors, r espectively, west and east = upper l i m i t s 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,.. . ( i i ) 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) ( i i i ) 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 l i m i t WGE <_ WGE — capacity of west-to-east p i p e l i n e WGD6 <_ WGD6 — l i m i t on capacity expansion of coal g a s i f i c a t i o n WGX5 _£ WGX5 — l i m i t on production of gas from biomass, west EGX3 <_ EGX3 — l i m i t on production of gas from biomass, east EGXI <_ EGXI ) — l i m i t s on production from eastern sources EGX2 < EGX2 ' 242 B.4. E l e c t r i c i t y a) L i s t of Variables WEX4,EEX4 = e l e c t r i c i t y from nuclear, west and east WEX5,EEX5 = h y d r o e l e c t r i c i t y production, west and east WEX6,EEX6 = e l e c t r i c i t y from biomass, wind, t i d a l , etc., west & east WEDi,EEDi, (i=4,5,6) = capacity expansions of above WED1,EED1 = capacity expansion of e l e c t r i c i t y from coal, west & east WED2,EED2 = capacity expansion of e l e c t r i c i t y from o i l , west & east WED3,EED3 = capacity expansion of e l e c t r i c i t y from gas, west & east WEX9,EEX9 = e l e c t r i c i t y f o r i n d u s t r i a l use, west and east WEX10,EEX10 = e l e c t r i c i t y f o r transportation ( e l e c t r i c c a r ) , west & east WEX11,EEX11 = e l e c t r i c i t y f o r DFC use, west and east WEEX, EEEX = e l e c t r i c i t y exports from west and east b) L i s t of Parameters ce4 = cost of e l e c t r i c i t y from nuclear ce5 = cost of h y d r o e l e c t r i c i t y ce6 = cost of e l e c t r i c i t y from biomass, etc. peex = p r i c e of e l e c t r i c i t y exports cec = cost of. e l e c t r i c i t y from coal, '.excluding coal cost c e l = cost of e l e c t r i c i t y from o i l , excluding o i l cost ceg = cost of e l e c t r i c i t y from gas, excluding gas cost bwe, bee = f r a c t i o n of e l e c t r i c i t y supply remaining a f t e r deduction of e l e c t r i c i t y use by energy supply i n d u s t r i e s , west and east ace = e l e c t r i c i t y output per un i t of coal input ale = e l e c t r i c i t y output per un i t of o i l input age = e l e c t r i c i t y output per un i t of gas input medw,meiw,j= e l e c t r i c i t y d i s t r i b u t i o n margins, to DFC and to I n d u s t r i a l mede,meie sectors, r e s p e c t i v e l y , west and east met = e l e c t r i c i t y road tax f o r transportation WEX5,EEX5 = maximum hydro e l e c t r i c c a p acities i n west and east WED4,EED4 = maximum:rate of nuclear e l e c t r i c capacity expansion i n west and east hdw, hde = maximum f r a c t i o n s of t o t a l e l e c t r i c capacity expansion which can be f i l l e d by hydro, i n 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 ( i i ) 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 ( i i i ) Other Constraints 6 WEMH: WED5 «• hdw(ace-WEDl + ale-WED2 + age-WED3 + E WEDi) i=4 6 EEMH: EED5 £ hde s(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 l i m i t s EEEX 244 B.5. ' Transportation End Use Sectors a) L i s t of Variables WLA, ELA = o i l for automobiles, west and east WTD1, ETD1 = capacity additions for e l e c t r i c autos, west and east WTD2, ETD2 = capacity additions f o r conventional autos, west and east WRTR, ERTR = t o t a l output energy, road transportation, west and east WOTR, EOTR = output energy, other transportation, west and east b) L i s t of Parameters aea = output energy per u n i t e l e c t r i c i t y input, for e l e c t r i c autos a l a = output energy per u n i t o i l input, for conventional autos alo = output energy per un i t o i l input, f o r other transportation e l = maximum f r a c t i o n of new autos that can be e l e c t r i c cea = d i f f e r e n t i a l cost of e l e c t r i c 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) ( i i ) 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 ( i i i ) E l e c t r i c Auto Constraints WTMEA: aea • WTDl « e l • (aea • WTDl + a l a • WTD2) ETMEA: aea • ETD1 ^ e l • (aea . ETD1 + a l a • ETD2) 245 B.6. Industrial" End 'Use - Sector WIND, EIND = Total output energy, i n d u s t r i a l sector, i n west and east, r e s p e c t i v e l y b) L i s t of Parameters agi = output energy per u n i t gas input, i n industry a l i = output energy per un i t o i l input, i n industry a c i = output energy per u n i t coal input, i n industry aei = output energy per un i t e l e c t r i c i t y input, i n industry lwg, l e g = lower l i m i t on f r a c t i o n of t o t a l output energy from gas, west and east lw l , l e i = lower l i m i t on f r a c t i o n of t o t a l output energy from o i l , west and east lwc, l e c = lower l i m i t on f r a c t i o n of t o t a l output energy from coal, west and east lwe, lee = lower l i m i t on f r a c t i o n of t o t a l output energy from e l e c t r i c i t y , west and east uwg, ueg = upper l i m i t on f r a c t i o n of t o t a l output energy from gas, west and east uwl, uel = upper l i m i t on f r a c t i o n of t o t a l output energy from o i l , west and east uwc, uec = upper l i m i t on f r a c t i o n of t o t a l output energy from coal west and east uwe, uee = upper l i m i t on f r a c t i o n of t o t a l output energy from e l e c t r i c i t y , west and east c) Constraints (i) Supply-Demand Balance WISB: agi • WGX9 + a l i • WLX3 + a c i • WCX6 + aei EISB: agi • EGX6 + a l i • ELX3 + a c i • 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< a c i • WCX6 ̂  uwc " WIND WISLE, WISUE : lwe • WIND<aei • WEX9i£ uwe • WIND EISLG, EISUG : l eg • EINDSagi • EGX6 ueg • EIND EISLL, EISUL : l e i • EINDSjali ' ELX3'£ uel • EIND EISLC, EISUC : l e c • EIND€ a c i • ECX4 £ uec • EIND EISLE, EISUE: lee•• EINDi a e i • EEX9 S uee • EIND 246 B.7. Domestic, Farm and Commercial (DFC) End Use Sector a) L i s t 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 = e l e c t r i c i t y f o r DFC e l e c t r i c resistance heating, west & east e l e c t r i c i t y f o r DFC heat pump, west and east e l e c t r i c i t y f o r DFC non-heating uses, west and east capacity expansions of DFC gas heating, west & east capacity expansions of DFC o i l heating, west & east capacity expansions of DFC e l e c t r i c resistance heating, west and east capacity expansions of DFC e l e c t r i c heat pump, west & east output energy of d i s t r i c t heating by cogeneration, west & east output energy of solar heating, west and east capacity expansions of WDX5, EDX5 capacity expansions of WDX6, EDX6 t o t a l output energy, DFC sector, west and east b) L i s t of Parameters chp, crh,| = non-fuel costs of heating by heat pump, e l e c t r i c resistance, coh, cgh o i l , gas, resp e c t i v e l y chs = cost of solar heat cdh = cost of d i s t r i c t heating by cogeneration agh = output energy per unit gas input, for DFC heating alh = output energy per un i t o i l input, f o r DFC heating aeh = output energy per unit e l e c t r i c i t y input, for DFC heat pump aer = output energy per unit e l e c t r i c i t y input, for DFC e l e c t r i c resistance heating aeo = output energy per unit e l e c t r i c i t y input, f o r DFC a >>. non-heating uses gwh, geh = f r a c t i o n of t o t a l DFC output energy for heating, west a .'.east hpw, hpe = maximum f r a c t i o n of heating due to heat pump, west & east sw, se = maximum f r a c t i o n of heating due to solar, west and east gw, ge = maximum f r a c t i o n of heating due to cogeneration, west & east fc = f r a c t i o n of new c o a l - e l e c t r i c capacity a v a i l a b l e f o r cogeneration fn = f r a c t i o n of new n u c l e a r - e l e c t r i c capacity a v a i l a b l e f o r 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 ( i i i ) 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) D i s t r i c t 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) L i s t of Variables EC " energy cost b) L i s t of Parameters d = s o c i a l discount rate ed, e i , j = p r i c e e l a s t i c i t i e s of demand for output energy i n the er, eo sectors DFC, industry, road transportation and other transportation, r e s p e c t i v e l y dwdjdwi,-^ = parameters derived from demand equation parameters for dwr,dwo, / the sectors DFC, industry, road transportation and ded,dei, j other transportation, i n west and east der,deo J c) Objective Function (Maximand) t-1975 (1-1/ed) (1-1/ed) OBJECTIV: E [l/(l+d)] • (dwd -WDFĈ  + ded -EDFC m . t t t t t £ T (1-1/ei) (1-1/ei) (1-1/er) + dwi -WIND̂  + 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 - EC t) 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, i t was assumed that there were nine 5-year time periods. To save computation time, and since there i s greater uncertainty associated with l a t e r time periods, l a t e r time periods have been aggregated i n the following way: three five-year periods / -followed by three 10-year periods.- The time index, t, . which marks the l a s t year i n each period, takes on values i n the set T = {l980,1985,1990,2000,2010,2020}', or a l t e r n a t i v e l y , {5,10,15,25,35,45} f o r b r e v i t y i n the computer coding. The forms of the i n t r a p e r i o d constraints described e a r l i e r do not change a f t e r aggregation. This-section i s concerned"with changes to the i n t e r - p e r i o d 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 b r e v i t y , l a b e l the time periods t=5,10,15,25,35, or 45. The method followed i s to consider what multiple of a capacity addition continues to produce i n l a t e r periods of d i f f e r i n g lengths. In the following, a bar on top of a variable indicates that the value of the variable i s a datum, f i x e d at i t s 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) ( i i ) 10-Year Lifetime (Automobiles) X(t) = D(t) + D(t-5) , f o r t=5,10,15 X(25) = D(25) + D(15) X(t) = D(t) , for t=35,45. ( i i i ) 15-Year Lifetime (Most Heating i n 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) , f o r t=35,45. bj_ Changes i n Production Decline Curves Cl) Crude O i l Usilng the data assumptions presented i n Appendix C, Section 2 - i . e . new capacity l a s t s 10 years, followed by a 15-year decline at 10% per year — t h e following may be derived X(t) = D(t) + D(t-S) + (.59) • D(t-10) , + (.35) • D(t-15) + (.21) • D(t-20) , f o r 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 ( i i ) Natural Gas Using the data assumptions presented i n Appendix C, Section 3 — i . e . new capacity l a s t s 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 f o r end e f f e c t s c orrection -- see next s e c t i o n ) . c) Changes to Reserves Limits Constraints There i s no change i n these constraints when- time periods are aggregated. B.10. Corrections f o r End E f f e c t s End e f f e c t s due to the f i n i t e time horizon are minimized by a pro- cedure based on the dual equilibrium method of Grinold (1980). He assumes that p r i c e s are constant a f t e r the time horizon i n h i s method for LP problems — i . e . the dual v a r i a b l e s are constant a f t e r the time horizon, i f expressed i n undiscounted d o l l a r s . This method has been extended s l i g h t l y to the NLP problem here by assuming that the output energy p r i c e s , derived from the gradient of the objective function, are also constant (in undiscounted d o l l a r s ) a f t e r the time horizon. This ex- tension a f f e c t s only the nonlinear variables i n the objective function. Presented below are the a l t e r a t i o n s to the l i n e a r constraints and the l i n e a r part of the objective function — that i s , of Grinold's dual equilibrium method applied to the LP problem associated with the NLP problem, obtained by f i x i n g the nonlinear variables exogenously. Next the a l t e r a t i o n s to the nonlinear p a r t of the objective function are shown. The procedure involves the addition of an extra time period, with a l t e r e d constraints. The vector of a l l exhaustible resource production l e v e l s i n period t i s represented by y , the vector of resource l i m i t s by R, and a l l other variables by X^. Period "0" below represents periods 5, 10 and 15 together. The matrix H defines the impact of x i n period t . The matrix represents the impact of X^ on period (t+10); i s the impact of X on period (t+20). Below, A and B are matrices i n v o l v i n g r e l a t i o n s among va r i a b l e s i n the same time period. I f d i s the s o c i a l discount rate, l e t a = l / ( l + d ) . The r i g h t hand side vector i s b = (h^,b^,h^^, . ..) . Following Grinold, l e t -cS^"" " 1 t-55 b 5 5 ( a ) = t=fe65,7.. \ , X__(a) = a t _ 5 5 X . 55 t=55,65,... t at-55 - Y_ c(a) = t=55,65,... Y , and b o — K ' • •>• t K l ( a ) = K l + a " V Grinold shows that the (LP) problem of minimizing the discounted cost of meeting the s p e c i f i e d energy demands (the nonlinear variables here) t with the dual equilibrium method i s : . . . 5 ^ t-1975 55, minimize a EC^ + a • ^EC^,. (a) subject to: A X + B :Y = b 0 0 0 0 0 H X + AX + BY = b 25 o 25 25 25 H_CX + K.XV_ + A I , + BY = b 35 o 1 25 35 35 35 H4 5 Xo + K2 X25 + K l X 3 5 + A X 4 5 + B Y 4 5 = b , 45 K2 X35 + K l ( a ) X 4 5 + ( A + K ! ( a ) ) x 5 5 ( a ) + " ' B Y 5 5 ( a ) = b 5 5 < a ) Y 0 + Y25 + Y35 + Y45 + Y 5 5 ( a ) ^ R " The. procedure involves the addition of one .variable to the objective function, EC__, and an extra set of constraints almost 55 i d e n t i c a l i n form to the constraints of period 45, but with some d i f f e r e n t c o e f f i c i e n t s and a r i g h t hand side which depend on the discount rate. In the f u l l NLP problem, these changes to the constraints and the l i n e a r part of the objective function are made, and extra nonlinear terms are added, r e l a t e d to the consumers' surplus i n the new, a d d i t i o n a l period 55. Since i t i s assumed that the' output energy p r i c e s (in undiscounted d o l l a r s ) are constant a f t e r period 45, i t follows that the output energy demands w i l l increase from t h e i r period 45 l e v e l s at rates influenced only by the exogenous determinants of demand such as population, r e a l domestic product, etc. Using the notation of chapter 4, f o r b r e v i t y , the objective function f o r the f u l l i n f i n i t e 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 i n sector i , i n period t, r /1 e i = the p r i c e e l a s t i c i t y of demand i n sector i , t = 5,10,15,25,35,... , and E. ^ = A • P? 6* I, t l , t I, t where P. = the p r i c e of output energy i n sector i and period t, and I , t A. = the product of the exogenous factors determining I , t demand i n sector i and period t . The assumption of constant p r i c e s i s -:. P. . = P. r r , for t > 55. i , t i,55 Assuming that the exogenous variables determining demand each grow at c e r t a i n rates per year a f t e r period 55 ( i t i s assumed that these rates are the rates of growth between t=45 and t=55 — see Appendix C for these r a t e s ) , i t follows that for some g i (i=l,...,8) which can e a s i l y be c a l c u l a t e d from the rates of growth and the various e l a s t i c i t i e s with respect to income, etc., A i , t = A i , 5 5 * ^ 1 + ^ t ~ 5 5 • a n d E i , t = E i , 5 5 • ^ t - 5 5 - Therefore, the objective function, under the constant p r i c e and the growth assumptions, i s 45 ^ 8 _, 1/ei 1-1/ei maximize a f c . ( £ ( e i ^ — ) • A E . - EC ) t=5 x=l ei-1 i , t i , t t + aZ • • A. (l + g i ) * • E - EC.) t-55' 1 = 1 ei-1 i,55 i , t t F i n a l l y , the i n f i n i t e sum can be collapsed into a f i n i t e sum of nine terms i n v o l v i n g the nonlinear variables E^ (provided a * (1+gi) ^ 1), and EC p r(a) (defined above), namely 55 8 2 a 5 5 - ( l / ( l - a • (1+gi))).-' {SL-) • A V ^ • E 1 " ^ ei-1 1,55 i,55 - a 5 5 • E C 5 5 ( a ) . Viewed from another perspective, t h i s method corrects f o r end e f f e c t s by adding another period representing the time beyond the planni horizon. The extra constraints' c o e f f i c i e n t s , bounds and r i g h t hand sides are given values which tend to make the variables larger than they-would be i f the extra period were an ordinary one. The extra period's consumers' surplus i s also weighted more heavily than i f i t were an ordinary period, o f f s e t t i n g the larger energy cost (EC) asso- ci a t e d with the larger values of the other v a r i a b l e s . The net e f f e c t i s to t r e a t the post-horizon period as one (very long) period, with appropriate weights to account for the length of the i n f i n i t e period, with discounting applied. 257 Appendix C. Data for the Base Case. The following abbreviations are used f o r 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 I n s t i t u t e , SC S t a t i s t i c s Canada. C.1;.0 Data for the. Coal Sector Throughout t h i s section, the thermal contents of various grades of coal are assumed to be those reported by S t a t i s t i c s Canada (cat. no. 57-207), i . e . , i n units of 10 6 BTU/short ton: Anthracite 25.4 Imported Bituminous 25.8 Canadian Bituminous 25.2 Sub-bituminous 17.0 L i g n i t e 13.2 C . l ~ l . .Costs and Remaining" Supplies I t i s assumed that the current cost of producing coal (the "low cost" i n the model) i s the reported at-mine p r i c e i n 1974 — i . e . before the rapid r i s e i n coal p r i c e s i n 1975., to avoid, i n c l u s i o n of "windfall p r o f i t s " or v a s t l y increased r o y a l t i e s . For bituminous coal i n the west, t h i s was about $.60/10^ (1975$), according to figures derived from EMR (1977f) and S t a t i s t i c s Canada ( cat. no. 26-206). However, the at-mine p r i c e of Alberta sub-bituminous coal and Saskatchewan l i g n i t e were about $.20/10^ BTU, using figures derived from the same sources. Since coal i s treated as one com- modity i n the model, we take the lower grade cost as the cost of coal at the low p r i c e - i . e . cwcl = .02. A d i s t r i b u t i o n margin of $.80/106BTU, i . e . mciw = .08, i s added to coal used i n western industry ( i n c l u d i n g that for l i q u e f a c t i o n or g a s i f i c a t i o n ) , to account f o r the t o t a l costs of coal to western industry i n 1970, $ 1.00/106BTU i n 1975 $, derived from S t a t i s t i c s Canada (cat. no. 57-506). The p r i c e of exported coal i n 1975 at the mine, using EMR (1977f) f i g u r e s , was about $1.43/106BTU, while, the production cost for t h i s bituminous coal was about $ I60:/10^BTU , f o r an economic rent of about $.83/106BTU. The l o g i c of the model requires that the export p r i c e equal production cost plus economic rent. Since c"> cwcl = .02 and rent (in 1975))= .083, the 1975 export p r i c e i s taken to be -.103. This p r i c e i s escalated at the rate of 2!1/2 % per year u n t i l the year 2000.(The i n t e r n a t i o n a l o i l p r i c e i s assumed to increase at 4% per year u n t i l 2000i The r e s u l t i s : Period 05 10 15 25,35 pcex .117 .132 .149 .191 The s i t u a t i o n i n the east i s simpler. The coal i s a l l bituminous, as are imports, and there are v i r t u a l l y no exports. The import p r i c e i n 1975 was $1.37/10 BTU, using EMR (1977f) f i g u r e s , and i s assumed to increase i n r e a l terms at 2 1/2 % per year, the same rate as export p r i c e s , u n t i l 2000. The result, i n model units, i s : Period 05 10 15 25 pcim .155 .175 .198 .254 The eastern cost of (bituminous) coal production i s determined i n Nova Scotia, where the l a r g e s t production i s . The 1974 at-mine p r i c e was $.80/106BTU, using EMR (1977f) f i g u r e s . Therefore, c e c i = .08 . The 1975 coal costs to e l e c t r i c u t i l i t i e s reported by E l l i s o n (1978. p.71), i n the cases where the coal used i s mined l o c a l l y , are reasonably close to the above values for cwcl and c e c i . The d i s t r i b u t i o n 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 S t a t i s t i c s Canada (cat. no. 57-506). The r e s u l t i s , mcie = .04 . The cost of transporting coal to the east from the west i s a r r i v e d at by subtracting the production cost from the p r i c e paid by Ontario Hydro for western c o a l . According to E l l i s o n ( 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 l i g n i t e from Saskatchewan i n 1975:,'. at costs of 135.8<V10 6BTU and 55.2C/106BTU res p e c t i v e l y . C a l c u l a t i n g an average weighted by the t o t a l BTU contents of the two types gives a p r i c e of 122.8<yi06BTU paid by Ontario Hydro. Subtracting 20C/10 6 BTU production cost leaves an average transport margin of 102.8C/106 BTU — i . e . c c t r = 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 u n i t s ) , 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 t o t a l amount, and the Latour-Christmas estimate mentioned i n HMA (1976, p.241), with the same proportional s p l i t of reserves'between cost l e v e l s . The proportional s p l i t of the reserves between east and west i s the same as that i n HMA (1976, p.240) for coal p o t e n t i a l reserves, by region ( i . e . west, 98.66%, east, 1.34%). F i n a l l y , the lower costs i n each region are those established above, and the higher cost l e v e l s are double the lower. The r e s u l t s are (in model u n i t s ) : cwcl = .02 WCR1 =1,587 , cwc2 = .04 WCR2 = 106 c e c i = .08 ECR1 = 22 cec2 = .16 ECR2 = 1.4 C.1.2 Energy Supply Industry Use Let bwc,bec = f r a c t i o n s of western and eastern coal supplies not used by western and eastern energy supply i n d u s t r i e s . These parameters are equal i n a l l periods to t h e i r 1971-1975 values of .9996 (west) and .9994 (east), using data from S t a t i s t i c s Canada (cat. no. 57-207). 261 C.1.3 Miscellaneous Limits In an EMR document (1976d, pp.96-97), i t i s stated that the coal 6 terminal at Thunder Bay i s to open i n 1979 at a capacity of 3.5 x 10 6 6 tons/year, of which 25 x 10 tons are bituminous co a l , and 1 x 10 tons 6 are l i g n i t e . The capacity can be expanded quickly to 6 x 10 tons, and eventually to 9 x 10 6 tons/year. Using t h i s information, and adding the 1971-75 amount transported through e x i s t i n g f a c i l i t i e s , expressed i n model units and 5-year c a p a c i t i e s puts upper l i m i t s oh west-to-east coal transportation for the f i r s t 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 u n r e a l i s t i c a l l y quickly. Therefore, the following upper l i m i t s have been placed on ECXl, corresponding to a doubling i n production every 5 years (about 15% increase per year): Period 05 10 15 ECXl .506 1.012 2.024 Because of the large s i z e of the coal reserves, and because the i n t e r n a t i o n a l p r i c e of coal i s so much higher than i t s cost of production, the model tends to export coal at an u n r e a l i s t i c a l l y high rate. There- fore, upper l i m i t s are placed on coal exports i n a l l periods, allowing exports to increase at about 5% per year (assuming a l e v e l l i n g - o f f of the rapid growth i n 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 O i l Sector C.2.1 Primary Costs and Remaining Supplies U n t i l a study on long-run supply curves for o i l and natural gas i s completed by EMR, the cost and supply data must be based on various sources. The cost of the "low cost" conventional o i l (cwol) of western Canada i s taken to be the wellhead p r i c e before the rapid p r i c e r i s e a f t e r 1973, based on data presented by the CPA (1977) - i . e . cwol = .4, i n model units, or $4/bbl. Based on estimates by EMR (1977c, p.31) of the costs of Lloydminster heavy o i l , using an 8% r a t e of return over a 15-year production time span, the higher cost of western "conventional" o i l i s taken to be cwo2 = .8, or $8/bbl. The t o t a l remaining reserves (after 1975) of conventional western 9 o i l , a t both cost l e v e l s , are taken to be 12 x 10 b b l , which i s the t o t a l of remaining reserves at the 100% p r o b a b i l i t y , plus undiscovered resources at the 40% p r o b a b i l i t y l e v e l reported by EMR (1977b) for western Canada. The amount of these reserves a l l o c a t e d to the lower cost l e v e l i s taken to be s u f f i c i e n t to allow e x i s t i n g conventional western o i l producing capacity to run the course of the o i l production decline curve ( i . e . to ensure model f e a s i b i l i t y ) . The a l l o c a t i o n WOR1 = 6.0, W0R2 = 6.0 works w e l l . The t o t a l remaining reserves of northern f r o n t i e r o i l (not i n - cluding northeast offshore-Labrador o i l , which i s a l l o c a t e d to the east i n the model) are taken to be 7.7 x 10̂ " b b l , based on the 40% p r o b a b i l i t y l e v e l i n EMR (1977b). The low and high costs f o r these reserves ( i . e . including transportation to southern Alberta) are based on various sources, namely an early d r a f t of the EMR (1977d) study on long run supply curves, and figures i n the report by HMA (1976). The costs chosen are $10/bbl and $14/bbl, or i n model units cwo3 = 1.0 cwo4 = 1.4 Based on the general shape of the tent a t i v e long-run supply curves i n EMR (1977d), the following a l l o c a t i o n of reserves between the two cost l e v e l s has been made: W0R3 = 4.4 W0R4 =3.3 Using cost estimates on t a r sands mining, by EMR (1977c, p. 31), and a r a t e of return on c a p i t a l of 8% over 30 years, the cost of syncrude i s set at $12/bbl, or i n model un i t s , cwo 5 = 1.2. (This i s the 1975 p r i c e of crude o i l 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 i n EMR (1978c), or i n model un i t s , W0R5 = 200.0. The "low cost" eastern o i l i s taken to be represented mostly by southeast offshore o i l , and the "high cost" by northeast offshore o i l . Based on the 40% p r o b a b i l i t y l e v e l of p o t e n t i a l resources i n 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 M i l l a n (1980) of development and operating costs f o r the Hibernia discovery a t an 8% rate 264 of return, the EMR d r a f t (1977d), and HMA (1976) — the landed costs of these are set a t $7/bbl and $10/bbl, r e s p e c t i v e l y , i . e . ceol = 0.7 ceo2 = 1.0. Once again, l i m i t s are placed on the rate of expansion of these sources i n the model (see the l a s t section, on l i m i t s ) . C.2.2 Import and Export Prices The p r i c e s of imports and exports are taken to be the same except for the o i l import subsidy i n the f i r s t three periods. The 1975 p r i c e of imported o i l , at North America, of $12/bbl, i s increased at the rate of 4% per year u n t i l the year 2000. Recall that a l l values are expressed i n 1975$ i n the model, and that the 4% per year f i g u r e i s therefore net of i n f l a t i o n . The f i g u r e of 4% has been chosen to r e f l e c t expectations of continuing rapid increases i n the p r i c e of i n t e r - national o i l , and because 4% per year i s a rate which would be i n the best i n t e r e s t s of consuming and producing countries, according to Manne (1978). With a subsidized eastern domestic p r i c e of about $10.80/bbl (calculated from H e l l i w e l l (1979)) i n 1978, the mid-year of the f i r s t period, and assuming the subsidy reaches zero by the fourth period, the p r i c e s e r i e s are: Period 0.5 10 15 25,35,45. . poex 1.46 1.78 2.16 3.20 poim 1.08 1.48 1.93 3.20 C.2.3 O i l Production Decline Curves The standard production t i m e - p r o f i l e presented by EMR (1973, p.80) i s a two-year buildup to a peak l a s t i n g seven years, followed by a decline at the rate of 15% per year. This r a t e of decline appears to be 265 too rapid when compared to the NEB (1978) pr o j e c t i o n of p r o d u c i b i l i t y from established l i g h t and heavy crude o i l reserves. The l a t t e r suggests a decline rate of 10% per year, which i s adopted i n t h i s model. In de r i v i n g the parameters ao(s), i t i s assumed as an approximation that new capacity established i n one year l a s t s at the same l e v e l for ten years, then declines at 10% per year f o r the next 15 years. See Appendix B, section 9, "Time Period Aggregation" f o r the d e t a i l e d r e s u l t s , taking into account the varying lengths of the time periods. C. 2.4. Coal Liquefaction 9 15 Let a c l = 10 bbl of l i q u e f i e d product per 10 BTU of coal input; and c l c = cost of l i q u e f a c t i o n of coa l , not including coal feed cost, i n un i t s of 10 1 2$ per 10 9 b b l . Using estimates by the SRI (1976, V o l . I I , p.IV-7), and a r e a l r a t e of return on c a p i t a l of 8% per annum, the parameters are set a t a c l = 0.1072 and c l c = .79, i n the model's u n i t s . The conversion e f f i c i e n c y corresponding to the above a c l i s 0.622. The e a r l i e s t date of introduction of coal l i q u e f a c t i o n , according to SRI (1976), i s 1987. I t i s assumed i n the model, therefore, that coal l i q u e f a c t i o n can be introduced a f t e r 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 f i g u r e s from Middleton Associates (1976, p. 316) $30/bbl i s the approximate cost. Since i n the model methanol from biomass enters the o i l stream, which i s subject to r e f i n i n g charges, i t i s necessary to subtract a r e f i n i n g charge of $4.20/bbl (from EMR (1977a, p. 53)). from the cost of methanol, a f i n i s h e d product. The r e s u l t , i n model 12 9 units of 10 $ per 10 bbl, i s cwo6 - ceo3 = 2.5. I t i s assumed that t h i s technology can be introduced a f t e r 1980, i . e . W0X6 = E0X3 =0.0 for t = 05 . C.2.6 West-to-East O i l Transportation Let cotr = cost of transporting o i l from west to east. An EMR report (1978a, p.50) gives $.60/bbl f o r t h i s o i l trans- portation margin i n 1977, from Edmonton to Port C r e d i t . In 1975$ and model un i t s , t h i s i s cotr = .05. Let opipe = f r a c t i o n of eastern crude o i l market ac c e s s i b l e to western c rud e supply. According to estimates i n Oilweek (Feb. 12, 1979, p. 31, table e n t i t l e d "Canadian Petroleum Consumption") the f r a c t i o n of eastern crude o i l supplied from western sources was 0.5355 i n 1978 ( i . e . a f t e r the ex- tension of the p i p e l i n e to Montreal). In the model, the following grad- ual approach towards f u l l a c c e s s i b i l i t y of western o i l to eastern markets i s assumed: period, t = 0.5 10 15,25... opipe .54 .77 1.0 C.2.7 D i s t r i b u t i o n and Refining Margins These costs have been estimated as the differences between the r e t a i l p r i c e s i n the end use sectors and the refinery-gate p r i c e of crude o i l , i n a p r e - " c r i s i s " year, reduced by an amount to prevent double- counting of the cost of crude o i l used by the energy supply industry 267 (mostly the s t i l l gas used i n the r e f i n i n g process). Used i n the DFC sector was the weighted average of the 1973 r e t a i l p r i c e s of l i g h t and heavy f u e l o i l s for industry, as reported by S t a t i s t i c s Canada (cat. no. 57-506), adjusted downward by the d i f f e r e n c e between the 1970 and 1973 wellhead p r i c e s of o i l , i n 1975$, as reported by the CPA (1977). The margins are mldw = 0.32, mlde = 0.21. Used i n the i n d u s t r i a l sector was the 1970 average r e t a i l p r i c e f o r a l l i n d u s t r i a l f u e l o i l s , as reported by S t a t i s t i c s Canada (cat. no. 57-506). The margins are mliw = 0.04, mlie = 0.01. Used f o r the "other" transportation sector were the 1973 r e t a i l p r i c e s to industry for heavy f u e l o i l and d i s e l o i l , adjusted downward by the d i f f e r e n c e between the 1973 and 1970 western Canadian wellhead o i l p r i c e s . An average p r i c e to "other" transportation was a r r i v e d at by weighting these p r i c e s by the 1970 consumption of heavy f u e l o i l , and d i e s e l o i l plus a v i a t i o n turbine f u e l . I t was assumed that the p r i c e of a v i a t i o n turbine f u e l was the same as the d i e s e l p r i c e , since the 1970 values per b a r r e l shipped from r e f i n e r i e s , derived from S t a t i s t i c s Canada (cat. no. 45-205, Table 6) for the two f u e l s , were almost equal (within 1% of each other). The margins are: mltw = 0.77, mite = 0.69. Used i n the road transportation sector was the 1970 r e t a i l gasoline p r i c e reported by EMR (1977a, Appendix C). Since the "other" transportation margins, mltw and mite, are applied to o i l products going to both "other" and "road" transportation sectors — i . e . to the variables WLX4 and ELX4 - i t i s 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 va r i a b l e s WLA and ELA. C.2.8 Energy Supply Industry Use of O i l Let bwl, b e l = f r a c t i o n s of the western and eastern supplies of o i l not used by the western energy supply i n d u s t r i e s (including r e f i n i n g ) . These parameters are equal i n a l l periods to t h e i r 1971-1975 values of .9272 (west) and .9262 (east), using data from S t a t i s t i c s 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 l i m i t s on o i l exports (including net product exports) are taken from the NEB reports (1977, 1978), and, for 1976 and 1977, from EMR (1978c) . The l i m i t s are assumed to be zero a f t e r 2000. The l i m i t s are Period 05 10 15 25 35,45 WOEX .597 .152 .073 .067 0.0 I t i s assumed that production from eastern onshore and southeast offshore sources i s no higher than the 1971-75 l e v e l , i n 1976-1980, and that i t can increase to 50 m i l l i o n b a r r e l s per year i n the 1986-1990 period, with a buildup i n the 1981-1985 period: 269 Period 05 10 15 E0X1 .004 .050 .250 I t i s assumed that production from northeast offshore sources cannot begin u n t i l a f t e r 1985, and that f o r t = 15, 25, i t i s no greater than southeast production i s allowed to be one period e a r l i e r , 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 U n t i l a study by EMR on long-run supply curves i s completed, the cost and supply data must be based on several sources. The cost of "low cost" conventional western gas i s taken to be $.30/Mcf. According to CPA (1977) data, the average wellhead p r i c e during 1971-1975 was $.21/Mcf (1975$). Thus $.30/Mcf i s a l i t t l e farther along the long- run supply curve. In model u n i t s , t h i s cost i s : cwgl = .03 The higher cost western conventional gas i s taken to be cwg2 = .08, somewhat a r b i t r a r i l y . The remaining reserve (after 1975) at the above cost l e v e l s are estimated roughly from the shape of the tentative long run supply curve of the EMR d r a f t (1977d), and using the t o t a l of remaining known reserves plus undiscovered resources, at the 40% p r o b a b i l i t y l e v e l , from EMR (1977b). They are: WGR1 = 39.0 WGR2 = 59.0. 270 The t o t a l remaining reserves of northern f r o n t i e r gas (not including northeast offshore gas, which i s al l o c a t e d to eastern production) 12 are taken to be 137 x 10 cu. f t . , which i s the figure f or p o t e n t i a l resources, at the 40% p r o b a b i l i t y l e v e l , from EMR (1977b). The low and high cost le v e l s (including transportation to southern Alberta) are based on various sources, namely an early d r a f t of the EMR study (1977d) on long-run supply curves, and figures i n the report by HMA (1976). The costs chosen are $2.50/Mcf and $3/Mcf, or, i n model un i t s : cwg3 = .25 cwg4 = .30. Based on the shapes of the tentative long-run supply curves of EMR (1977d), the following a l l o c a t i o n of reserves between the two cost l e v e l s has been made: WGR3 =44.4 WGR4 = 93.0. The low cost eastern gas i s taken to be represented by southeast off-shore gas, and the high cost eastern gas by northeast offshore gas. Based on the 40% p r o b a b i l i t y l e v e l of p o t e n t i a l resources i n these two areas, reported by EMR (1977b), the reserves are taken to be EGR1 =16.0 EGR2 = 29.0. Based on the EMR d r a f t (1977d) and HMA (1976), the landed costs of these are set at $.60/Mcf and $3.00/Mcf, r e s p e c t i v e l y . In model u n i t s , 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 l i m i t s ) . C.3.2 Export Price The 1976 EMR "Energy Strategy" report (1976a) lays out the p o l i c y 271 that prices of gas exports should be competitive i n the markets where they are sold. The 1978 (mid-year of f i r s t period) gas export p r i c e was $1.92/Mcf, according to H e l l i w e l l (1979X. Assuming gas export p r i c e s follow the same pattern assumed for o i l p r i c e s , the r e a l gas p r i c e i s escalated at the rate of 4% per year u n t i l the year 2000. Since the l o g i c of the model requires export prices to be equal to production cost plus economic rent, and since there i s no provision i n the model fo r gas transport charges from the wellhead to the border., the trans- port charge — about $.25/Mcf — must be subtracted from the above. The r e s u l t , i n model u n i t s , i s : Period 05 10 15 25,35,45 pgex .167 .209 .259 .396 C.3.3 Gas Production Decline Curves The standard production t i m e - p r o f i l e presented by EMR (1973, p. 80) has the peak rate being achieved i n the f i r s t 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 o i l production, i t i s assumed that production declines at 10% per year. The d e t a i l e d r e s u l t s for the values ag(s), based on the assumptions that capacity established i n one year l a s t s 15 years, followed by a decline of 10% per year f o r X another 15 years, are i n Appendix B> section 9, "Time Period Aggregation". C.3.4 Coal G a s i f i c a t i o n 12 15 Let acg = 10 c u . f t . of gas output per 10 BTU coal input; and cgc = cost of coal g a s i f i c a t i o n , not including coal feed cost, i n units of 1 0 1 2 $ per 10 1 5cu. f t . Using estimates by the SRI (1976, Vol. I I , pp. IV-4,5), the parameters are set at acg = 0.567 and cgc = 0.124. These are arrived at by averaging the conversion e f f i c i e n c i e s and costs f o r the Lurgi process, and an "Advanced" process, as estimated by SRI (1976), and converting to model u n i t s . The average conversion e f f i c i e n c y corresponding to the above acg i s 0.587. The e a r l i e s t dates of introduction of coal g a s i f i c a t i o n , according to SRI (1976), are 1984 f o r the Lurgi process, and 1987 for the "Advanced" process. The approximate date of 1985-86 i s modeled by f i x i n g capacity additions at the zero l e v e l f o r the periods ending 1980 and 1985, i . e . WGDG = and s e t t i n g i n i t i a l capacity equal to zero. C.3.5 Synthetic Gas from Biomass Middleton Associates (1976, pp. 300-301) give a cost range for p y r o l y s i s (gas and l i q u i d output) of $1.50-$3.50 per m i l l i o n BTU(MMBTU). An average value of $2.50 per MMBTU (or $2.50 per MCF of gas) i s taken fo r the model. In model un i t s , t h i s i s cwg5 = ceg3 -= 0.25. I t i s assumed that t h i s technology i s a v a i l a b l e a f t e r 1980. In order to model t h i s , production i s set equal to 0.0 i n the f i r s t period. For l a t e r periods, low upper l i m i t s are placed on production from t h i s 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 c g t r = cost of transporting gas from west to east. 273 H e l l i w e l l (1976, appendices) gives $.44/mcf f o r t h i s cost. In model units, t h i s i s cgtr = .044. I t i s assumed that the west-to-east transportation of gas can increase from the 1971-1975 l e v e l up to 3.5% per year u n t i l 1985, when the Quebec & Maritimes p i p e l i n e may be b u i l t . Since t h i s p i p e l i n e w i l l make the eastern market p o t e n t i a l l y 43% larger (based on population shares), an additional amount (above 3.5% growth) i s added, equal to 1/2 the p o t e n t i a l increase ( i . e . 21.5% more), since i t takes time to e s t a b l i s h the new markets. There i s no upper l i m i t a f t e r 1990. The r e s u l t s are: Period 05 10 15 WGE 4.092 4.860 7.008 C.3.7 D i s t r i b u t i o n Margins The margins for the two sectors i n d u s t r i a l (mgiw, mgie) and DFC (mgdw, mgde), are taken to be the differences between the average revenues and wellhead p r i c e (Toronto c i t y gate, for the east) i n 1970, a p r e - " c r i s i s " year. The average revenues were derived from S t a t i s t i c s Canada (cat. no. 57-205), the wellhead p r i c e from the CPA (1977) and the Toronto c i t y gate p r i c e from the sum of the wellhead p r i c e 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 = f r a c t i o n s of the western and eastern supplies of gas not used by the western and eastern energy supply i n d u s t r i e s . These parameters are equal i n a l l periods to t h e i r 1971-1975 values of .8832 (west) and .958 (east), using data from S t a t i s t i c s Canada (cat. no. 57-207). 274 C.3.9 Miscellaneous Limits Upper l i m i t s on future gas exports are set at the l e v e l of currently approved exports, according to the NEB (1979, Table G-12) — i . e . , i n model un i t s , Period 05 10 15 25 35,45 WGEX 5.4 8.4 3.7 0.3 0.0 Eastern production (mostly offshore) i s assumed to be able to reach up to 0.8 Tcf per year i n the year 1988, following comments by Walters (1979) on the a v a i l a b i l i t y of Sable Island gas, and assuming a l l eastern offshore gas i s a v a i l a b l e , s t a r t i n g i n 1988. I t i s assumed that the northeast offshore gas i s a v a i l a b l e a f t e r 1990 (existing onshore production makes a small contribution i n the f i r s t two periods). The upper l i m i t s are: Period 05 10 15 25 35, -45 EGX1 0.001 0.001 2.4 no l i m i t no l i m i t EGX2 0.0 0.0 0.0 4.8 no l i m i t C.4.0 Data f o r the E l e c t r i c i t y Sector C.4.1 C a p i t a l and Non-fuel Operating Costs f o r Secondary E l e c t r i c i t y Production The source for the basic data i s the report by HMA (1976, p. 250). The data given below, i n model u n i t s , were derived using a r e a l rate of return of 8% over 30 years. ( M u l t i p l i c a t i o n by 10 y i e l d s the costs i n mills/kWh.). Fuel Gas Coal O i l Cost ceg==.54 cec = .76 ce l = .66 275 C.4.2 F u e l - t o - E l e c t r i c i t y Conversion C o e f f i c i e n t s 12 12 Let age = 10 kWh e l e c t r i c i t y output per 10 cu. f t . gas input? 12 15 ace = 10 kWh e l e c t r i c i t y output per 10 BTU coal input, and 12 9 ale = 10 kWfe e l e c t r i c i t y output per 10 b b l o i l input. From data compiled by S t a t i s t i c s Canada (cat. no. 57-207) for 1971- 1975, the above parameters can be estimated. The parameter values, with approximate corresponding conversion e f f i c i e n c i e s are: Parameter age ale ace Value i n Model .0788 .4621 .09396 Corresponding .2689 .2718 .32 Conversion E f f i c i e n c y For the base case, the conversion factors for gas, o i l and coal are increased i n the f i r s t three periods i n approximately the same amount as assumed by EMR (1977a, p. 68). In addition, coal e l e c t r i c production i s assumed to increase i n e f f i c i e n c y to 38%, due to introduction of f l u i d i z e d bed combustion (using estimates by Keairns, et a l . (1975, p. 10)), by the period 2000. The r e s u l t s 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 e l e c t r i c i t y from nuclear power i s taken to be 10 mills/kwh, or ce4 = 1.0, i n model un i t s . This figure i s based on c a p i t a l and non-fuel operating costs of 8.9 mills/kwh, derived from estimates by HMA (1976), with a r e a l rate of return of 8% over 30 years, and 276 f u e l l i n g 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 i s assumed for nuclear e l e c t r i c i t y . In l a t e r time periods, t h i s technology may be thought of as the thorium near-breeder, or a fusion system. Because of the long lead times i n e s t a b l i s h i n g nuclear capacity, and because there i s no nuclear power yet i n the west, the following r e s t r i c t i o n i s s p e c i f i e d : WED4 = 0.0 , t = 05,10 . C.4.4 Cost of H y d r o e l e c t r i c i t y - P r o t t i (1978, p.56) gives the c a p i t a l cost of a recent, large hydro i n s t a l l a t i o n i n Manitoba. Using t h i s information, i n 1975 d o l l a r s , and a rate of return on c a p i t a l of 8% over 30 years, together with the non- f u e l operating costs assumed f o r c o a l - e l e c t r i c production by HMA (1976, p. 250), the cost of h y d r o - e l e c t r i c i t y i s taken to be 7.7 mills/kwh, or i n model units, ce5 = .77 C.4.5 Limitations on H y d r o e l e c t r i c i t y Using estimates i n the report by HMA (1976, p.242), the maximum hydr o e l e c t r i c production, per 5-year period, that can be r e a l i z e d i n 12 12 the future i s about 1.27 x 10 kwh i n the west, and 2.21 x 10 kwh i n the east. From S t a t i s t i c s Canada (cat. no. 57-207), the 1971-1975 hydro 12 12 productions were 0.24 x 10 kwh f o r the west and 0.71 x 10 kwh f o r the east. Assuming that the future p o t e n t i a l can be reached no sooner than the period ending 2000, and allowing a l i n e a r increase i n capacity u n t i l then, the values for the parameters i n the model are ( r e c a l l that the f i r s t 277 3 periods are 5 years long, and the r e s t 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 r e l a t i v e lack of hydro p o t e n t i a l i n some provinces of each region, i t i s assumed that the proportion of e l e c t r i c capacity expansion due to hydro cannot exceed the 1971-1975 f r a c t i o n of t o t a l e l e c t r i c i t y production coming from hydro — i . e . , using figures from S t a t i s t i c s Canada (cat. no. 57-207, and 57-204) , hdw = .753, hde = .779. C.4.6 Cost of E l e c t r i c i t y from Biomass According to Middleton Associates (1976, p. 287), the cost of wood chip input i s approximately $1.50/MMBTU, i f we reduce Middleton's figures somewhat to account f o r the higher c a p i t a l cost (10%) than i s assumed i n t h i s model (8%). The thermal e f f i c i e n c y of generation i s 34%. Therefore, the f u e l cost i s $1.50 = $4.50 per MMBTU of output. .34 Converting to units of mills/kwh, the f u e l cost i s 15.3. Assuming the c a p i t a l and non-fuel operating costs are the same as f o r coal (7.6 m i l l s / kWK), the t o t a l cost, expressed i n model units i s ce6 = 2.29. C.4.7 E l e c t r i c i t y Exports Manne (1976) presents a proje c t i o n of U.S. e l e c t r i c i t y p r i c e s , which can be approximated by 18 mills/kWh i n the period 1975-1990T and 23 millsAWh i n the period 2000-2025, expressed i n 1970$. The CPA (1977, Section XI, Table 3), presents s t a t i s t i c s on quantity and value of e l e c t r i c i t y exports. The 1975 average export p r i c e i s 14.5 m i l l s / kWh. Appling a factor of 14.5/18.0 to the Manne (1976) p r o j e c t i o n 278 produces the pr o j e c t i o n used i n the model (model u n i t s are presented i n the t a b l e ) : Period 05 10 15 25,35,45 peex 1.45 1.45 1.45 1.86 E l e c t r i c i t y exports are allowed to be no greater than the l e v e l i n 1971-75, increased at a r a t e 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 E l e c t r i c i t y D i s t r i b u t i o n Margins The margins f o r the two sectors i n d u s t r i a l (meiw, meie) and DFC (medw, mede) are taken to be the diff e r e n c e s between the average revenues and average generation costs i n 1971, a p r e - " c r i s i s " year. The average revenues were derived from S t a t i s t i c s Canada (cat. no. 57-202), and the average generation costs from S t a t i s t i c s Canada (cat. no. 57-207), using the u n i t generation costs and f u e l costs derived above. The margin for e l e c t r i c i t y used'in road transportation (met) — i . e . for e l e c t r i c automobiles — i s based on two assumptions: f i r s t , that there would be a road tax equivalent to the road tax on gasoline, and second that the recharging of e l e c t r i c autos would receive off-peak p r i c e discounts. S p e c i f i c a l l y , the road tax of approximately 13 cents per ga l l o n across the country (according to S t a t i s t i c s Canada (cat. no. 68-201)) i s converted to d o l l a r s per output BTU, and then converted to d o l l a r s per kWh of e l e c t r i c i t y used for e l e c t r i c autos. I t i s assumed that revenue from e l e c t r i c i t y sales to the road transportation sector covers only generation costs and the road tax — i . e . there i s no d i s t r i b u t i o n 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 E l e c t r i c i t y Let bw, bee = f r a c t i o n s of the western and eastern supplies of e l e c t r i c i t y not used by the western and eastern energy supply i n d u s t r i e s (including transmission l o s s e s ) . These parameters are equal i n the period 1971-1975 to .8938 (west) and .9096 (east), using data from S t a t i s t i c s Canada (cat. no. 57-207). They are a l t e r e d i n the f i r s t three periods roughly i n accordance with the assumptions of EMR (1977a, p. 71). The r e s u l t s 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 a l a = 10 BTU output per 10 bbl input, conventional autos, 15 12 aea = 10 BTU output per 10 kWh input, e l e c t r i c autos, and 15 9 alo = 10 BTU output per 10 bbl input, non-auto transportation. EMR (1977a, p. 28) estimates the u t i l i z a t i o n e f f i c i e n c y f or gasoline to be 20%. Using the factor f o r conversion of gasoline u n i t s to BTU's ; a l a = .2 x 5.222 = 1.0444. Assuming an improvement i n f u e l economy bringing average mileage from the present 17.5 miles per g a l l o n to 33 miles per g a l l o n a f t e r 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 e f f i c i e n c y f o r e l e c t r i c autos i s the basic operating e f f i c i e n c y of 70%, given by Swinton (1976, p. 29). M u l t i p l y i n g by the f a c t o r for conversion of e l e c t r i c a l u n i t s to BTUs, aea = .7 x 3.412 = 2.388. For non-auto transportation, a weighted average of u t i l i z a t i o n e f f i c i e n c i e s given by EMR (1977a, p. 28) for r a i l , a i r and marine transport, using l i q u i d f u e l s , y i e l d s a conversion e f f i c i e n c y of 24%. (Coal, already i n l i t t l e use by 1975 i n transportation, i s assumed not to be used i n transportation.) With an approximate average factor for conversion of l i q u i d f u e l units to BTUs, alo = .24 x 5.8 = 1.41. A i r , truck and bus energy e f f i c i e n c y measures discussed i n EMR (1977e, p. 28) are expected to amount to 18%-20% f u e l savings i n 1990. Assuming the f u e l savings w i l l a c t u a l l y be 15%, by 2000, and more modest improve- ments a f t e r 2000, the conversion f a c t o r , 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 E l e c t r i c Auto Growth R e s t r i c t i o n s Let e l = maximum f r a c t i o n of new autos that can be e l e c t r i c , i n west and east. From the discussion by Hedley, et a l . (1976, p. 13) on the "free market" penetration of e l e c t r i c autos, i t i s assumed that / 0, t = 05, 10 e l = J I .15, t = 15 but that a 60% penetration can be achieved by 2010, i . e . 281 .375, t = 25 e l = ^.6, t = 35, 45. C.5.3 D i f f e r e n t i a l Cost of E l e c t r i c Auto over Conventional Auto The l a t e s t information on the U.S. e l e c t r i c t e s t v e h i c l e , ETV-1, suggests an i n i t i a l cost d i f f e r e n c e of approximately $1500 extra for the e l e c t r i c auto, i n Canadian 1975$, according to Wayne (1979, p. 13). Lower maintenance costs for the e l e c t r i c car would be o f f s e t by battery replacement charges. Amortized over 10 years, a t a r a t e of return on c a p i t a l of 8%, the annual extra cost i s $224. Assuming the v e h i c l e t r a v e l s 10,000 miles i n a year, t h i s i s $0.0224 per mile extra for the e l e c t r i c car. Since a l a = 1.0444 corresponds to 17.5 miles per gallon, the quantity of output energy per mile driven i s (1.0444/(35 x 10 9 x 17.5) = (1.705 x 10~ 1 2) x 10 1 5BTU per mile. (Dividing by aea = 2.388 gives the number of kwh per mile, 0.714 kwh per mile. This f a l l s w i t h i n the range given by Wayne (1979, p. 10), of 0.5 - 1.5 kwh per mile.) Therefore, the d i f f e r e n t i a l cost of e l e c t r i c auto output energy 3 i s $.0224/1.705 = $.0132 per 10 BTU, or i n model u n i t s , cea = 1.32. C.6.0 Data f o r I n d u s t r i a l End-Use Sector C.6.1 Conversion Factors ^ n n " 12 a g i = 10 BTU per 10 cu. f t . gas used i n i n d u s t r i a l sector, 15 9 a l i = 10 BTU per 10 bbl l i q u i d hydrocarbon ( o i l ) used i n i n d u s t r i a l sector, 15 15 a c i •= 10 BTU per 10 BTU coal used i n i n d u s t r i a l sector, and 15 12 a e i = 10 BTU per 10 kWh e l e c t r i c i t y used i n i n d u s t r i a l sector. 282 EMR (1977a, p. 28) has estimated average u t i l i z a t i o n e f f i c i e n c i e s f o r the d i f f e r e n t f u e l s i n the i n d u s t r i a l sector. The above parameters are set at EMR estimates, expressed i n model un i t s , f o r a l l time periods. Since EMR deals separately with d i f f e r e n t l i q u i d f u e l s , i t i s necessary to take a weighted average of the l i q u i d f u e l conversion e f f i c i e n c i e s , for the model. The parameter values, and associated conversion e f f i c i e n c i e s , are: Parameter agi a l i a c i \ a e i Value i n Model .85 • .4.13 .87 ; 3.412 Corresponding Con- version E f f i c i e n c y .85 '• .70 ,87 1.00 C.6.2 Upper and Lower Limits on Fractions of Total I n d u s t r i a l Output' Energy A v a i l a b l e from the D i f f e r e n t Fuels HMA (1976, p. 148) present estimates of these upper and lower l i m i t s f o r the year 2000. I t i s assumed that these parameters change l i n e a r l y from t h e i r 1971-1975 values (when upper l i m i t = lower l i m i t = actual f r a c t i o n ) , estimated from S t a t i s t i c s Canada (cat. no. 57-207), to the HMA (1976) values for 2000, and remain constant a f t e r t h i s . The r e s u l t s are presented i n Table 69. Non-energy uses of o i l and gas (e.g. f o r petrochemicals, asphalt, etc.) are included i n i n d u s t r i a l uses. 283 Table 69. Bounds on I n d u s t r i a l Fuel Shares Period Fuel Limit Base 05 10 15 25,35,... Coal lwc .030 .044 .058 .072 .10 l e c .172 .158 .143 .129 .10 uwc .030 0084 .138 .192 .30 uec .172 .198 .223 .249 .30 O i l l wl .279 .243 .207 .172 .10 l e i .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 E l e c t r i c i t y 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 e f f i c i e n c i e s for fuels i n the DFC sector are presented below, along with the corresponding values f o r the conversion fac t o r s . The e f f i c i e n c i e s are taken from EMR (1977a, p. 28), except i n the case of the heat pump, f o r which the SRI (1976, Vol. I I , pp. IX-14,15) figure i s used. There i s close agreement between the EMR and SRI e f f i c i e n c y values for e l e c t r i c resistance heating, o i l heat, and gas heat. 284 Process Thermal E f f i c i e n c y Conversion Factor E l e c t r i c a l , non-heating 1.0 aeo = 3.412 E l e c t r i c - heat pump 2.0 aeh = 6.824 E l e c t r i c - r e s i s t a n c e 1.0 aer = 3.412 heating Gas heat 0.76 agh = 0.76 O i l heat 0.65 a l h = 3.835 C.7.2 Heating Costs Except for d i s t r i c t heating by cogeneration, the following costs are taken from SRI (1976, V o l . I I , pp. IX-14,15). The heat pump cost i s reduced to 5/6 of the SRI value, under the assumptions that 1/2 of the users would have a i r conditioning even without a heat pump, and that the a i r conditioning function of the heat pump would be used 1/3 of the time, for a t o t a l c r e d i t of 1/6 of the non-fuel cost. The d i s t r i c t heat cost i s taken from estimates by Berthin (1980) of c a p i t a l costs f o r plant equipment changes, piping, and in-home heat exchangers, amortized over 30 years at an 8% ra t e of return, plus system maintenance costs of $25/ yr./house, plus in-home maintenance costs of $37/yr./home (the maintenance cost f or gas heat assumed by SRI (1976)), with the same annual heating load of 94.7 x 10 6BTU/yr. as assumed by SRI (1976). 3 Process Non-Fuel Cost ($/10 BTU) E l e c t r i c Resistance crh = .105 Heating Gas Heat cgh = .251 O i l Heat coh = .336 Heat Pump chp = .466 Solar Heat chs = .706 D i s t r i c t Heat cdh = .662 by Cogeneration 285 C.7.3 Heat Pump Limits I t i s assumed that the heat pump i s commercially available only a f t e r 1980, and that the upper l i m i t on the f r a c t i o n of heating done by heat pump r i s e s l i n e a r l y from 0 i n 1980 to 1 i n 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 p a r t i a l s o l a r system providing 70% of a structure's heating and hot water demands. He further assumes (p. 119) a 15% penetration of s o l a r home heating by 2000. Using the 70% and the l a t t e r c r i t e r i a puts an upper l i m i t on the f r a c t i o n of heating that can be done by s o l a r . I t i s assumed that t h i s l e v e l i s achievable by 2000, that a furth e r doubling can take place by 2010, another doubling by 2020, that s o l a r heating i s at v i r t u a l l y zero l e v e l u n t i l a f t e r 1980, and that the sol a r p o t e n t i a l increases l i n e a r l y 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 D i s t r i c t Heating by Cogeneration According to Berthin (1980) the t o t a l combined e f f i c i e n c y of c o a l - steam-electric plus d i s t r i c t heat i s 72%, with 27% f o r e l e c t r i c i t y and 45% for heating. To si m p l i f y matters, i t i s assumed that 32% i s used f o r e l e c t r i c i t y (as with no d i s t r i c t heating), and that 40% (= 72% - 32%) of the input energy i s available f o r ' d i s t r i c t heating. Therefore, the c o e f f i c i e n t r e l a t i n g new c o a l - e l e c t r i c capacity to the maximum new capacity of d i s t r i c t heating i s fc = .40. 286 Assuming that heat from waste heat of nuclear power generation would be p u b l i c a l l y unacceptable, the c o e f f i c i e n t r e l a t i n g new nuclear e l e c t r i c i t y capacity to the maximum new capacity of d i s t r i c t heating i s zero i n the base case: fn = 0.0. It i s assumed that d i s t r i c t heating by cogeneration i s not possible i n Newfoundland, Quebec, Manitoba or B.C., where e l e c t r i c i t y i s produced mainly by hydro. I f these areas are elminated i n proportion to t h e i r populations, as given by S t a t i s t i c s Canada,(1978, p. 186), and the r e s u l t i n g upper l i m i t s are taken to be achievable by 2000, with l i n e a r increase from 0 i n 1980 then the maximum fra c t i o n s of t o t a l heating due to d i s t r i c t 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 f o r Heating The values (for 1974 of energy used by end-use function, pre- sented by EMR (1977a, pp. 20-21), adjusted for end use e f f i c i e n c i e s using EMR (1977a, p. 28) data gives gwh = geh = .8661. This value i s taken to be constant i n a l l time periods. C.8.0 Data f o r the Objective Function C.8.1 S o c i a l Discount Rate The.real s o c i a l discount rate i s taken to be 10%, that i s d = 0.10. This i s the figure derived by Jenkins (1977, p. 140) f o r the s o c i a l opportunity cost of government funds. A r e a l discount rate of 10% i s also 287 the rate preferred by the NEB (1979) i n the calc u l a t i o n s of costs and benefits of proposed exports of natural gas. C.8.2 Price E l a s t i c i t i e s of Demand The der i v a t i o n of the p r i c e e l a s t i c i t i e s of demand i s discussed i n Appendix A. For completeness of t h i s section, they are presented here: ed = 0.81, for DFC, e i = 0.48, for industry, er = 0.36, f o r road transportation, and eo = 0.36, f o r other transportation. C.8.3 Base Year Prices and Quantities For the c a l c u l a t i o n of the parameters dwd, dwi, e t c . , i t i s necessary to have estimates of the prices and quantities of output energy used i n a base year. The base year chosen i s 19$0, since t h i s year was before the rapid escalation of petroleum p r i c e s and was thus l i k e l y an equilibrium year i n energy markets. The base year quantities of output,energy were calculated from S t a t i s t i c s Canada (cat. no. 57-207), which gives the input energy to the end use sectors, and from the end use conversion e f f i c i e n c i e s s p e c i f i e d i n sections 5, 6 and 7 above, which were adapted mostly from EMR (1977a, p. 28) . The base year prices were calculated i n two stages. F i r s t , the base year prices of the f u e l s , i n natural units and i n 1975$, were calculated f o r each end use sector. Secondly, the t o t a l energy costs i n each end use sector were calculated, using the base year f u e l p r i c e s and input energy q u a n t i t i e s , then divided by the t o t a l output energy quantities f o r each sector. In the DFC sectors, the non-fuel costs of heating, as presented i n section 7 above, are also incorporated i n t o the p r i c e . The base year natural gas pr i c e s i n the DFC and i n d u s t r i a l sectors of the west and east were estimated by c a l c u l a t i n g the average revenues, from data i n S t a t i s t i c s Canada (cat. no. 57-205). The r e s i d e n t i a l and commercial categories were combined f or the DFC c a l c u l a t i o n . The base year e l e c t r i c i t y p r i c e s i n the DFC and i n d u s t r i a l sectors of the west and east were estimated by c a l c u l a t i n g the average revenues, from data i n S t a t i s t i c s Canada (cat. no. 57-202). The r e s i d e n t i a l , commercial and s t r e e t l i g h t i n g categories were combined f or the DFC c a l - c u l a t i o n . The 1971 data were used to ca l c u l a t e e l e c t r i c i t y p r i c e s . This should not introduce much erro r since, as i s w e l l known, r e a l energy p r i c e s were quite stable between 1970 and 1971. The base year coal p r i c e s f o r industry i n the west and east were estimated by c a l c u l a t i n g the average cost to industry of coal and coke, from data i n S t a t i s t i c s Canada (cat. no. 57-506). Weighted averages of the gasoline p r i c e s i n f i v e regions, from EMR (1977a, Appendix C), were used f o r the base year f u e l p r i c e s i n the road transportation sectors of the west and east. The base year p r i c e s of o i l used i n the western and eastern in= d u s t r i a l sectors were estimated by c a l c u l a t i n g the average cost to industry of a l l o i l products consumed, from data i n S t a t i s t i c s Canada (cat. no. 57-506). There are no r e a d i l y a v a i l a b l e s t a t i s t i c s f o r the base year p r i c e s of o i l i n the DFC sector. The p r i c e s of l i g h t f u e l o i l and heavy f u e l o i l to western and eastern industry were ca l c u l a t e d from S t a t i s t i c s 289 Canada (cat. no. 57-506). Since l i g h t and heavy f u e l o i l s are the pre- dominant o i l f u e l s used i n the DFC sector, averages of these two p r i c e s were ca l c u l a t e d for the west and the east, weighted by the proportions of the 1970 consumption of the two f u e l s i n each region. Since S t a t i s t i c s Canada (cat. no. 57-506) does not d i s t i n g u i s h between l i g h t and heavy f u e l o i l s u n t i l 1973, the 1973 p r i c e s were used, but adjusted downward by the d i f f e r e n c e between the 1973 and 1970 western Canadian wellhead o i l p r i c e s , i n 1975$, as reported by the CPA (1977). The base year p r i c e s of o i l products i n "other" transportation are weighted averages of the p r i c e s to industry of heavy f u e l o i l , d i e s e l o i l and a v i a t i o n turbo f u e l . The p r i c e s of heavy f u e l o i l and d i e s e l o i l were c a l c u l a t e d from S t a t i s t i c s Canada (cat. no. 57-506) f o r 1973, when these products were f i r s t distinguished separately, but adjusted downward by the d i f f e r e n c e between the 1973 and 1970 western Canadian wellhead o i l p r i c e s , as reported by the CPA (1977). The p r i c e of a v i a t i o n turbine f u e l was taken to be the same as the p r i c e of d i e s e l f u e l o i l , since the values per b a r r e l shipped from r e f i n e r i e s i n 1970 of the two commodities were very nearly equal, according to data i n S t a t i s t i c s Canada (cat. no. 45-205, Table 6). A summary of the c a l c u l a t i o n s for the output energy p r i c e s i s presented i n the tables below. The input f u e l p r i c e s are expressed i n f a m i l i a r units, but a l l other quantities and monetary values are expressed i n model u n i t s . 290 Sector Fuel Input Price Output Energy T o t a l Cost Road Transportation, o i l $.67/gallon .056951 .1281 West Output Price = 2.2501 Road Transportation, o i l $.70/gallon .127151 .2995 East Output Price = 2.3554 Other Transportation, o i l $.33/gallon .019503 .0161 West Output P r i c e = .8261 Other Transportation, o i l $.32/gallon .049652 .0400 East Output Price = .8046 Industry, West coal $1 T00/10 6BTU .0110254 .00127 gas $.386/mcf .131535 .00597 o i l $.13/galIon .09044 .01007 e l e c t r i c i t y 1.17*r/kwh .0806339 .02765 To t a l s : .3136343 .04496 Output Price .14335 Industry, East coal $.88/106BTU .2170946 .02196 gas $.774/mcf .2076631 .01891 o i l $.12/gallon .42497 .04219 e l e c t r i c i t y 1.06<r/kwh .2503984 .07779 T o t a l s : 1.1001261 .16085 Output Price .14621 DFC, West gas $.975/mcf . .175376 .379 (Note: Total Cost o i l $.21/gallon .103850 .512 e l e c t r i c i t y 2 ..54<r/kwh .073094 .782 T o t a l : .352320 Output Price = .5018 DFC, East gas $1.57/mcf .154927 .458 (Note: Total Cost o i l $.17/gallon .940832 .482 i s per u n i t of e l e c t r i c i t y 2.16 <r/kwh .225452 .656 output energy, *i n p l n H " i i-i rr n n n — T o t a l : 1.321211 iiiui n̂-Liiy iiwii f u e l cost) Output Price = .5089 C.8.4 Base Year Values of Exogenous Parameters For the c a l c u l a t i o n of the objective function parameters dwd, dwi, etc., i t i s necessary to have base year (1970) estimates ofrthe indices (1973 = 1) of population, income per capita, r e a l domestic product and c a p i t a l output r a t i o . I t i s assumed that the 1970 indices of population 291 and r e a l domestic product are the same i n the west and the east — i . e . that there was not much differ e n c e between west and east i n the percentage changes of these quantities from 1970 to 1973. Income per c a p i t a i s personal disposable income, divided by population. The indices and data sources are shown below. Source Index- Value population .9662 income per c a p i t a .8217 r e a l domestic product .8249 Capit a l output r a t i o 1.0343 S t a t i s t i c s Canada (cat. no. 91-201) S t a t i s t i c s Canada (cat. no. 13-531, and cat. no. 91-201) S t a t i s t i c s Canada (cat. no. 13-531) EMR (1977a, Appendix C) C.8.5 Projections of Exogeneous Parameters For the c a l c u l a t i o n of the parameters dwd, dwi, e t c . , projections are needed for the indices of western and eastern population, income per capita, western and eastern r e a l domestic product, and c a p i t a l output r a t i o . The population indices for the base case are a r r i v e d at by taking s l i g h t l y lower values than the NEB's base case projections f o r a l l of Canada, i n Douglas and Nichols (1979), u n t i l the year 2000, and applying the regional population proportions i n EMR (1977a, Appendix C) to derive separate indices f o r the west and east. The NEB's base case projections have been lowered s l i g h t l y because they are d e l i b e r a t e l y a l i t t l e on the high side. Population growth a f t e r 2000 i s taken to be at the same rate i n both regions, using the midpoint of the four main projections i n S t a t i s t i c s Canada (cat. no. 91-520). The p r o j e c t i o n s , expressed i n 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 p r o j e c t i o n of income per capita- u n t i l 2000 i s s l i g h t l y lower than the base case NEB p r o j e c t i o n s , i n Douglas and Nichols (1979), which are a l i t t l e on the high side. (Because the NEB i s evaluating proposed new gas exports, any errors i n domestic demand pr o j e c t i o n should be on the high s i d e ) . A f t e r 2000, the rate of growth of income per c a p i t a i s 2.3% per year, under the assumptions that the proportion of the population i n the work force w i l l have s t a b i l i z e d by that time, and that the main source o f the increase i n income per capita w i l l be the increase i n output per worker due to technological change, which has t y p i c a l l y been about 2% per year. The p r o j e c t i o n i s : 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 r e a l domestic product u n t i l 2000 are s l i g h t l y lower than the NEB projections f o r a l l of Canada, i n Douglas and Nichols (1979X , with the s p l i t between west and east chosen to make the r e a l domestic product per c a p i t a increase at the same rate i n each region. A f t e r 2000, the rates of growth i n 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 p r o j e c t i o n of the c a p i t a l output r a t i o ( i . e . c a p i t a l stock divided by output) i s based on the projections by EMR (1977a, Appendix C) of 293 i n d u s t r i a l c a p i t a l stock and i n d u s t r i a l r e a l domestic product, u n t i l 1990. A f t e r 1990, the r a t e of growth of the c a p i t a l output r a t i o i s assumed to gradually slow to zero — i . e . that i n d u s t r i a l c a p i t a l stock and output eventually grow at the same rate. The p r o j e c t i o n i s : Period 1980 1985 1990 : 2000 : 2010 : 2020 2030 C a p i t a l Output Ratio, %/yr. 2.0 2.1 2.8 1.0 0.5 0.0 0.0 In a l l of the above projections, the rate of growth i n the period ending 2030 i s used i n the end e f f e c t s modifications as the r a t e of growth i n every period a f t e r the time horizon, 2020. C.9.0 Right-Hand Side Values ( I n i t i a l Conditions) The i n t e r p e r i o d constraints of the f i r s t few time periods r e l a t e the values of v a r i a b l e s to h i s t o r i c a l (pre-1976) values. These h i s t o - r i c a l values combine i n various ways to form the non-zero r i g h t hand sides of the model's constraints. (The values of various bounds on v a r i a b l e s have been outlined i n e a r l i e r s e c t i o n s ) . These r i g h t hand sides involve combinations of production l e v e l s and capacity additions i n h i s t o r i c a l periods. Since s t a t i s t i c s f o r production l e v e l s are easy to obtain, but s t a t i s t i c s f o r capacity additions are not, estimates of the capacity additions are made by a simple procedure from the data on production l e v e l s . The annual growth: r a t e of a production l e v e l i n h i s t o r i c a l periods i s estimated using two years separated by several years. I t i s then assumed that the growth rate of capacity additions i s the same as that estimated for the production l e v e l , and a simple expression r e l a t i n g the capacity additions to the production l e v e l i n the period 1971-1975 i s derived. I t i s then a simple matter to evaluate the r i g h t hand side. 294 In the following, l e t X(t)"represent a-production l e v e l , and D(t) represent., a capacity addition. C.9.1 'Capacity Expansion and Retirement — 30 Year Lifetime The equations with non-zero r i g h t hand sides, separated i n t o unknowns on the l e f t and h i s t o r i c a l values on the r i g h t 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 i n 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 ) ~ 1 0 + (1 + r ) " 1 5 + (l+r)~ 2° + (1+r)" 2 5] = D(0) ' [l-(l+r)" 3°] / [1 - (1+r)" 5] . Therefore, D(0) =X(0) - [1 - (1+r)" 5] / [1 - ( 1 + r ) " 3 0 ] , and D(t) = D(0) • (l+r) f c , for t = -5,-10,-15,-20,-25 . The c a l c u l a t i o n s f o r each of the technologies having 30-year l i f e t i m e s and e x i s t i n g i n the past are 295 Right Hand Side, f o r 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 e l e c t r i c i t y , hydro, west .049 .239 .067 ' , 219 -.026 -.033 .187 e l e c t r i c i t y , hydro, east .049 .708 .169 .657 -.065 -.083 .471 coal f o r e l e c t r i c i t y , west .099 .562 .225 .541 -.034 -.055 .590 coal f o r e l e c t r i c i t y , east .099 1.240 .496 1.193 -.075 -.120 1.301 gas f o r e l e c t r i c i t y , west .099 .449 .180 .432 -.027 -.044 .472 gas f o r e l e c t r i c i t y , east .099 .317 .127 .305 -.019 -.031 .333 o i l f o r e l e c t r i c i t y , west .099 .014 .006 .013 -.001 -.002 .016 o i l f o r e l e c t r i c i t y , east .099 .076 .030 .073 -.005 -.007 .079 e l e c t r i c i t y , wood, west .099 .004 .0016 .004 0 0 .004 e l e c t r i c i t y , nuclear, east(*) .051 .046 .051 0 0 .096 o i l from t a r sands(*) .088 .059 .088 0 0 .147 (*) - r i g h t hand side take d i r e c t l y from data sources. The estimates f o r r and X(0) are based upon s t a t i s t i c s i n SC(26-206) for coal, CPA (1977) f o r o i l from the tar sands, and SC(57-207) f o r the r e s t . 0.9,-2 - Capacity Expansion and Retirement - IQ Year Lifetime These are conventional and e l e c t r i c automobiles. The only relevant equation i s X(5) - D(5) = D(0) , with a non-zero r i g h t hand side only f o r conventional autos i n each region, since there have been v i r t u a l l y no e l e c t r i c autos i n recent h i s t o r y . Since X(0) = D(0) + DJt-5)- = D(0) • [1 + (1+r)" 5] , i t 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 r i g h t hand sides. C.9.3 Capacity Expansion .and Retirement - 15-Year Lifetime These technologies are a l l of the DFC heating, except d i s t r i c t heat by cogeneration. The relevant equations are X(5) - D(5) = D(0) + D(-5) , and X(10) - D(10) - D(5) = D(0). I t i s easy to show that D(0) = X(0) / [1 + (1+r)" 5 + (1+r)" 1 0] , and D(-5) = D(0) • (1+r)" 5 . The chart below shows the estimates f o r r and X(0), taken from SC(57-207), and the ca l c u l a t e d r i g h t hand sides f o r the three h i s t o r i c a l heating fuels - gas, o i l and e l e c t r i c resistance. In the c a l c u l a t i o n s f o r e l e c t r i c resistance, i t i s necessary f i r s t to estimate the proportion of DFC e l e c t r i c i t y use which i s for heating purposes, since the s t a t i s t i c s i n SC(57-207) are for a l l e l e c t r i c i t y used i n the DFC sector. This i s done by estimating the quantities of t o t a l output energy used i n 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 o i l to a r r i v e at a r e s i d u a l which i s presumed to be heating output energy supplied by e l e c t r i c i t y . This quantity i s converted to secondary energy i n the form of input kilowatt-hours of e l e c t r i c i t y using the end-use conversion c o e f f i c i e n t l i s t e d i n section 7.1 above. The r e s u l t s are 297 Right Hand Side, f o r t = Heating by r X(0) 5 10 gas, west .045 1.534 : 1.13 .627 gas, east .073 1.329 1.03 .605 o i l , west -.006 .155 .102 .05 o i l , east -.047 .664 .388 .171 elec. resistance, west .091 .088 .07 .043 elec. resistance, east .081 .293 .23 .137 C.9.4 O i l 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 r e l a t i o n s h i p between X(0) and D(0) i s D(0) = X(0) / [1 + (1+r)" 5 + (0.59) (1 + r ) " 1 0 + (0.35)(1+r)" 1 5 + (0.21)(l+ r)" 2 0]. As above, D(t) = D(0) • (1+r) 1, f o r t = -5,-10,-15 . The values of r are estimated from data i n CPA (1977), and X(0) from SC(57-207). The chart below shows the r e s u l t s f o r the low cost conventional o i l of each region, which i s assumed to be the only h i s t o r i c a l l y e x i s t i n g o i l production ( o i l from the t a r sands i s covered i n section 9.1 above). • D(-15), • D(-10) , 298 O i l 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) . I t i s easy to show that D(0) = X(0) / [1 + (1+r)" 5 + ( 1 + r ) " 1 0 + (0.59)(1+r)" 1 5 + (0.35)(1+r)" 2° + (0.21)(1+r)" 2 5] and D(t) = D(0) • (l+rjS f o r t = -5,-10,-15,-20. The value of r i s estimated from CPA (1977), and X(0) from SC (57-207). The chart below shows the r e s u l t s f o r the low cost conventional gas production i n the two regions. Gas from r X(0) R 5 i g h t Hand S: 10 Lde, f o r 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 variabl e s , and sixteen p r i c e s , i n undiscounted, 1975$. The f i r s t eight rows i n the table are p r i c e s , whose names begin with "P", followed by the name of the constraint from which the dual a c t i v i t y was taken f or the p r i c e c a l c u l a t i o n . The next eight rows are the variables which enter nonlinearly into the objective function, expressed as average annual flows i n each period. The next eight rows i n 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 v a r i a b l e . The remaining rows i n the table are a l l the other v a r i a b l e s , expressed as average values f o r each period. 300 BASE CASE P e r i o d Ending: 1980 1985 1990 2000 2010 2020 end e f f e c t s 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 P e r i o d Ending: 1980 1985 1990 2000 2010 2020 end e f f e c t s 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 P e r i o d Ending: 1980 1985 1990 2000 2010 2020 end e f f e c t s 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 P e r i o d Ending: 1980 1985 1990 2000 2010 2020 end e f f e c t s 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 l i s t the values of .the va r i a b l e s , and sixteen prices f o r the high, and low demand cases. The p r i c e s , prefixed by "P", are derived i n the same manner as f o r the Base Case d e t a i l e d output l i s t i n g , i n Appendix D." 305 HIGH CASE Period Ending: 1980 1985 1990 2000 2010 2020 end e f f e c t s 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 ' i O S B L 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.