Mohan Munasinghe The Economics of Power System Reliability and Planning Theory and Case Study UNN-352 HD9685S.A2 M 1979 c.2 The economics of power system reliability and planning the A "0 316 71 -13i-h PRCPno iof' ENERGY LIBRARY . B. R. ~q9 The Economics of Power System Reliability and Planning SECTORAL LIBRARY INTERNATIONAL BANK FOR RECONSIRUCHON AND DFVELOPMENF SEP 0 3 1987 PR""'? M ~ OF ENERGY LIBRARY A. k Rord A World Bank Research Publication d Mohan Munasinghe The Economics of Power System Reliability and Planning Theory and Case Study SECTORAL LIBRARY INTERNAfiONAL BANK FOR RECONSTRUCTION AND DFVE[OPMENT with contributions by Walter G. Scott and Mark Gellerson Published for the World Bank The Johns Hopkins University Press Baltimore and London Copyright @ 1979 by the International Bank for Reconstruction and Development / The World Bank 1818 H Street, N.W., Washington, D.C. 20433, U.S.A. All rights reserved Manufactured in the United States of America The views and interpretations in this book are the author's and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting in their behalf. Library of Congress Cataloging in Publication Data Munasinghe, Mohan. I The economics of power system reliability and planning. Bibliography: p. 306. 1. Electric power systems-Reliability-Economic aspects. 2. Underdeveloped areas-Electric utilities- Case studies. I. Scott, Walter G. II. Gellerson, Mark. III. Title. HD9685.A2M85 338.4'3 79-2182 ISBN 0-8018-2276-9 ISBN 0-8018-2277-7 PBK. Foreword In evaluating the merits of the investment programs it finances, the World Bank has generally sought to adopt a national viewpoint, by con- sidering not only the supply costs incurred by the borrowing institution, but also the effect of these investments on other individuals and enter- prises in the economy. In view of the increasing dependence of modern economies on electric power, the capital-intensive nature of the power sector, and the shortage of economic resources in the developing coun- tries, the Bank's wider concerns have focused on, among other things, the trade-off between the rising unit costs of electricity supply and the costs imposed on consumers by the reduced reliability or quality of supply. I believe that this is the first book that seeks to provide a well- balanced and integrated economic-engineering treatment of the topic of power system reliability. It demonstrates that in order to maximize the net social benefit of consuming electric power, it is necessary to mini- mize total social costs, which consist of both the supply costs to the power authority and the costs to the consumer that are likely to result from supply shortages or power outages. This approach, which estab- lishes socially optimum reliability levels, subsumes the traditional sys- tem planning criterion based upon minimization of system costs alone. Thus the methodology presented here is both timely and relevant, not only in the Third World, but also in the developed countries. v Vi FOREWORD This book is an integral part of the World Bank's continuing research program in energy, and as such it is linked to and contributes to other elements in the overall research effort. Thus, the book analyzes the sub- ject of optimum system reliability within a broader context by discussing a range of related topics that are of more general application, including demand forecasting, system expansion planning, shadow pricing, and optimum tariff policy. YVES ROVANI Director Energy Department The World Bank Contents Foreword v Figures xi Tables xiii Preface xv Definitions xix Part One. Theory 1 Chapter 1. Objectives and Methodology 3 Summary of Methodology and Conclusions 5 Chapter 2. Introduction to Reliability 9 Reliability Concepts 9 Measures of Reliability 16 The Need for Economic Criteria 24 Chapter 3. Method of Optimizing Reliability 28 Features of the Model 28 Reliability Optimizing Planning Model 33 Outage Simulations and Optimum Reliability Levels 37 vii viii CONTENTS Chapter 4. Estimation of Outage Costs (with Mark Gellerson) 45 Nature of Outage Costs 45 Methods of Estimating Outage Costs 49 Review of Previous Studies 54 Measurement of outage costs 55 Treatment of electricity consumers by category 58 Relation between outage costs and outage duration 60 Conclusion 61 Chapter 5. Residential Outage Costs 62 Household Activities 63 Value of Foregone Leisure 65 Empirical Estimation 69 Chapter 6. Industrial Outage Costs 72 Types of Outage Costs 72 Spoiled Product Cost 74 Idle Factor Cost 75 Overtime Production Cost 77 Chapter 7. Other Outage Costs 80 Commercial 80 Public Services 82 Special Institutions 83 Rural 85 Secondary Effects 85 Chapter 8. Power System Planning and Supply Costs 87 The Investment Decision 87 Load Forecast 89 System Design and Planning 94 Costing 102 Chapter 9. Shadow Pricing 105 General Principles 105 Numeraire 109 Application of Shadow Prices 110 CONTENTS ix Part Two. Case Study 117 Chapter 10. Demand Forecast (with Walter G. Scott) 119 Land Use and Occupancy by Geographic Cell 120 Residential Electricity Consumption 124 Industrial Electricity Consumption 129 Other Electricity Consumption 131 Summary of Demand Forecast 131 Chapter 11. Long-Range Distribution System Planning (with Walter G. Scott) 134 Stages of Distribution System Development 134 Definitions and Design Criteria 135 Distribution systems 136 Voltage standards for distribution systems 137 Reliability criteria for distribution systems 139 Construction design criteria for distribution systems 142 Outage Parameters 146 Analysis of past outage data 146 Load duration analysis 148 Frequency and duration factors 149 System Design 152 Reliability, Losses, and System Costs 154 Chapter 12. Outage Cost Measurement (with Mark Gellerson) 163 Residential Consumers 163 Industrial Consumers 169 Other Consumers 174 Chapter 13. Distribution System Optimization and Conclusions 176 Modified Framework for Cost-Benefit Analysis 176 General Characteristics of Outage and Supply Costs 179 Hybrid Systems and Optimum Reliability Levels 183 Effects of Social Weighting 191 Summary and Conclusions 193 Appendixes 197 A. Basic Mathematical Concepts for Reliability Modeling 199 Laws of Probability 199 X CONTENTS Discrete State Continuous Transition Markov Process 201 Monte Carlo Simulation 208 B. Shadow Pricing Concepts 210 Conversion Factors 210 Income Effects 214 C. Load Forecasting and Distribution Primary Models (with Walter G. Scott) 217 Land Use and Distribution of Population 217 Allocation of Residential Consumers 218 Commercial Requirements 221 Street Lighting Requirements 222 Land Use and Load Forecast 224 Distribution Primary Model 229 Alternative System Configurations 246 D. Outage and Supply Cost Computations 262 Outage Costs and Energy 262 Supply Costs and Sensitivity Testing 264 E. Comparison with Previous Studies 295 F. Survey Questionnaires 300 Residential Consumers 300 Industrial Consumers 302 Glossary 303 References 306 Index 315 Figures 1.1. Flowchart of the Principal Steps in the Methodology 4 2.1 Schematic of a Simple Electric Power System 12 3.1. Reliability Level Trajectories over Time Associated with Three Alternative Expansion Plans for the Given Local Service Area 39 3.2. Total Costs Curve 40 3.3. Marginal Supply Costs and Negative Marginal Outage Costs as Functions of Reliability 41 4.1. Relation between Total Outage Costs and the Levels of Actual and Expected Reliability 47 4.2. Envelope Curve of Total Outage Costs 48 4.3. Marginal and Inframarginal Consumer's Surplus Lost 51 8.1. Size and Timing of Generation Additions to Meet Peak Demand for Power 97 8.2. Types (or Mix) of Generating Plant Required to Meet the Annual Load Duration Curve 98 9.1. Effect of Shadow Pricing on the Optimal Reliability Level 107 10.1. Cascavel Urban Zoning Classification 122 10.2. Cascavel Cell Grid, Saturations 1, 2, 3, and Layout of Principal Roads 126 10.3. Relation between Average Electricity Consumption and Net Income of Households, by Income Class, 1976 129 11.1. Major Components of a Typical Distribution Network 137 11.2. Typical Distribution Substation Layout 144 11.3. Cascavel Distribution System: Load Duration Analysis 151 11.4. Substation Locations, 1966 156 11.5. Substation Additions 158 12.1. Relation between Outage Cost and Net Income Earning Rate for Residential Customers 167 13.1. Optimization of the Outage System: Costs Versus Outage Rate 185 13.2. Medium-Reliability Plan B: Present Discounted Value of Outage Costs, by Cell 186 Xi Xii FIGURES 13.3. Medium-Reliability Plan B: Outage Cost per Kilowatt-hour Lost, by Cell 188 13.4. Evolution of Outage Rate over Time 191 A.1 Basic Markov State-Space Representation of a Single Generator 202 A.2. State-Space Diagram of Two Generators in Parallel 205 B. 1. Conversion Factor for an Importable Commodity 211 C.1. Cell Initializing Schedule for Load Forecast, by Cell 226 C.2. Service Area in 1976 230 C.3. Kilowatt Demand in 1976, by Cell 232 C.4. Load Density in 1976 234 C.5. Service Area in 1996 236 C 6. Kilowatt Demand in 1996, by Cell 238 C.7. Load Densities in 1996 240 C.8. Distribution System Model: Data Bank and Program Modules 242 C.9. Cascavel Distribution System: Circuit Number 4 243 C.10. Areas Served by Four Existing Circuits in 1976 248 C.11. Areas Served by Low- and Medium-Reliability Circuits in 1988 250 C.12. Areas Served by Low- and Medium-Reliability Circuits in 1996 252 C.13. Areas Served by High-Reliability Circuits in 1988 254 C.14 Areas Served by High-Reliability Circuits in 1996 256 D. 1. Medium-Reliability Plan B: Present Discounted Value of Outage Energy, by Cell 284 D.2. Medium-Reliability Plan B: Present Discounted Value of Total Energy, by Cell 286 D.3. Medium-Reliability Plan B: Outage Rate, by Cell 288 D.4. Relation between Costs and Outage Rate 294 Tables 10.1. Forecast of the Cascavel Urban Population, Electricity Service, Electricity Consumption, and Income 128 10.2. Industrial Electricity Consumption 130 10 3. Summary of Demand Forecast 132 11.1. Division of Voltage Variation over the Distribution System Components 139 11.2. Alternative Distribution System Characteristics 140 11.3. System Reserve Requirements, Voltage Drops, and Conductor Loading 145 11.4. Analysis of Permanent Faults during 1975 and 1976 147 11.5. Outage Statistics Based on 1975-1976 Data 148 11.6. Loading, by Period 149 11.7. Load Duration Analysis 150 11.8. Outage Durations for the Low-Reliability System 152 11.9 Outage Frequency and Duration Parameters for the Three System Designs 153 11.10. Substation Capacities 154 11.11 Number of Feeders and Length of Lines 155 11.12. Average Annual Frequency of Outages 159 11.13. Maximum Outage Duration 159 11.14. Energy and Demand Losses 160 11.15. Substation Construction Costs 160 11 16. Line Construction Costs 161 11.17. Street Light Costs 161 11.18. Annual Recurrent Costs 162 11.19. Cumulative Annual Costs 162 12.1. Residential Consumer Survey Results 166 12 2. Analysis of Regression Results 168 12.3. Industrial Outage Cost Functions 172 13.1. Global Characteristics of the Four Basic Alternative Distribution System Plans 178 13.2. Energy Use and Outage Costs, by Major Consumer Category 180 13.3. Disaggregate Energy Use and Outage Costs of Residential and Main Industrial Consumers 181 Xiii Xiv TABLES 13.4. Data for Optimization of the Distribution System 184 A. 1. Characteristics of Two Generators in Parallel 204 A.2. Characteristics of the Capacity States 206 C 1. Land Use, by Zone 218 C.2. Allocation of Residential Land, by Income Class 219 C.3. Ratio of Floor Area to Land Area 219 C.4. 1996 Saturation Factors, by Saturation Region 220 C.5. Average Residential Lot Size and Apartment Floor Area, by Income Class 220 C.6. Commercial Load Forecast Parameters 222 C.7. Summary of the Survey of Commercial Consumers 223 C.8. Standard Street Types and Lighting Characteristics 224 C.9. Allocation of Streets and Street Lighting Energy Requirements 225 C.10. Summary of the Residential Forecast 228 C.1 1. Summary of the Forecast: Commercial, Industrial, Public Lighting, Special Institutions, and No Load Forecast 229 C.12. Lengths of Feeders for the Low-Reliability System 244 C.13. Lengths of Feeders for the High-Reliability System 245 C. 14. Annual Outages, by Feeder, for the Low- and Medium-Reliability Systems 258 C.15. Annual Outages, by Feeder, for the High-Reliability System 260 D.l. Medium-Reliability Plan B: Disaggregate Data 266 D.2. Medium-Reliability Plan B: Residential, Public Illumination, and Hospital Outage Costs, by Year 269 D.3. Medium-Reliability Plan B: Industrial Outage Costs, by Year and Kind of Industry 270 D 4. Medium-Reliability Plan B: Present Discounted Values of Outage Costs 272 D.5. Medium-Reliability Plan B: Present Discounted Values of Outage Energy 274 D.6. Medium-Reliability Plan B: Present Discounted Values of Total Energy 276 D.7. Medium-Reliability Plan B: Present Discounted Values of Outage Rates 278 D.8. Medium-Reliability Plan B: Present Discounted Values of Outage Costs 280 D.9. Medium-Reliability Plan B: Grand Total, by Year 282 D.10. Medium-Reliability Plan B: Present Discounted Values of the Grand Totals 283 D. 11. Low-Reliability Distribution System Costs and Losses 290 D.12. Medium-Reliability A Distribution System Costs and Losses 291 D.13. Medium-Reliability B Distribution System Costs and Losses 292 D.14. High-Reliability Distribution System Costs and Losses 293 E. 1. Industrial Outage Costs 296 E.2. Residential Outage Costs 298 Preface The original impetus for this research arose from the need to examine all opportunities for using the scarce resources of the developing coun- tries as efficiently as possible in the electric power sector. The World Bank has pursued the goal of economically efficient use of limited re- sources in the power sector in two principal ways. On the demand side, basic research and case studies in marginal cost pricing have been carried out. The Bank is now encouraging and assist- ing the electricity authorities in Third World countries to develop and to implement power tariff structures based on long-run marginal costs. On the supply side, the Bank has researched and promoted the use of system planning and cost minimization techniques. This work has focused on the application of economic principles for choosing among established technologies, while leaving the research and development of new hardware to manufacturers and other institutions, which are bet- ter equipped to address such problems. In this spirit, the Bank's research study, "Standards of Reliability of Urban Electricity Supply" (RES 670-67), from which this book stems, was originally designed to exam- ine the possibilities for realizing system cost savings by varying power supply reliability standards. My previous work in least-cost system expansion planning had left me dissatisfied with the common practice in the developing countries of using reliability standards that often were arbitrarily borrowed from the industrialized nations. Then, about two years ago, while we were working on the applications of optimal electricity pricing rules, Jeremy Warford drew my attention to a hitherto neglected aspect of power economics involving system reliability. He suggested that it might be interesting to examine the possibilities of broadening the cost savings xv xvi PREFACE approach to include the notion of outage costs or costs incurred be- cause of poor reliability and resulting power failures. I felt that it was logical, therefore, to combine the study of reliability standards, system planning, and outage costs by expanding the basic framework of research project RES 670-67. Richard Sheehan, who was overseeing the research effort, quickly supported the idea. The eco- nomic principle developed in the study was the planning of power sys- tems to minimize the total costs to society, defined as system costs plus outage costs. This criterion for power system planning leads to the development of economically optimal reliability levels. Therefore, this broader criterion subsumes the more traditional principle of minimizing just the power system costs to meet some (arbitrary) target reliability level. The results of the research project also illustrate the close links be- tween different aspects of electricity economics, such as marginal cost prices, optimal reliability levels, and system planning. In particular, cost savings are important, because several factors have recently contributed to massive increases in both the developing and developed countries' power system expansion requirements. The 1973 OPEC oil price in- creases have resulted in a shift to more capital-intensive plants involving hydroelectric, coal, and nuclear generators. At the same time the pos- sibilities for realizing significant cost savings through economies of scale and technological advances have diminished, while the progressive electrification of rural and other areas of low consumer densities at relatively high unit costs is accelerating. Potential net savings to society resulting from the use of the new method could arise from voluntary decreases in reliability and resultant system cost decreases, from planned improvements in reliability and consequent outage cost reductions, or from a combination of both effects in different geographic areas. Although the case study presented here involved distribution system planning in a city of a developing country, the theory and principles are general enough to be applied, with some modifications, to total system planning, including generation and transmission system optimiza- tion. The method is also applicable in the developed countries. It is fitting that this research study, which was designed to improve develop- ing country reliability standards, because these standards were borrowed ad hoc from the industrialized countries, should produce results that were also relevant to the developed world. The issue of optimum relia- bility levels has recently attracted increasing attention in North America and Europe, especially following several recent major power failures, PREFACE XVii such as the New York City blackout of July 1977 and the widespread blackouts in Western Europe during the winter of 1978-79. I am grateful to my colleagues Walter Scott and Mark Gellerson for their contributions, especially their work on the case study. I enjoyed collaborating with them both in Brazil and the United States. I am also indebted to the management and staff of the Compania Paranaense de Energia ElItrica (COPEL), including Arturo Andrcoli, Edson Neves Guimaraes, Joa6 Calvo, Roberto Schulman, Amadeu Busnardo, Antonio Marcos Ferreira, Alceu Pacheco, Claudio Mesniki, Ademar Luiz Pastro, and especially Victor Waszczynskyj, for their hospitality and assistance with the case study. Thanks are due to many Bank staff members, including Yves Rovani, Richard S. Sheehan, Herman van der Tak, Fred Howell, Edward Moore, John Davis, Charles MacNealy, Carlos Mena, Cheruvari Chandran, Orville Grimes, the Research Committee, Vinod Dubey, Ardie Stout- jesdijk, David Green, Benjamin King, Frank Lamson-Scribner, Everardo Wessels, and Vatsal Thakor, for general advice and support; and to Jeremy Warford, Yuji Kubo, DeAnne Julius, Robert Saunders, Ted Minnig, Jim Fish, Colin Warren, Dennis Anderson, Alistair Stone, David Hughart, Robin Bates, Karl Jechoutek, Joseph Gilling, Ibrahim Elwan, Anandarup Ray, Lyn Squire, and Johannes Linn for illuminating discussions of a more technical nature. Among those outside the Bank, comments from Robert L. Sullivan, Alton D. Patton, Ezra Mishan, and Ralph Turvey were most helpful. Acknowledgments are also due to Anura De Silva, Michael Telson, Gerry Farnell, and John Chang for general assistance; to Monica Scott, David Teitelbaum, Emerito Asuncion, and Maria de Guillen for helping with the computations; to the municipal authorities of Cascavel, Brazil, for helpful information; and to Julieta Valencia and the staff of the MTST unit, as well as Beverley Rollins, Cindy Urban, Cecily Orr, and Pattie Koh for preparing the manuscript. My thanks also to Romesh Dias-Bandaranaike for careful proofreading and final corrections. Last but not least, I owe much to my wife Sria and children Anusha and Ranjiva for their patience, understanding, and support, and to my parents and siblings for their constant encouragement. Needless to say the responsibility for all remaining errors in the text is mine. An early draft of the text was edited by Roberta Maggenti; the final draft was edited by Judy Barry. The charts were prepared by Raphael Blow and the text was indexed by Professional Indexing of Atlanta, Georgia.  Definitions ARI Accounting rate of interest AWG American Wire Gauge CCL Critical consumption level CES Constant elasticity of substitution CF Conversion factor Cr$ Cruzerio = US$0.081 (end 1976) DU Dwelling unit EHV Extra high voltage ESWR Efficiency shadow wage rate EUSE Expected unserviced energy FAD Frequency and duration of outage FC Factor cost FTER Free trade exchange rate HV High voltage IFC Idle factor cost LDC Load duration curve LF Load factor LOEE Loss of energy expectation LOLP Loss of load probability LRMC Long-run marginal cost MCM Thousands of circular mills MOC Marginal outage cost MRS Marginal rate of substitution MsB Marginal social benefit Msc Marginal social cost MSC Marginal supply cost NFC Nonfactor cost OC Outage cost OCC Opportunity cost of capital OCF Outage cost function OCK Outage cost per kilowatt-hour lost xix XX DEFINITIONS OE Outage energy OER Official exchange rate OLSQ Ordinary least squares (regression) OR Outage rate PDV Present discounted value R Reliability level R* Reliability expectation of consumers RC Recovered cost SC System supply cost SCF Standard conversion factor SER Shadow exchange rate SPC Spoiled product cost SRMC Short-run marginal cost SWR Shadow wage rate TC Total cost VAR Reactive volt-amps XLOL Expected loss of load Part One Theory During the twentieth century, the electric power industry has emerged as one of the most vital and capital-intensive sectors of the economy in almost every country. In 1978 the United States used about 560 giga- watts of installed capacity to generate 2,200 terawatt-hours of electrical energy, or approximately 10,500 kilowatt-hours annually per capita, making it the largest and the second most energy-intensive economy in the world.' The United States devoted more than US$30 billion to in- vestments in the electric power sector in that year.2 With electric energy requirements growing at an average rate of more than 4 percent during the 1980's, these investments will exceed US$70 billion by 1990.3 In the developing countries the 1978 installed capacity and production of electricity were about 210 gigawatts and 820 terawatt-hours, respec- tively.4 Rates of growth of the demand for electricity are expected to average nearly 10 percent and will have to be met by investments of approximately US$25 billion a year during the next decade, accounting 1. Gigawatt = 10, kilowatts; terawatt-hour = 109 kilowatt-hours. 2. "Twenty-ninth Annual Electrical Industry Forecast," Electrical World (Sep- tember 15, 1978), pp. 61-76. 3 All investment costs are given in constant 1978 dollars. 4. Edward A. Moore, "Electricity Supply Forecast for the Developing Coun- tries," Energy, Water, and Telecommunication Department, the World Bank (a re- stricted circulation document) (Washington, D.C, December 1978; processed). 1 2 THEORY for more than 20 percent of all public sector investments in these countries. The worldwide trend of increases in the real costs of supplying elec- tric power is likely to continue, because of the rapid growth of demand and such factors as the shift, following the oil crisis, toward more costly coal and nuclear generating plants and the dwindling availability of cheaply exploitable hydroelectric sources. Also, there are few oppor- tunities to realize further significant economies of scale, especially as systems continue to expand into areas of lower population density at higher unit costs. The massive investment needs for power imply that even small im- provements in efficiency will lead to significant savings. These are espe- cially important for those developing countries that face shortages of both local and foreign-exchange resources. Traditionally, the major em- phasis has been placed on improving technical and financial efficiency through least-cost, long-range planning for system expansion, as well as by optimizing short- and medium-term system operation and provid- ing better management of utilities. These considerations on "the supply side" of the supply-demand equation have been tackled with a remark- able degree of success, usually by engineers using technically and finan- cially oriented solutions. More recently, power economists have focused attention on the objectives of economic efficiency in the national con- text. These developments will have a growing and significant effect on "the demand side," chiefly by the application of the principles of rhar- ginal cost pricing. On the supply side as well, the acceptance of economic arguments is reflected in the use of economic opportunity costs. These costs are represented by shadow prices that are the true costs of eco- nomic resources, instead of purely financial or accounting costs. Chapter 1 Objectives and Methodology The current emphasis on economic efficiency in the electric power sec- tor, especially in the areas of marginal cost pricing and improved tariff policy, is welcome and long overdue. But the topic of electric power system reliability, or dependable quality of electricity service, has pre- viously received detailed treatment only from the supply side, using engineering models and analysis. The socioeconomic effect of the re- liability of electricity supply on consumers has been examined in a more general and descriptive way. Thus, the traditional design and planning of power systems has been based on the principle of minimizing the supply costs required to meet a certain load at a given level of relia- bility. Increasingly, economists are realizing that even the most sophis- ticated planning models for least-cost expansion of power systems are usually developed with respect to arbitrary standards of supply relia- bility. These standards are derived from past practice and vague notions about the quality of service that would be acceptable to the electricity- consuming public. Until recently, investigators have ignored the effects on the demand side that relate to the economic worth of reliability. The problems in- volved in measuring the economic benefits of improved quality of service were the primary reasons for this neglect. As reliability is presented in this book, the imbalance is addressed by considering the level of relia- bility as a variable for which optimum values would be developed during the system planning process, rather than as an arbitrarily imposed stand- 3 Figure 1.1. Flowchart of the Principal Steps in the Methodology mEstimate of marginal Iteratve fedback oop (, R*)supply costs and new SC'R" F--------------------price and reliability expectation projections Systm moelsDesign feedback and data Revised s p, R* forecastT O *ltordsivtnad p,pan R*d forecas an-orcs 4: rgnl p *La-eadSC" Cost-benefit analysis Optimal system Original p* n Load-demand R* forecastprojections I Outage cost Revised models and Esimt ofecst marina L Iterative feedback loop (R*) J Note: p = price; R* = consumer's reliability expectation- R = reliability level, SC = supply costs OC - outage costs, TC -total costs; and NB = net benefits. Maximizing NB yields the optimal system plan m and the corresponding reliability R"' at the minimum value of TC' = SC' + aC'. OBJECTIVES AND METHODOLOGY 5 ard. To achieve this goal, a social cost-benefit analysis is needed to evaluate the inherent tradeoff between the increase in the power system supply costs required to achieve a higher level of reliability and the cor- responding decline in outage costs: that is, the economic costs incurred by electricity consumers because of power shortages. In other words, at a given electricity price the optimum reliability level, which maximizes the benefits that consumers receive by using electricity after subtracting the supply costs, should be established at the point at which the marginal increase in the supply costs is exactly offset by the marginal decrease in outage costs. In most countries such a plan would result in significant net economic savings. This study highlights the importance of developing and applying a new criterion for power system planning that is based on optimal relia- bility levels. Using a dual economic-engineering method, it is shown both theoretically and operationally that it is possible to establish an optimum plan for long-run power system expansion and a correspond- ing range of reliability levels that will produce the greatest net social benefits. Such a balanced treatment of the effects of reliability on both the supply and demand side requires accurate estimates of system costs and outage costs. Estimates of system costs may be determined from straightforward engineering-economic considerations normally associ- ated with power system design and planning. Estimating outage costs is a more difficult task, however. Therefore, new models and detailed methods are presented for analyzing the various ways in which elec- tricity is used by different categories of consumers. Summary of Methodology and Conclusions Figure 1.1 is a schematic representation of the basic steps involved in the methodology presented in this book. There are two major parts to the text: the theory and a case study. The order of the chapters fol- lows the logic of the flow chart shown in the figure. First, a framework and a set of models are developed to analyze the economic costs incurred by different categories of consumers-residen- tial, industrial, and others-as a result of electric power shortages of vary- ing intensity. Concurrently, a disaggregate long-range, load-demand fore- cast of perhaps twenty years is estimated, based on an assumed evolution of electricity prices within the area to be served by the electric power utility. Next, using system models and data, several alternative (least- 6 THEORY cost) power system plans are prepared that will meet this future load at different levels of reliability. The expected annual frequency and the duration of power failures associated with each alternative system de- sign or plan are estimated for the entire period that is forecast. In addition, the time these shortages occur and the average numbers and kinds of consumers affected are also projected. To determine the total future outage costs for each system plan, the outage frequency and duration results are used in the consumer outage- cost models. On the supply side, the investment and operating costs of each alternative design can also be estimated. A cost-benefit model is then used to compare the outage costs with the corresponding power system costs attributable to each alternative plan. At this stage, some preliminary feedback of forecast frequency and duration data, as well as disaggregate outage costs and system costs from the cost-benefit module, may be used to improve system design even further. Finally, the optimum long-run system expansion plan and a range of associated reliability levels are established, which maximize the net social benefits or, equivalently, minimize the total costs to society-both system costs and outage costs. At this optimal point, the marginal supply costs of improving system reliability are equal to the corresponding benefits from the expected marginal outage costs avoided. Two further pbssibilities exist for incorporating feedback effects, as shown by the optional iterative loops in figure 1.1. The principal return path is through the effect of electricity prices on the load forecast. This would occur if the new optimized system plan requires changes in the original assumptions regarding the future prices that were used to make the initial projection of demand. A similar but less important feedback effect may also be incorporated into the analysis. This would involve the effect of changes in consumers' reliability expectation on both de- mand and outage costs. Therefore, if necessary, it is possible to repeat these computations by iterating through the model several times to arrive at a mutually self-consistent set of price, demand, and optimal reliability levels. Generally, such feedback effects would be important mainly in the theoretical sense, and, therefore, in practice a single iteration may often be considered sufficient. This optimizing methodology adds an extra dimension to the more traditional procedure followed by system designers. In this approach, the reliability level is treated as a variable. The sum of the outage and the power system supply costs is minimized, while the system meets the load requirements without violating various technical and other con- OBJECTIVES AND METHODOLOGY 7 straints. This broader framework effectively subsumes the conventional technique of system planning, in which only the supply costs are mini- mized, subject to meeting some predetermined target level of reliability, the load requirements, and all other constraints. The model presented here is flexible enough to permit a further level of sophistication in the analysis by allowing the demand forecast to be varied by the effects of price feedback. The theoretically important point concerning the simul- taneous optimization of both price and reliability levels is also accounted for in this practical way. The costs consumers incur as a result of electric power shortages may be either direct or indirect outage costs. The direct costs occur when an outage actually takes place. Indirect costs arise if consumers adapt their activities by paying more to become less susceptible to outages, or if they resort to standby energy sources. Therefore, the relative im- portance of the direct and indirect components in total outage costs depends on consumers' expectations about the reliability of future sup- ply and the extent of behavior changes to avoid outages. In estimating outage costs, disruptions in the productive activity of electricity users is a better indicator than consumers' surplus. If con- sumers' surplus is used, outage costs probably will be underestimated because the customers' "willingness-to-pay" for planned electricity con- sumption is generally much less than the economic costs incurred be- cause of an unexpected outage. System supply costs must be based on the physical and operating characteristics of the power system. These costs should be estimated in the national economic context, by using shadow prices when market prices are distorted This method is prefer- able to the common practice of using only financial or accounting con- cepts and costs, which are more relevant from the viewpoint of a private electric power utility company. To test the methodology, a case was designed that optimized the re- liability of the distribution system in Cascavel, Brazil-a small city in a developing country. The study demonstrated that it was possible to optimize the long-range design of a distribution system to minimize the total costs to society and thereby realize substantial net social savings. The results also indicated that a better optimum may be achieved by varying the reliability of the distribution system according to the intensity of outage costs imposed on consumers in different geographic areas. In general, the practical implementation of the theory was quite straight- forward, using data as inputs to three basic computerized models de- veloped specifically to determine (a) the demand forecast, (b) the alter- 8 THEORY native designs of the distribution systems, and (c) the corresponding system costs and outage costs. Since the economic aspects of the meth- odology used were quite general, it would be possible to treat generation and transmission system reliability in the same way: that is, to optimize the design of the entire electric power system. From the theoretical model of household behavior presented here, two conclusions may be reached. First, to the residential electricity con- sumers, the principal outage cost incurred is the loss of evening leisure caused by lack of electricity. It is assumed that daytime domestic activi- ties interrupted by outages could be rescheduled without much incon- venience. Second, the marginal monetary value of this leisure is equal to the net effective wage or income earning rate of the household, on the basis of the consumers' labor-leisure choice. Both hypotheses were verified in the case study. The survey showed that residential consumers were willing to pay in the short-run to avoid unexpected outages. Industrial outage costs by major kinds of industrial users also were analyzed in detail. They included spoilage, idle factors of production, and recovery of lost production during regular working hours, as well as overtime. The analysis was helpful in identifying the industries that are most sensitive to outages. Such information would be useful in the context of load shedding, for example, to rank industries by outage cost per kilowatt-hour lost. Techniques for measuring the outage costs of other kinds of consumers are also discussed, but these were found to be rather insignificant in the case study. Because every country and power system has unique characteristics, the results of the case study cannot be used to draw wide-ranging con- clusions regarding generally desirable levels for power system reliability in other countries. The overall methodology, however, remains valid and could be applied elsewhere. The net savings to society that could have been realized by adopting the reliability-optimizing approach amounted to approximately 0.04 percent of the total value added, or about 5 percent of power system investment in Cascavel. If a conserva- tive estimate of one-half of these figures were accepted as a benchmark, the total potential net savings on the sum of system and outage costs in the capital-scarce developing countries alone would amount to ap- proximately US$4 to 5 billion (in constant 1978 dollars) during the next ten years. Before these estimates can be confirmed, however, the new methodology must be applied further to problems of power system optimization, especially at the generation and transmission level. The potential case studies should involve several consumer categories in different physical and socioeconomic environments. Chapter 2 Introduction to Reliability Electric power system reliability and security is a broad topic with a voluminous bibliography.' This chapter summarizes those aspects of reliability that are relevant to the economics of power systems, but no attempt is made to review the literature completely.2 The various meas- ures of reliability currently used are defined and described, and the weaknesses of the existing concepts of reliability are discussed, as well as the need for developing reliability standards that are based on explicit economic criteria. Reliability Concepts A relatively simple concept of reliability applicable to nonrepairable systems was originally developed in the aerospace industry. Reliability 1. See, for example, S. Vemur, "An Annotated Bibliography of Power System Reliability Literature," Proceedings of the IEEE Power Engineering Society Sum- mer Meeting, Los Angeles, July 1978, paper no A78548-0; and Roy Billinton, "Bibliography on the Application of Probability Methods in Power System Relia- bility Evaluation," IEEE Tiansaction on Power Appaiatus and System, vol. PAS-91 (March-April 1972), pp 649-60. 2 See, for example, A D Patton and A. K Ayoub, "Reliability Evaluation," Systems Engineering for Power: Status and Piospects, USERDA Conference, Hen- niker, New Hampshite, August 1975, NTIS no. CONF-750867, pp. 275-89; N. D. Reppen, R J. Ringlee, B. F. Wollenberg, A. J. Wood, and K. A. Clements, "Proba- bilistic Methodologies-A Critical Review," Systems Engineering for Power: Status and Prospects, pp. 290-310. 9 10 THEORY was broadly defined as the probability that a component or system would perform its intended functions satisfactorily during a given period of time under actual operating conditions.3 The more modern and ap- propriate concept is to think of the repairable electric power system component as existing in one of many possible states. The simplest example would involve two states typically labeled "up," or functioning, and "down," or unavailable (see appendix A for details). When the component fails, it undergoes a transition from the up to the down state, and, conversely, when repairs are completed, it returns from the down to the up state. The concept of reliability during some period may then be introduced as the fraction of total time that the component spends in the up state. Greater sophistication of analysis is possible by defining additional intermediate states in which the component is only partially functioning. The concept of reliability for an electric power system is similar, but more difficult to determine, because the system consists of many com- ponents, and their interaction adds greatly to the complexity of the analysis. Thus, the reliability or ability of the system to perform its task satisfactorily will depend on the functioning of many components. Also, because of redundancy, the system may perform adequately even though some of its components are nonfunctioning or not functioning perfectly. The interaction of individual components in the system is easiest to analyze when their failures are mutually independent; if the failure of one component is related to or influences the failure of others, the determination of overall system reliability again becomes more complicated. Clearly, the definition of system reliability requires that acceptable levels of performance for the system be carefully defined in relation to its purpose. An electric power system must supply electricity to con- sumers at the power level they want and at the time and place of their choosing, while maintaining an acceptable quality of service: that is, voltage and frequency levels must lie within specified limits. Therefore, before discussing reliability concepts, the different components of a typical power system are described briefly. The basic constituent ele- ments of a power system may be analyzed in terms of their functions: generation, transmission, and distribution. The concept of a generating 3 See Igor Bazovsky, Reliability Engineering and Practice, Prentice-Hall Space Technology Series (Englewood Cliffs, N.J.: Prentice-Hall, 1961). INTRODUCTION TO RELIABILITY 11 source or power plant is relatively unambiguous. Both transmission and distribution facilities carry the electric power from the source to the consumer. These ideas are further clarified in figure 2.1, a schematic diagram of a simple power system. The output from two power generating plants G, and G2 (hydro- electric or thermal) is increased to the high voltage (Hv) level at source by the respective transformers TF, and TF2 and is fed into the busbars in transmission substation TS via the HV transmission links T, and T2. At TS, the voltage is further increased to the extra high voltage (EHV) level, before the power is transmitted through the EHV line T, to substa- tion TS2. A voltage reduction occurs at TS2, after which the electric power is fed, through i-v transmission lines T, and T,, into the distribu- tion substations DS, and DS2 located close to the load centers. Another voltage reduction occurs at DS, and DS2, and then power flows out of the distribution substation busbars, through primary feeders such as F,, to various distribution transformers (for example, DT,), where the voltage is decreased further. Finally, the power is delivered to a repre- sentative consumer, through the secondary distribution line S., and service inlet and meter M. In transporting power the general principle is that voltage level de- pends on distance and power flow. Transmission lines are used to carry large amounts of power over long distances, while distribution lines in- volve smaller power flows over shorter distances. The technical dis- tinction between transmission and distribution facilities is usually made on the basis of their operating voltages. Although voltage standards vary greatly from country to country, broadly accepted definitions for voltage levels are as follows: EHV transmission, more than 220 kilovolts; Iiv transmission, 45 to 220 kilovolts; primary distribution, 6 to 25 kilo- volts; and secondary distribution, 110 to 380 volts. In practice, con- siderable overlap is likely, and facilities operating at voltages in the range of 25 to 45 kilovolts (often called subtransmission), may be in- cluded within the distribution or transmission category, depending on their function. An operating power system is much more complex than the one de- scribed above and in general has many generating sources linked to many load centers via an interconnected transmission network. Trans- mission interconnections may be used to tie the power systems of sev- eral different utilities together to form an even larger power pool. The distribution grid at a single load center would serve thousands of con- sumers. Furthermore, many other components, including protective and 12 THEORY Figure 2.1. Schematic of a Simple Electric Power System G, G TF, TFTFy TT2 TS, -III TS, I I L.-- ---J To T, t sion s o S DS2 , DT2itibto ubttos I II - - Fy eFu Ms DTI Note: G , G2 generators; TF,, TF d = voltage transformers; T, TS2, T,, T = HV transmission lines; TS,, TS2 = transmission substations, T, = EHV transmission, DS,, DS2 = distribution substations; F,, F2 = primary feeders (or circuits); DT,, DTL = distribution transformers; S,, S2 = secondary kines; M,, M = customer service inlets and meters, INTRODUCTION TO RELIABILITY 13 relaying devices as well as load control and dispatching equipment, would play important roles in a large interconnected system. Therefore, an ideal electric power system that unfailingly supplies power to consumers whenever required is by definition a perfectly re- liable one, and, conversely, a system that is never able to deliver elec- tricity to users could be termed totally unreliable. All real world power systems lie between these two extremes. As a system's reliability level is improved, a trade-off occurs between increased costs of supply and reduced inconvenience and costs to consumers from fewer power short- ages. Therefore, criteria and methods to assess and rank systems by reliability level must be developed. Before discussing measures or in- dexes of reliability, an examination of the causes and manifestations of supply shortages would be helpful. As in the case of any other good or service, electric power shortages occur when demand exceeds supply. Power systems are usually planned so that the supply is sufficient to meet forecast demand. In general, however, there will be unexpected variations in both projected supply and demand which would result in shortages; that is, less than perfect reliability of supply. The stochastic or random nature of demand is mani- fested by unforeseen increases in the magnitude of the load. One example is the demand placed on a system when unusually warm weather causes consumers to use their airconditioners unexpectedly. Similarly, the supply of power may also be subject to random variations. The unex- pected failure or outage of the various components of a power system or the lack of water for hydroelectric generation caused by an unusual drought are two examples of potential supply problems.4 In recognition of these random changes in supply and demand, sys- tem planners accept that any system will suffer a certain number of future shortages. The expected long-run level of these built-in shortages, which may be estimated with the help of past data, constitutes the static element of system reliability. There is also a dynamic component of reliability, because to the extent that the planners have failed to cor- rectly anticipate and analyze these supply and demand uncertainties, the actual incidence of shortages will not correspond to the planned static level. Furthermore even when the demand forecast is accurate and the system is well planned, the level of long-run reliability may fall 4. For a detailed definition of a component outage, see IEEE Standard no. 346- 1973 (New York: IEEE, 1973). 14 THEORY below the expected level because of inadequate short-run operating cri- teria and procedures, as described later in this chapter. From the consumers' viewpoint, power shortages manifest themselves in several ways, including complete interruptions of supply (blackouts), frequency and voltage reductions (brownouts), and unstable service caused by erratic frequency fluctuations and power surges. Although all these phenomena are likely to inconvenience and to impose costs on consumers, the consequences of supply interruptions are the most se- vere. For example, supply interruptions at night will disrupt most ac- tivity, but a voltage reduction may cause lesser effects, ranging from the inconvenience of dimmed lights to excessive current drain, over- heating, inefficient operation, and reduced lifetime of electric motors. The decreased life-span of fluorescent lights is another long-term result of brownouts. Frequency variations would affect a power system's auto- matic control equipment, as well as other synchronous devices such as electric clocks. Power surges could also damage some equipment, but these consequences are difficult to identify. The definition of outage costs and the theoretical framework developed in chapters 4 to 7 for estimating these costs encompass the expenses consumers incur because of all types of shortages. In practice, however, the principal emphasis will be on the effect of supply interruptions. Moreover, the effects of random or unexpected interruptions will be stressed, since they are likely to impose much greater hardships on users than known or planned power cuts. (See chapter 4, Estimation of Outage Costs.) Sufficient redundancy and excess capacity throughout the system to meet unexpected contingencies are the major safeguards against short- ages. Once a failure has occurred, the cause of the problem should be analyzed as quickly as possible, and a set of predetermined emergency procedures implemented to restore the system rapidly to normal op- eration. At the generation level, excess capacity is expressed in the form of reserves. In the short-run context, spinning reserves are maintained by practically all systems to follow minute-by-minute load variations and to meet sudden contingencies, such as the forced outage or unexpected failure of a generating unit. These reserves consist of generators that are already connected to the busbars and are ready to take the load immediately, for example, machines that are operating at less than full output. Rapidly interruptible loads and generators, such as hydroelectric units operating in the pumping mode, are also considered equivalent to spinning reserves and are often loosely included in this category. Ma- chines that require longer times to connect to the system to carry load INTRODUCTION TO RELIABILITY 15 constitute the system's nonspinning reserves, typically ranging from fast-starting hydroelectric units and gas turbines to slow-starting thermal units. In the longer run, the system's operating reserves, which include both spinning and nonspinning components, are available to meet supply shortages. Operating reserves are especially useful when the need for more 'eneration is predicted sufficiently in advance of the shortage for example, when it is anticipated that load would build up more rapidly than originally projected because of a load forecasting error. The terms hot and cold reserves are also used in system operation. Hot reserve usually refers to a thermal plant available for service within a few minutes, such as a generator with a hot boiler, that only requires startup of the turbine. Cold reserve consists of a plant that has to be brought into operation from "cold" conditions, with startup times ranging from several minutes for hydroelectric generators to many hours for thermal units In an emergency, as the demand approaches the total supply (includ- ing all reserves, generators operating at overload levels, and the maxi- mum possible amount of power purchased from neighboring systems), measures must be taken to reduce the load. These would include vol- untary decreases in demand, voltage and frequency reductions, and either operator-controlled or automatic load shedding.5 The connecting and disconnecting of generators and loads to the system also cause technical problems involving sequencing, matching, and synchronization, that may affect the level of reliability, but these are usually handled routinely If the excess demand is not curtailed in this way, the system could become unstable, with frequency fluctuations and power surges, the tripping of and damage to generators and lines, and so on, that finally culminate in widespread and unpredictable blackouts. Therefore the orderly reduction of load will help to limit shortage costs, especially by decreasing the number of consumers who would suffer the most drastic form of shortage-a supply interruption Decreasing the system voltage and frequency levels constitutes one of the most effective methods of reducing modest amounts of load and thereby significantly lowering the incidence of supply interruptions. Voltage reductions are generally preferred, because decreasing the sys- 5. See, for example, U. Di Caprio and R. Marconato, "Automatic Load Shed- ding in Multiarea Elastic Power Systems," Electric Power and Energy Systems, vol. 1 (April 1979), pp 21-29. 16 THEORY tem frequency is often unacceptable where the system is interconnected with other systems, and it also results in stability and synchronization problems with the generators within the system. For example, the Cen- tral Electricity Generating Board (CEGB) in England, which operates one of the world's largest fully integrated systems, can rapidly shed up to 7.5 percent of the load by appropriate voltage and frequency reduc- tions of 6 percent and 0.5 hertz, respectively, before disconnecting consumers. These measures would result in about a tenfold decrease in the risk of interruptions.6 In a typical large interconnected system, a 0.2 percent drop in the operating frequency is likely to be associated with about 0.5 percent reduction in the demand, whereas 0.5 percent drop in the voltage level of the system would also have a comparable effect on the load. Bulk transmission reserve capability is ensured by following basic design principles such as: (a) having adequate thermal margins (to prevent overheating); (b) ensuring steady state, dynamic, and transient stability against disturbances such as the buildup of large voltage oscil- lations following a lightning stroke; (c) avoiding bottlenecks in power flows; and (d) providing alternative pathways to feed load centers by using ring systems. In an interconnected system, it is important to avoid prolonged and extensive blackouts caused by the progressive overloading and cascading failure of many lines, following the initial outage of a single link resultilg, for example, from a three-phase fault to ground.7 The design of distribution networks also provides some redundancy. These design techniques allow extra safety margins for substation ca- pacity and for power flow along feeders, and use switches to isolate faulted sections of line and to connect customers temporarily to circuits unaffected by the outage. Measures of Reliability Two different but related concepts will be discussed in this section: the assessment of power system security and the use of system relia- bility measures. The first has an essentially short-term objective of 6 See: R. W. Werts, "International Criteria and Practices for System 'Relia- bility," Symposium on Reliability Criteria for System Dynamic Performance, IEEE Publication no. 77Chl221-1-lPWR (New York, 1977), pp. 24-28 7. See, for example, G. L. Wilson and P. Zarakas, "Anatomy of a Power Fail- ure," IEEE Spectrum (February 1978), pp. 39-46. INTRODUCTION TO RELIABILITY 17 guiding system operations on an hourly or daily basis; the second in- volves reliability evaluation for the long-range planning and design of power systems over many years. Since this book is particularly concerned with the long-run potential tradeoff between system costs and outage costs, the second concept is more relevant. To provide a more complete perspective, however, the first viewpoint is briefly summarized before the second aspect is discussed in greater detail.8 Because of the basi- cally mathematical nature of the models underlying these concepts, some jargon is unavoidable, but an attempt is made to keep the presentation as nonmathematical as possible. A more rigorous treatment of some of the more important mathematical concepts is given in appendix A. Power system security assessment and enhancement in the short run involve the use of preventive measures and on-line decisions to main- tain or to improve the security level of a power system in operation. In the modern (probabilistic) view of a secure operation, the system is essentially characterized by several states.o A contingency may cause the transition of the system from the normal or secure state, in which loads are met subject to the operating constraints, to the alert or insecure state. Unless preventive action is taken to restore the secure state, a further transition to the emergency state could occur. This is equivalent to the conditions of shortage described earlier. Corrective or emergency controls are required to return the system directly, or through the "re- storative" state, to the alert state, from which a further transition to the secure state may be made. Security assessment helps to characterize the various states in relation to security indexes or functions, and to deter- mine the appropriate response of the system controller.' Control may be exercised by taking simple (deterministic) but in- herently inflexible actions, for example, implementing a predetermined operator response to a specified contingency. More sophisticated re- 8. For details, see, A. R. Debs and A. S Benson, "Security Assessment of Power Systems," Systems Engineering foi Power: Status and Prospects, pp 144-76, and L. P Hajdu and R Podmore, "Security Enhancement for Power Systems," Systems Engineering for Power. Status and Prospects, pp 177-95. 9. See Thomas E. DyLiacco, "The Emerging Concept of Security Control," Proceedings of the 1970 Symposium on Power Systems (Lafayette, Ind.: Purdue University, May 1970). 10 See Tor-odd Berntsen and Arne T. Holen, "Security Control in Network System Operation," Reliability of Power Supply Systems, IEE Conference Publi- cation no. 148 (London- Institute of Electrical Engineers, February 1977), pp. 154-57; and Karel Janac, "Control of Large Power Systems Based on Situation Recognition and High Speed Simulation," IEEE Transactions on Power Apparatus and Systems, vol. PAS-98 (May/June 1979), pp. 710-15. 18 THEORY sponses would involve rapid on-line analysis of a (probabilistic) com- puter model of the system, such as the one described earlier. The model would use an existing data base and on-line telemetered input values of key system variables to identify and to characterize the con- tingency. The essential link between this concept of system security and the long-run viewpoint used in system planning is the use of probabilistic security/reliability indexes to describe the state of the system. The models used in each case are generally different, however, with system security assessment relying on time-dependent probabilities to charac- terize system states, whereas long-run system reliability (discussed be- low) is based on corresponding steady-state probabilities. In the context of long-range system expansion planning, reliability concepts are required to establish target reliability levels and to analyze and compare the future reliability levels of different system design op- tions with these target values. The initial use of reliability criteria in sys- tem planning relied on simple rule-of-thumb, deterministic approaches. For example, the concept of ensuring an adequate reserve margin (such as 20 percent above the expected peak demand) or use of a single or double-worst-fault design criterion (that is, the capability of the system to meet the load after the loss of the largest or the two largest gener- ating units respectively) was common for many years in generation planning. Such rules are still used by some smaller systems. Combined deterministic criteria may also be used, for example, one requiring suf- ficient capacity to withstand the loss of the largest unit, and to still retain an adequate reserve margin. Given the basically probabilistic character of system reliability and component outages, the next stage of sophistication in reliability analysis led to the development of combinatorial (probabilistic) methods. These combinatorial models made it possible to compute the long-run expecta- tion of the future state of a large and complex system. One example would be the system's inability to meet the predicted load. In these mod- els relevant load data and information regarding the probable avail- ability of the individual system components are appropriately combined according to the axioms of probability "1 Familiar reliability indexes such 11. The basic laws of probability involved are the well-known ones that define additivity, multiplicability, and complementarity. In this context, the assumption regarding the independence of random events is particularly critical and should be carefully verified, since it implies that different system components fail and are repaired independently of one another. (See appendix A for a more detailed discussion.) INTRODUCTION TO RELIABILITY 19 as the loss-of-load-probability (LOLP) and loss-of-energy-expectation (LOEE) were estimated using this approach.12 The latest generation of probabilistic tools for power system relia- bility analysis involves overlaying the combinatorial method by the more recent concept of the system viewed as a stochastic process evolv- ing over time. In this instance, the system commonly is modeled as a discrete-state, continuous-transition Markov process, which is discussed below." At any given moment the system may change from one state to another, because of events such as component outages or actions designed to restore normal operation. The system may be analyzed when all the possible states are identified, and the rates of transition between them are known. The transition rates are determined by the correspond- ing contingencies or restorative control actions. The transition rate ma- trix, which specifies the transition rates between all possible pairs of states, provides a useful mathematical summary of the Markov process. The latter also may be visually depicted by a state-space diagram, with several closed boxes representing the system states and with a series of lines joining the boxes representing the possible transitions. This type of model facilitates the estimation of the expected frequencies and dura- tions of outages, the modeling of the effect of exogenous shocks, such as the imposition of a sudden load on the system, and the treatment of nonindependent events, for example, the failure and repair of different system components. Given its importance, a mathematical treatment of the Markov model is provided in appendix A. The several indexes of reliability currently used are summarized in this section, including their advantages, disadvantages, and the methods of computing them. The following discussion begins with the proba- bilistic measures of system reliability, since the simple rule-of-thumb criteria, such as the reserve margin, have already been described. The LOLP criterion is commonly used, especially in generation plan- ning. System failure is most often defined in terms of inability to meet the daily peak load. (See chapter 8, Power System Supply Costs, for a 12 The LOLP measure was introduced first in 1947, see G Calabrese, "Gen- eration Reserve Capacity Determined by the Probability Method," AIEE Tians- actions, vol 66 (1947), pp. 1439-50 For a more recent review of probabilistic reliability indexes, see Roy Billinton, Robert J Ringlee, and Allen J. Wood, Power System Reliability Calculations (Cambridge, Mass.- MIT Press, 1973). 13. See Chanan Singh and Roy Billinton, "Frequency and Duration Concepts in System Reliability Evaluation," IEEE Transactions on Reliability, vol. R-24 (April 1975), pp. 31-36. 20 THEORY discussion of the load characteristics.) Therefore, in the context of a generation study, the LOLP is usually computed not as a strict proba- bility, but rather as an expectation; this may be interpreted as the aver- age number of days over a long period, during which the daily peak demand is expected to exceed the available generating capacity. With this definition the LOLP is also less frequently, but more correctly, re- ferred to as the loss-of-load expectation or LOLE. For example, the tar- get LOLP frequently used in the United States is one day in ten years; in European countries, the corresponding standard varies from one day in fifteen years to one day in two and a half years. In transmission and distribution planning, time is measured continuously, rather than in terms of the daily load cycle, and therefore the LOLP is given in terms of the long-run average fraction of total time the system is expected to be in a state of failure.14 The latter might be defined as an interrup- tion of supply, or sometimes as a voltage reduction or component over- load. The LOLP is often supplemented by the expected-loss-of-load (XLOL) index, which indicates the expected magnitude of the unsupplied load, given that a failure has occurred; therefore, XLOL is a conditional expec- tation. Another index that measures the magnitude of system failure is the loss-of-energy expectation or LOEE (also called the expected un- serviced energy or EUSE). The LOEE is the expected amount of energy not supplied because of outages in the long run, and it may be expressed in units of energy or as a fraction of the total energy demanded during a certain period. The expected frequency or mean recurrence time be- tween outages and their expected duration is another pair of reliability indexes (frequency and duration or FAD). These indexes are used widely in transmission and distribution system planning, but rather infrequently in generation studies. Several general points about measures of reliability should be noted. First, each of the indexes has its strengths and weaknesses, and cannot individually provide a complete description of outages. For example, although it is a measure of the probability of system failure, the LOLP does not indicate the expected magnitude of the load lost during such a contingency. In contrast, the XLOL provides the expected magnitude, but neither the probability nor the average duration of an outage. Like 14. See T. P. Hayes, Jr., R. P. Webb, and J. T. Day, "A Quantitative Method for Transmission System Reliability Calculations," Proceedings of the IEEE Power Engineering Society Summer Meeting, Los Angeles, July 1978, paper no. A78566-2. INTRODUCTION TO RELIABILITY 21 the LOLP, the FAD measure also does not indicate the mean size of the failure, but because the FAD indexes are specified at the load-point or particular point of consumption, the number of affected customers and the magnitude of the interrupted load may be deduced. Second, because the underlying models, the methods of computation, and their interpretation may vary considerably, the indexes are generally neither comparable, nor consistent in the sense that they could yield different rankings of systems by reliability level. Often, even the same index may be calculated in more than one way. For example, the LOLP can be derived by using a conventional model in which each generator is represented in two or more discrete states, or alternatively, by model- ing the whole generating system as a normal distribution." Similarly, the FAD measure of outages would be interpreted differently, if it is defined at the load-point than if it is specified as a systemwide generation- transmission index.'6 Finally, if the LOLP and LOEE criteria are com- pared, the former index will rank a system that has a long-lasting failure on one day above a system with two short failures on separate days, whereas the latter measure is likely to reverse the order of ranking. The third and perhaps the most important point is that because of the way that reliability indexes are usually computed as predictors of long-run average system performance, they often do not reflect actual experience well. The basic reason for this divergence between prediction and observation is that the effects of operating procedures and con- straints are rarely considered when long-run reliability indexes are com- puted. These operating criteria are important in short-run security assessment models, as discussed earlier, and, therefore, also modify the long-run system reliability. In particular, including operating considera- tions in generation and transmission system reliability studies leads to formidable computational difficulties, especially those caused by genera- 15. See, for example, R N. Allan and F. N. Takieddine, "Generation Model- ling in Power System Reliability Evaluation," Reliability of Power Supply Sys- tems, IEEE Conference Publication no. 148 (London: Institute of Electrical Engi- neers, February 1977), pp. 47-50. 16. See, for example, R N. Allan and F. N. Takieddine, "Network Limitations on Generating Systems Reliability Evaluation Techniques," Proceedings of the IEEE Power Engineering Society Winter Meeting, New Yoik, January-Februaly 1978, paper no. A78070-5; and G. E. Marko, "A Method of Combining High Speed Contingency Load Flow Analysis with Stochastic Probability Methods to Calculate a Quantitative Measure of Overall Power System Reliability," Pro- ceedings of the IEEE Power Engineering Society Summer Meeting, Los Angeles, July 1978, paper no. A78053-1. 22 THEORY tor dependencies. Therefore, their effects traditionally have been ignored, except in Monte Carlo simulation and in advanced analytical models. These methods are described later in this chapter. Furthermore, relia- bility indexes that encompass large blocks of load and a chain of voltage levels cannot capture the variations in reliability experienced by indi- vidual consumers. For these reasons, the estimated indexes may be much more significant in the relative rather than the absolute sense. In this respect, forecast values of distribution system reliability indexes are likely to be somewhat more accurate than comparable generation and transmission system indexes. Two broad categories of mathematical techniques are used to calculate the values of power system reliability indexes. The analytical methods rely on the direct, or analytical, manipulation of the basic probability axioms.17 In contrast, the Monte Carlo methods use the computer first to simulate various random events in a way that is similar to throwing dice. The simulated events include the mean time to failure and repair time of components. Then, the system reliability levels are estimated (see appendix A).18 Analytical models tend to be compact and elegant, but become in- creasingly difficult to solve as the complexity of the system increases. Monte Carlo methods, however, always yield results with a minimum of assumptions and without explicit specification of stochastic system behavior. Yet they generally use large amounts of computer time and often require resimulation of the entire system, even when small param- eter changes are made. Using the analytical methods, a partial or per- turbation technique could suffice. Two types of Monte Carlo techniques, called sequential simulation and independent increment simulation, are in use; the second method is faster, but, unlike the first, it provides no information on the frequency and duration of outages. Generally, this method would be appropriate when the failure and repair of individual system components are mutually independent of each other. A recent assessment, in which a relatively simple system is modeled, shows that both the conventional analytical and the Monte Carlo simulation meth- 17. See Roy Billinton, Power System Reliability Evaluation (New York: Gor- don and Breach, 1970). 18. See P L. Noferi, L. Paris, and L. Salvaderi, "Monte Carlo Methods for Power System Reliability Evaluation in Transmission and Generation Planning," Proceedings of the Annual Reliability and Maintainability Symposium, Washing- ton, D.C., January 1975, pp. 460-69. INTRODUCTION TO RELIABILITY 23 ods are likely to yield closely similar results of reliability indexes, pro- vided that the assumptions underlying the models are specified clearly and consistently.1o Analytical studies of generation systems usually require explicit speci- fication of discrete generating capacity as well as load models; both generators and loads are assumed to be aggregated or lumped, and to be connected to a common terminal. The LOLP is the most commonly computed index, although the FAD measure is becoming increasingly popular. Techniques are also available to evaluate energy-limited, rather than capacity-limited, generating systems.20 Monte Carlo sequential sim- ulation methods are useful when no analytical method exists. An example would be systems with severe operating constraints, such as heavy reliance on energy-limited hydro or peaking units.21 Both analytical22 and Monte Carlo23 methods have been used in trans- mission and distribution system reliability analysis. The FAD measure is computed most often in these studies. The analytical approach includes techniques that directly solve an explicit Markov model, as well as those that implicitly use Markov concepts to compute reliability indexes on a step-by-step basis. This is done after determining the minimal cut sets of the system: that is, the least number of components whose failure will cause a supply interruption. Transmission and distribution studies have also been made using the Monte Carlo sequential and the independent increments simulation techniques. The latter method only provides the probability of system failure, as mentioned earlier. For this discussion, the most relevant studies are those that treat the 19. See Khai D. Le, "Conventional Probability Methods and Monte Carlo Simulation Techniques: A Comparison of Results," Proceedings of the IEEE Power Engineering Society Winter Meeting, New York, January-February 1978, paper no. A78238-8. 20. See Roy Billinton and P. G. Harrington, "Reliability Evaluation in Energy Limited Generating Capacity Studies," Proceedings of the IEEE Power Engineer- ing Society Winter Meeting, New York, January-February 1978, paper no. F78004-4. 21. See L. Paris and L. Salvaderi, "Optimization of the Basic Characteristics of Pumped Storage Plants," Proceedings of the IEEE Power Engineering Society Winter Meeting, New York, January-February 1974, paper no C74158-2. 22. See Roy Billington and M. S. Grover, "Reliability Evaluation in Distribu- tion and Transmission Systems," Proceedings of the IEEE, vol. 122 (May 1975), pp. 517-23. 23. See P. L. Noferi, L. Paris, and L. Salvaderi, "Monte Carlo Methods for Power System Reliability Evaluation in Transmission and Generation Planning." 24 THEORY system as a whole. The problem of unifying the evaluation of genera- tion, transmission, and distribution system reliability is complicated by the large and intractable number of network capacity states. Analytical techniques are available, however, for combined generation and trans- mission reliability analysis. Some of these studies basically deal with the LOLP;24 others yield the FAD indexes either at the load point25 or for the entire generation-transmission system.26 A basic choice arises with ana- lytical methods. Should generation and transmission failures be modeled independently to derive separate reliability indexes that may be com- bined later? Or are transmission flow patterns and the status or behavior of generators so closely linked that an integrated and inherently more complicated treatment of the generation/transmission composite is re- quired?27 The Monte Carlo independent increments simulation method has also been applied to system-wide reliability studies.28 The Need for Economic Criteria The earlier discussion of reliability focused almost exclusively on the analysis of the system in relation to the supply side. Target levels of reliability, however, are required for planning, against which the relia- bility indexes of future system performance could be compared. The determination of such standard levels requires analysis of demand side considerations as well, and this constitutes a difficult problem that has not yet been addressed successfully. More specifically, rational economic criteria have not been used to establish target reliability levels. Most current reliability standards are based on past practice, and gen- eral notions regarding the quality of service that would be acceptable to electricity users. Sometimes, when the reliability level could be raised 24. See, for example, C. K Pang, R L. Watt, and J. A. Bruggeman, "Multi- Area Generation Reliability Studies," Proceedings of the IEEE Power Engineering Society Summer Meeting, Los Angeles, July 1978, paper no. A78546-4. 25. See G. E. Marko, "A Method of Combining High Speed Contingency Load Flow Analysis with Stochastic Probability Methods to Calculate a Quantitative Measure of Overall Power System Reliability." 26. See R. N. Allan and F. N. Takieddine, "Generation Modelling in Power System Reliability Evaluation." 27. See Roy Billinton, "Composite System Reliability Evaluation," IEEE Trans- actions on Power Apparatus and Systems (April 1969), pp. 276-80. 28. See P. L. Noferi, L Paris, and L. Salvaderi, "Monte Carlo Methods for Power System Reliability Evaluation in Transmission and Generation Planning." INTRODUCTION TO RELIABILITY 25 at relatively little expense, it has been increased to the point where fur- ther improvements would sharply increase system costs, that is, until the sharp "knee," found in most curves of supply costs versus reliability level, was reached (see figure 13.1, chapter 13). Because of the for- midable problems associated with estimating the economic worth or benefits of improved reliability, however, only very recently have some preliminary attempts been made to measure the benefits of the quality of service in relation to the corresponding costs.29 (For a review of these earlier studies, see chapter 4, Estimation of Outage Costs.) Given the highly capital-intensive nature of the electric power sector and the increasing demand, massive investments in power systems will continue to be needed. (See chapter 1, Overview.) Whereas the costs of electricity supply will remain high, modern nations are so heavily dependent on electric power that disruptions caused by power failures would also be considerable. Therefore, given the large investment in- volved and the significance of the quality of electricity supply, the relia- bility standard must be based on economic considerations, rather than on arbitrary choice. The situation is particularly serious in the developing countries that are capital and foreign exchange scarce and that often adopt inappropriate reliability standards borrowed from industrialized nations. Clearly, a balanced analysis of both the supply and the demand of electricity is required. Therefore, the basic economic criterion presented in this book would establish socially optimal reliability levels at the point where the marginal benefits of further improvements in reliability (meas- ured in terms of avoided shortage costs) are equal to the marginal costs of supply.0 A cost-benefit model is developed in the next chapter to achieve this objective. In theory, the optimal power system expansion plan, which is the least- cost long-range design corresponding to the optimal reliability level, 29 See, for example, Michael L. Telson, "The Economics of Alternative Levels of Reliability for Electric Power Generation Systems," The Bell Journal of Eco- nomics, vol. 6 (Autumn 1975), pp. 675-94, and Z Reguly, "Costs Evaluation of Power Supply Reliability," Reliability of Power Supply Systems, IEE Conference Publication no. 148 (London: Institute of Electrical Engineers, February 1977), pp. 13-16; and Mohan Munasinghe and Mark Gellerson, "Economic Criteria for Optimizing Power System Reliability Levels," The Bell Journal of Economics, vol. 10 (Spring 1979), pp. 353-65. 30. For a true social optimum, both the electricity price and the reliability level should be optimized together, as discussed in the next chapter. 26 THEORY could be determined independently of the specific measure of reliability used. As the case study indicates, however, in practice it is important to develop reliability indexes that satisfy two basic criteria. These indexes must not only characterize future system performance in a way that is helpful for traditional system planning, but also should be meaningful at the consumer level, and easily usable to determine the costs of shortages incurred by users, as discussed in chapters 4 to 7. From this viewpoint, load-point indexes of the FAD type, by time of day, referred to individual consumers on a disaggregate basis, would be the most convenient meas- ures to use. In particular, in estimating these indexes, the effect of operating criteria on system reliability should be considered wherever possible, as previously discussed. Generally, the more disaggregate and complete the information re- garding the reliability indexes, the greater would be the accuracy of the corresponding estimates of outage costs. For example, since outage costs are generally a nonlinear function of outage duration, ideally, the probability distribution of outage duration should be computed. In gen- eral, this would be possible with Monte Carlo simulation methods.31 But, given the many other sources of error in the estimation of outage costs (see chapters 4 to 7), it would be difficult to justify devoting con- siderable effort to estimating probability density functions for outage duration. Therefore, in practice, a knowledge of the average duration at specific times may be sufficient, for example, during the periods of peak, shoulder, and off-peak demand. Knowing the mean outage dura- tion during given periods of the day would improve the accuracy of the outage cost estimates in two ways. First, if the day were subdivided into smaller intervals of time, the actual values of outage duration estimated for these periods would be more tightly clustered around the correspond- ing expected values, because the duration could vary by time of day, depending on such factors as the load and the availability of repair crews. Second, even the costs associated with an outage of fixed duration would tend to vary by time of day. By estimating reliability indexes (and consequently outage costs) at specific times that coincided with the rating periods used in tariff setting, 31. An analytical model for incorporating the effect of uncertainty in LOLP-LOLE calculations by estimating the variance of this index is discussed in Roy Billinton and G Hamond, "Considerations in Including Uncertainty in LOLE Calculations for Practical Systems," Proceedings of the IEEE Power Engineering Society Win- ter Meeting, New York, 1979, paper no. A79075-3. INTRODUCTION TO RELIABILITY 27 it would also be possible to establish links with optimum electricity pricing policy. This is because the theory of peak load pricing suggests that the marginal capacity costs of supply be allocated among the dif- ferent rating periods-such as peak, shoulder, and off-peak-in propor- tion to the corresponding marginal outage costs in each period. (See chapter 3, Method of Optimizing Reliability, for a discussion of the re- lations between optimum reliability and price levels.) Chapter 3 Method of Optimizing Reliability The discussion in the previous chapters indicates that the procedure for optimizing reliability levels should be both theoretically rigorous and operationally useful: that is, it should bring together supply and demand side effects within a consistent economic-engineering framework that would be relatively simple to apply and would use readily available in- formation. Accordingly, the economic theory for the optimization model that follows is drawn mainly from cost-benefit analysis, whereas the en- gineering aspects are strongly influenced by the practical approach used in power system planning. A range of optimum reliability levels, which maximizes the net social benefit of electricity consumption, may be de- termined by identifying the system expansion program that minimizes the sum of system and outage costs to society during the planning period. Equivalently, the reliability level should be increased up to the point at which the marginal supply costs of increasing reliability are equal to the expected benefits from the marginal shortage costs avoided because of the improvements in reliability. Features of the Model Several important features of the reliability optimizing planning model presented here should be emphasized. First, this method adds a new dimension to traditional system expansion planning. Usually, the power 28 METHOD OF OPTIMIZING RELIABILITY 29 authorities examine several alternative long-range power system plans designed to meet a basically fixed-load forecast at some predetermined, desired level of reliability. The plans are also subject to other political, environmental, and legal constraints, and often variation in the growth of demand may be considered for sensitivity testing. (For details, see chapter 2, Introduction to Reliability.) Then, the plan with the lowest value of the present discounted value (PDv) of total costs is chosen. The PDV concept is defined in the next section. This cost minimization method is equivalent to the maximization of net benefits criterion used in cost-benefit analysis if the benefit streams of the alternatives being compared are identical. In the more general approach described in the next section, the relia- bility level is also a variable to be optimized. The system planner must design a number of alternative systems to meet the future demand, which is initially assumed to be fixed, at each of several target reliability levels, still subject to the other constraints mentioned above. Then these alter- natives are compared, and the one that minimizes the total costs, defined as the sum of the outage costs and the system costs, is chosen. There- fore, the more conventional system planning criterion of minimizing only the system costs is subsumed within the broader procedure of minimizing total costs that is presented here I Second, the new reliability model introduces another level of sophis- tication to system expansion planning by considering variations in the demand forecast. This method focuses primarily on the reliability level, which is optimized subject to a fixed initial forecast of load growth. It follows logically that a fixed evolution of electricity prices is assumed. Although it would be ideal from an economic point of view to optimize price and reliability simultaneously, electricity tariffs in the real world usually are fixed, and not necessarily at optimum levels. In this model, it is more practical to assume a given evolution of prices when the first round of optimum reliability levels is determined. Any changes in the pricing assumptions resulting from the first iteration can be fed back into the model to improve the optimal choice. Third, this approach underlines the importance of accurately measur- ing outage costs based on detailed economic activity models for different kinds of electricity consumers. Outage costs should be estimated in 1. See Mohan Munasinghe, "A New Approach to Power System Planning," IEEE Transactions on Power Apparatus and Systems, vol PAS-99 (January/ February 1980). 30 THEORY disaggregate form, in particular, using load point frequency and duration reliability indexes rather than aggregate measures such as the loss-of- load-probability (LoLP), and recognizing variations in outage costs by time of day, by outage duration, and by specific type of customer, rather than using average concepts such as costs per kilowatt-hour or kilowatt not served. The framework for evaluating outage costs as well as system costs is basically economic and is more appropriate in the context of the national economy, or society as a whole, rather than from the finan- cial or accounting viewpoint of a private power utility company. Thus the goods and services used as inputs to the electric power system-such as labor, land, physical assets, and materials-are considered scarce eco- nomic resources, which could be used in alternative production, and they are valued accordingly. In particular, if markets are highly dis- torted, shadow prices may be used (see chapter 9, Shadow Pricing). Such an approach is especially relevant in the case of a publicly owned power utility, a situation that occurs very often in the developing coun- tries. As examined below, however, the proposed approach does not require explicitly the existence of a single nationwide power system. Fourth, the model facilitates optimization of power systems at various levels of aggregation. It may be applied to any complete power system or subsystem, even in cases when there are many such entities serving a single country. Thus, the planning of several power systems could be optimized: (a) globally, assuming full interconnection among them; (b) partially, with only limited interties and possibilities for buying and selling capacity (that is, reliability); and (c) singly, allowing no pro- visions for interties. Clearly, the global optimum would be the best and most economically rational one, providing the maximum net benefit of electricity consumption to society. Political, administrative, and other constraints, however, may force decisionmakers to adopt the options with limited or no interties, leading to local optima for each of the sys- tems, which are collectively not as good as the global optimum for the country. Similarly, although it would be best to optimize the planning of a power system in its entirety (that is, generation, transmission, and dis- tribution), it is still possible to apply the proposed method to a sub- system, such as a distribution network. Thus, the case study presented in Part II is an example of such a distribution subsystem optimization, in which the generation and transmission reliability of bulk supply to an urban distribution grid is assumed to be fixed. Once again, system-wide planning is superior to partial (or subsystem-by-subsystem) planning. METHOD OF OPTIMIZING RELIABILITY 31 If the latter option is pursued, however, the transfer price for bulk serv- ices between different parts of the system (for example, bulk power sales from a generation to distribution utility) should reflect the true incre- mental economic costs of the service. As discussed next, this point has much wider relevance to the establishment of prices that accurately signal the cost of service to customers (whether they are individuals or utilities), so that they may adjust their purchases of electricity to eco- nomically efficient levels. Before developing the cost minimizing model, the simultaneous op- timization of price and reliability or capacity levels should be discussed further, given its theoretical importance.2 The closely related issues of optimal capacity levels and electric power system reliability have received attention recently as part of the more general economic literature con- cerning public utility pricing under conditions of uncertainty: that is, with stochastic demand and supply. In this case, the utility is typically modeled as a net welfare maximizer, where net social welfare equals the expected willingness-to-pay for electricity, minus either the expected supply costs (Brown and Johnson) or the sum of expected supply costs plus the costs of rationing electricity according to consumers' willingness- to-pay (Crew and Kleindorfer, 1976, 1978). Such studies indicate that, ideally, both price and reliability should be simultaneously optimized to achieve maximum net social welfare. This complex analysis can be expressed simply.4 Economic efficiency would be maximized if the price were set equal to marginal cost and the capacity level were fixed at the point where the marginal cost of adding to capacity (net of the energy saved) was equal to the marginal con- 2 Optimizing reliability and capacity are equivalent in this context. 3. See, for example, Gardner Brown Jr., and M Bruce Johnson, "Public Utility Pricing and Output Under Risk," Ameiican Economic Review (March 1969), pp. 119-28; Michael A Crew and Paul R Kleindorfer, "Peak Load Pricing with a Diverse Technology," The Bell Journal of Economics (Spring 1976), pp. 207-31; Roger Sherman, and Michael Visscher. "Second Best Pricing with Stochastic De- mand," Ameiican Economic Review (March 1978), pp. 41-53, Michael A. Crew and Paul R. Kleindorfer, "Reliability and Public Utility Pricing," American Eco- nomic Review (March 1978), pp 31-40; Ralph Turvey and Dennis Anderson, Electricity Economics (Baltimore- Johns Hopkins University Press for the World Bank, 1977), chap. 14. 4. See Mohan Munasinghe, "Electric Power Pricing Policy," LDC Energy Man- agement Training Seminar, State University of New Yolk-Brookhaven National Laboratory, Stony Brook, New York, November 1978; and Mohan Munasinghe and Mark Gellerson, "Economic Criteria for Optimizing Power System Reliability Levels," The Bell Journal of Economics (Spring 1979), pp. 353-65. 32 THEORY sumer benefits from averted corresponding electric power shortages. Setting the capacity level would also automatically determine the relia- bility level. The optimal pricing and capacity rules interact in several ways. First, if system capacity is optimally planned (and operated), then the short- and long-run marginal costs (SRMc and LRMC) are equal, where SRMC and LRMc are defined as the costs of meeting one unit of incremental electricity consumption with capacity fixed and with capacity varying optimally, respectively. If the system plan is suboptimal, SRMc and LRMC diverge, and the pricing policy must reflect some appropriate compro- mise between these values. Second, the marginal costs of supply include both capacity and energy components. For pricing purposes, the optimal marginal capacity costs may be allocated among different rating periods in proportion to the corresponding expected marginal shortage costs during these periods.' In the simple case of a peak and off-peak pricing model (where it is assumed that no shortages occur during the off-peak period), all marginal capacity costs would be imposed on peak con- sumers. Both peak and off-peak users would have to pay marginal energy costs. Given a rationing or load-shedding scheme, previous studies maxi- mized net welfare by satisfying simultaneous first-order conditions: that is, by equating to zero the partial derivatives of net welfare with respect to prices and capacity. This indicates that partial models attempting to optimize reliability subject to given prices would not guarantee the maxi- mization of net benefits. That is, satisfying the first-order condition with respect to capacity alone does not ensure that the objective function is maximized, because a different combination of prices, capacity, and, therefore, reliability may lead to greater net social benefits. Since electricity tariffs are in practice often not readily subject to change, it is appropriate to try to optimize reliability, subject to fixed tariffs, at least to a first approximation. To the extent that this is accom- plished, the net benefits derived from the provision of electricity should 5. See, for example, Yves Balasko, "On Designing Public Utility Tariffs with Applications to Electricity," Electricile de France Report, Paris (1974); and Joseph Vardi, Jacob Zahavi, and Benjamin Avi-Itzhak, "Variable Load Pricing in the Face of Loss of Load Probability," The Bell Journal of Economics, vol. 8 (Spring 1977), pp. 270-88; where it is proposed that marginal capacity costs be allocated in inverse proportion to a reliability index such as the loss-of-load prob- ability (LOLP). This would be inappropriate, however, because these aggregate indexes are poor proxies for prorating outage costs. METHOD OF OPTIMIZING RELIABILITY 33 at least increase. Therefore, it is possible to develop a method of op- timizing reliability by comparing the costs and benefits associated with alternative levels of reliability. The costs incurred by consumers because of electricity supply interruptions or outages decrease as reliability in- creases, and the costs of providing electric power increase. Therefore, given a demand forecast based on the assumed tariffs, reliability should be optimized where the marginal system costs of further increasing reliability are equal to the marginal social costs of outages that are averted because of greater reliability. Moreover, as shown in the model developed in the next section, this method of optimizing reliability, given the tariff level, can be used iteratively to optimize reliability and price simultaneously. Supply and demand uncertainties are implicitly recog- nized in the model by considering outage costs. To simplify the presen- tation, however, supply and demand are not modeled as stochastic processes, and the conditions for simultaneous optimization of price and reliability have not been derived. Incorporation of these features in the model would not alter the basic results developed here. Reliability Optimizing Planning Model The first step is to formulate the hierarchical model of an electric power system required to serve a large region consisting of N smaller geographic areas for a long time interval, which also may be divided into r distinct periods. Consider M alternative long-run investment plans or expansion paths arising from different power system designs prepared by the system planners. Let the set R, that characterizes the global relia- bility level for the region and is associated with the ith power system expansion plan, be defined as: RI = R; j = 1 to N, and t = 1 to T, for i = 1 to M; where the superscript i and the subscripts j and t relating to the variable R denote values of R corresponding to system expansion plan i, in geographic area j, and during time period t, respectively. Generally in any given areaj, there are limits to the variation of the reliability level in adjacent time periods, and the values taken by R!, over time will be related because of the indivisibility or lumpiness of power system investments. 34 THEORY Next, the set representing global demand for electricty services is defined by: D = Djt j = 1 to N and t = 1 tor. Each component of demand is a function of other variables and the equation may be written: (3.1) D,t = D,(P, Y,t, R,*t, Z") where P is the electricity price, Y is the income variable that represents the level of economic activity, R* is the expected value of reliability, and Z is a vector of other independent variables affecting demand. Ini- tially, it is assumed that the demand forecast is determined by the exogenously given evolution over time of the values of arguments on the right-hand side of equation (3.1). As described in chapter 4 (Estimation of Outage Costs), the costs suffered by electricity consumers because of electric power shortages may be represented as a geographically localized function of the target reliability level, forecast demand, and reliability expectation: (3.2) OC't = OC),(R',, D,t, R*,t). Power system supply costs, incurred as a consequence of providing elec- tricity services, may be written: (3.3) SQ = SC(R', D). Both outage and supply costs are defined as economic costs; the methods of estimating them are described in chapters 4 to 9. If the system planners must consider several alternative designs asso- ciated with any single reliability configuration R1, they would select the plan with the lowest present discounted value (PDV) of total costs (PDV is defined in the next paragraph). The supply costs described in equation (3.3) correspond to such least cost system designs, where appropriate. SCI should include the capital and operating expenses as well as the kilowatt and the kilowatt-hour losses in the system, appropriately valued (at the marginal cost of supply), but net of the marginal supply costs of kilowatt-hours not delivered because of outages. Disaggregation of system costs by geographic area would not be meaningful, because the effect of certain investments, primarily at the generation and transmis- METHOD OF OPTIMIZING RELIABILITY 35 sion levels, are unlikely to be localized. A similar argument may be advanced regarding disaggregation by time period, but this breakdown is required to facilitate discounting over time, as described later. The arguments on the right side of equation (3.3) further emphasize that because power system investments are lumpy, in general, the supply cost in any given period could be associated with several components of reliability and demand, spanning many geographic areas and time periods. A simple expression for the present discounted value of the net bene- fit of electricity consumption resulting from system expansion plan i is: T N (3.4) NB% = _E (TB,t - OC,) - SC /(1 + r)l where TBte = TB,,(D,t) is the total benefit of electricity consumption in the absence of outages, and r is the appropriate discount rate or accounting rate of interest, as described in chapter 9, Shadow Pricing. Because of the long lifetime of some investments, the discounting time horizon T is usually chosen to be greater than the planning time horizon, 7- to eliminate end-effects.' Consider what happens when system expansion plan i + 1 is derived from plan i by changing plan i slightly. At one extreme, a change in the generation expansion plan may alter the reliability level globally in all the geographic areas served by the power system; at the other extreme, a modification in local distribution system design would affect only the reliability level in a single area. Using equations (3.1), (3.2), (3.3), and (3.4), the resultant change in net benefit is given by: (3.5) ANBI =NB' - NB, = E a(TBt - OC,,).AD,t - a .ARX] asc; asc - .ARt - *AD /(1 + r)', 6. For the period r to T, TB,, and OC', may be held constant, and only operating and maintenance costs are included in the SC) stream. Since the lifetime of some system components could exceed T, it may be necessary to deduct the residual deprecia- ted value of such items from the cost stream in the final year T. The large discount factor will minimize the effect of this correction. 36 THEORY where AR', = R)t1 - RI,, AD;, = (8D1,/8R,)AR't, and so on. The respective terms [(aSC,/8R)*AR%] and [(aSC/aD)-AD] are not vector expressions in the strict mathematical sense, but rather, symbolically represent partial changes in supply costs associated with (a) changes in the set of reliability levels alone, that is, holding demand constant; and (b) variations in the set of demand levels induced by the changes in the corresponding set of reliability levels. The secondary effect on demand and outage cost occurs because of a change in the reliability expectation, which is induced by the change in the reliability level. Derivatives of the form aD,,/aR', and 80C,/aR, could be de- fined so as to include this effect. Equation (3.5) may be greatly streamlined by assuming that aD,/aR;, = 0, at least in the first approximation so that AD,, = 0, and AD = 0. On the basis of equation (3.1), this assumption has two implications. First, the direct effect of reliability level changes on de- mand via the reliability expection R* is negligible. Such a supposition is particularly true when the range of variation in R being considered is relatively small. Furthermore, to be practical, the problems of esti- mating such direct feedback effects of reliability on predicted demand are likely to outweigh by far any resulting advantages from the small refinement in the numerical results. Second, the indirect effect of reli- ability-level changes on demand resulting from any associated price change is also ignored. Both these assumptions may be modified later, however, by iterating, or running, through the model on subsequent rounds, as discussed later in this chapter. On the basis of the foregoing discussion, a simplified version of equa- tion (3.5) can be written: (3.6) ANB = -AOC' - ASC' T N where AOC = _ E [(a0C,/aR;)*AR1]/(l + r)', and t-0 .-=1 T ASC = Z [(aSC,/aRI).ARz]/(l + r)'. To interpret equation (3.6), it is assumed that the change from system expansion plan i to plan i + 1 involves an overall unambiguous improvement in reliability, specifically that each component of ARs is METHOD OF OPTIMIZING RELIABILITY 37 nonnegative. In general, this implies correspondingly that AOCI < 0 and ASC& > 0. In this case, equation (3.6) yields: (3.7) 1ANBI = IAOC'I - IASC' Therefore, to maximize the net economic benefits of supplying electricity to society, the reliability level should be increased as long as the cor- responding decrease in incremental outage costs exceeds the increase in incremental supply costs and vice versa. An equivalent way of inter- preting equation (3.7) is to state that the net benefit NB is maximized when the present discounted value of the sum of outage costs and supply costs is minimized, since the total benefit TB is assumed to be independ- ent of reliability R.7 Outage Simulations and Optimum Reliability Levels In this section, the characteristics of the model and the methodology are further explored. (See also figure 1.1, chapter 1, Objectives and Methodology.) To analyze and present the results so that the practical implications of this approach are emphasized, it is necessary to simplify the theoretical model. First, the measure of reliability R, which was in- troduced earlier in a rather abstract way, will be defined more precisely. Second, ways of meaningfully aggregating variables such as R, OC, and SC will be developed after they have been estimated at the disaggregate level. One specific load point reliability measure could be written: R', = (ft, d,t) where f and d are the mean frequency and duration of outages, respec- tively, during the period, t. As discussed in the previous chapter, accu- rate estimation of outage costs generally would require further detailed information relating to f and d, such as the time of day outages occur and 7. This formulation may be modified in various ways. For example, the total avail- able investment funds (1) for the power system may be fixed over the planning period. In this case NB would typically have to be maximized subject to a budget constraint of the form: I - F_ SC/(1 + r) = 0, t-p using the method of Lagrangian multipliers. 38 THEORY , the numbers and types of consumers affected. For the exposition of the model, however, it is more convenient to use the simpler measure: (3.8) R' = 1 - (OE),/TE,,) where OE is the electric energy not supplied because of outages, and TE is the total energy that would have been supplied if there had been no outages. The above measure is analogous to the loss-of-energy- expectation (LOEE) criterion used in generation system planning (see chapter 2, Introduction to Reliability) and is related to the bulk power energy curtailment index defined by IEEE.8 For a given plan i, and area j, the local reliability R, may be plotted against time t. Figure 3.1 depicts three such evolutionary paths of local reliability for a given demand forecast, starting from the existing level a. and extending over the planning horizon, 0 to 7. Each path corresponds to a system expansion plan i that seeks to achieve the desired local reliability level a,. In general, the paths will vary about the target values because of capital indivisibilities (or lumpiness). A similar figure may be plotted for each of the N geographic areas served by the power system. Furthermore, by appropriately specifying the scalar index: N N it = I - _ OE,,/E TE,, 3=1 J=1 it is possible to depict graphically the evolution of global reliability for the entire system over time (cl1). The impact of the global reliability level on the present value of outage and supply costs may be summarized by the following global scalar measures: T N T N aR = I - [F F_ OE,/(1 + r)']/[E E TEj/(1 + r)'], t=0 y=1 t=0 y-1 8. Reliability indexes for evaluating system adequacy are discussed in IEEE PES Working Group, "Reliability Indices for Use in Bulk Supply Adequacy Eval- uation," IEEE Transactions on Power Appaiatus and Systems, vol PAS-97 (July- August 1978), pp. 1097-1103; and Roy Billinton, T. K. P. Medicherla, and M. S. Sachdev, "Adequacy Indexes for Composite Generation and Transmission System Reliability Evaluation," Pioceedings of the IEEE Power Engineering Society Win- ter Meeting, New York 1979, paper no. A79024-1. METHOD OF OPTIMIZING RELIABILITY 39 T N OC' = _ _ OC,/(1 + r), t=O 1=1 T SCI = F SC,/(1 + r)', and t=o total costs: TC = OC + SCI. The model developed in the previous section indicates that the optimum expansion path, i, is the one in which TC is minimized. It should be re- emphasized that before the simplifying aggregations described above, values of R, OC, and SC are assumed to have been estimated at a very disaggregate level, for example, by starting with values of the underlying frequencies and durations of outages. A typical set of results might appear as shown by the solid curve in figure 3.2. Starting with the low reliability run (RI, increasing the overall reliability level results in decreasing socal costs, TC, to a minimum at (Rm Further improvements in reliability are not justified beyond this Figure 3.1. Reliability Level Trajectories over Time Associated with Three Alternative Expansion Plans-i = 1, 2, and 3- for the Given Local Service Area, j. UI Czak----- --------- -------- - - I R) 0 Time 40 THEORY Figure 3.2. Total Costs Curve I T11 0/ TC: I -- TC/ 1I I I I III I I I I I I ( RW R2 Rm' R- R- I Global reliability index (R) Note: TC =first-round estimate; TC' = revised estimate after feedback and reiteration. point, because the marginal costs of supply exceed the marginal benefits due to averted outage costs. The same result is shown in somewhat dif- ferent form in Figure 3.3. The optimal reliability level 61- corresponds to the point at which marginal supply costs (MSC) are equal to negative marginal costs outage (-MOC), reflecting the optimality condition ANB = 0 in equation (3.6). In this formulation, the reliability measure is defined only generally. Therefore, in the context of the theoretical model, the selection of the optimum system plan and the associated reliability level may be made on the basis of economic cost-benefit analysis and is quite independent METHOD OF OPTIMIZING RELIABILITY 41 Figure 3.3. Marginal Supply Costs (MSC) and Negative Marginal Outage Costs (-MOC) as Functions of Reliability 0 MC I I I I I I I I ( R- Global reliability index (R) of the actual index of reliability. In practice, however, the nature of the specific reliability measure to be used is important, because it would be required for the empirical estimation of all outage costs. Because of the large number of variations possible, especially at the distribution level, each global alternative expansion path i is likely to have a unique set of indexes R, associated with it. Yet, more than one such path may correspond to a single value of the global index (R,, a highly aggregate scalar quantity. Furthermore, if R;, is defined as in equation (3.8), in theory, two separate expansion paths with different values of outage frequency and duration might even yield the same sets of indexes R1, although this would be highly improbable in practice. Given this discussion, two slightly different conceptual interpretations of the method of optimization become possible. In the first, each long- range system design and corresponding index set RI may be considered as a strictly distinct one. Therefore, the system planner designs several alternative expansion paths that span a sufficiently wide spectrum of reliability levels, and then directly determines the optimum one that has the minimum value of the sum of outage and supply costs. In the 42 THEORY other interpretation, the optimization procedure may be broken down into two stages. Initially, several specific levels of the global, scalar index (RI that fell within a suitable range would be selected, and the alternative systems would be designed to be clustered tightly around these reliability values. For example, if there are m target reliability levels and a cluster of n distinct system plans associated with each level, then a total of mn alternative expansion paths would have to be considered. In any one cluster the global supply costs (SCI) could vary widely, but the total outage costs (OC) would be similar. The first step in this method essen- tially consists of choosing the cheapest alternative system design from each cluster. This technique closely parallels the conventional system planning process. In the next step, these m least-cost alternatives would be compared to determine the optimum long-range system expansion plan, which minimized the total social costs (TCI). The first interpretation is theoretically more correct because no as- sumption is required regarding the equality of values of OC for different expansion plans in the same cluster. The second, however, follows more naturally from the procedure used in traditional system expansion planning In practice, the two interpretations would tend to merge, since the system designing process is discrete: that is, it does not move smoothly or continuously from one path to the next, and time con- straints prevent simulation of too many alternative system designs. Thus, engineering judgment often must be relied on to reduce the num- ber of least-cost expansion paths to be considered. By choosing sensible nonintersecting and smoothly varying trajectories for R), situations in which paths with lower (RI values corresponded to higher expenditures (SCI) can be avoided. Because such variations are possible, it would be better to speak of a target band of optimum reliability levels around (Rm, rather than a unique optimum value. A similar conclusion would apply in cases where the graph of total costs versus reliability had a fairly broad and flat minimum. In particular, varying the reliability at the generation, transmis- sion, and distribution levels must be done in a balanced way, as im- plied by equation (3.6). Suppose that starting from the value (Rm within the optimum reliability range, a small improvement AR- in the reliability level and a corresponding decrease in outage costs -AOCm may be realized by an increase in only the incremental costs of gene- ration ASCG, keeping transmission and distribution costs constant. Similarly, let ASCT and ASC be the increments in transmission costs METHOD OF OPTIMIZING RELIABILITY 43 only and distribution costs only, respectively, each of which will sepa- rately bring about the same reliability increase AR- and outage cost decrease -,AOC-. Then the optimality condition for balanced improve- ments in generation, transmission, and distribution would require that: ASC. = ASCT = ASC; = -AOCm. Equivalently and with a change of notation, it is possible to write this condition in the forms: asc; asc? asch" -aoc"'; (3.9) - at (R= am OR 0R OR OR The partial derivative OSC7/OR symbolically represents the ratio ASC /AR- where only the costs of generation are permitted to change, and aSC;/R and aSC"/OR may be similarly interpreted. If, for example, OSC2/OR = -OCIOR F aSC7/R 5 aSCG/ R, then this represents a partial optimization of the distribution subsystem alone. The case study of urban distribution network optimization presented in Part Two of this book corresponds to the above situation. A more global optimum for the whole system as represented by equation (3.9) would be better than the aggregate of three separate optima-one for each of the generation, transmission, and distribution subsystems. This is because the global optimum will result in a lower minimum value of total costs TC, or equivalently, a higher value of net social benefits NB. In cases involving the interaction of several different power sys- tems, similar optimality conditions and arguments may be developed concerning the superiority of the global optimum for fully intercon- nected systems relative to the group of separate optima on a system- by-system basis. Finally, consider a situation in which the stream of system supply costs SCm associated with the optimum expansion plan i = m, on the first round, requires significant changes in the assumptions about the evolution of prices that were used to determine the initial demand forecast. For example, the application of a marginal cost pricing rule or a simple financial requirement, such as an adequate rate of return on fixed assets, may require previously unforeseen changes in future electricity tariffs to compensate for the new supply costs. Such a shift in prices would directly affect load growth. Furthermore, the new 44 THEORY target reliability levels implied by the first round optimum path i = m, may affect reliability expectation, thus having a secondary effect on demand and outage costs (see equations (3.1) and (3.2)). In the situation described above, the effect of the new sets of price and expected reliability levels on the demand forecast and outage cost estimates may be determined by iterating through the model again. In general, this reiteration would shift the whole total cost (TC) curve as shown by the broken line in figure 3.2, leading to a new optimum plan m'. In this way, the direct and indirect feedback effects of relia- bility on demand may be considered iteratively, until the optimum set of self-consistent (simultaneous) price, demand, and reliability levels are determined (see feedback loop in figure 1.1, chapter 1). Clearly, the implementation of such an iterative procedure would require consid- erable additional information, such as the probable evolution of pricing policy, the elasticities of demand with respect to price for various types of electricity consumers, the effects of changing outage expectation on outage costs, and so on. Therefore, although the simultaneous optimiza- tion of price and reliability is theoretically elegant, in practice only a single iteration through the model probably would be attempted, assum- ing exogenously fixed prices and demand. If the first-round iteration results indicate that prices and reliability levels do have to be changed, often it would be more practical to im- plement these changes and to then observe their effect on demand and outage costs over some period of time. The optimizing procedure then could be repeated in the light of revised forecasts. The emphasis would be on recalculating results at different times to approach the optimum gradually over the years, rather than on attempting to compute the opti- mum by repeated iteration right at the beginning. This procedure is also more sensible in light of uncertainties in demand forecasts, system costs, and outage costs, which may require application of statistical decision theory, scenario analysis, or fuzzy set theory, as discussed in chapter 8, Power System Planning and Supply Costs. Chapter 4 Estimation of Outage Costs Throughout this book, the term "outage costs" is used to encompass all the economic costs suffered by society when the supply of electricity is not perfectly reliable or when it is not expected to be perfectly reliable. In this chapter the types of outage costs and the general problems asso- ciated with estimating them are discussed in relation to previous attempts to measure costs. It is concluded that outage costs should be estimated on the assumption that all electricity is used for productive purposes: that is, electricity is combined with other inputs and intermediate prod- ucts to produce various outputs. These outputs either would be marketed by industrial, commercial, and agricultural producers; consumed di- rectly, by households, for example; or distributed without specifically related charges by the public sector. Since electricity is used in all these production processes, the economic costs associated with imperfect ac- tual, or expected reliability levels can be measured relative to their effects on production. Detailed methodologies and models of outage cost estimation for different categories of electricity consumers are presented in subsequent chapters. Nature of Outage Costs As discussed in chapter 2, Introduction to Reliability, electric power supply shortages are manifested in various ways, ranging from power surges, frequency variations, and voltage level drops (brownouts) to 45 46 THEORY load shedding and complete interruptions of supply (blackouts). These effects impose certain economic costs on consumers, of which the most important and perhaps the most simple to measure are the costs of interruptions. Outage costs are direct when they occur during or following an outage, but are considered indirect when they are incurred because an outage is expected. For example, during an outage, consumers will suffer direct outage costs, since normal productive activity is disrupted. Indirect out- age costs are incurred because consumers may adapt their behavior pat- terns in ways that are less efficient or more costly, but less susceptible to outage disruptions. They may also purchase alternative (standby) sources of energy. Although indirect outage costs do not result from a specific outage, they should be considered when attempting to estimate the eco- nomic costs associated with alternative reliability levels, because they depend on the general level of reliability and represent real resource costs Generally direct outage costs are related more to the short-term effect of unexpected outages; indirect outage costs arise from longer- term considerations of outage expectation, including the effects of planned power cuts. In practice, it would often be difficult not only to estimate total outage costs associated with a particular level of relia- bility, but also to distinguish clearly between the direct and indirect components. The direct and indirect outage costs associated with a given level of reliability depend, other things being equal, on both the expected and the actual levels of reliability. The nature of this dependence can best be illustrated by considering the following two situations. (a) If a low level of reliability is expected (RL*), then, to reduce direct outage costs, consumers are likely either to adjust their house- hold and productive activities or to purchase alternative sources of en- ergy. As noted earlier, these behavior modifications result in indirect outage costs. Total outage costs also depend on the actual level of re- liability. If the latter is low, direct outage costs are still significant de- spite the indirect or preventive outage costs consumers incur. In this case, total outage costs will likely be high. With high actual reliability, direct outage costs will be smaller, and, therefore, total outage costs will be less than in the case of low actual reliability. (b) If high reliability is expected (Rh*), individuals probably do lit- tle to adjust their behavior, and, therefore, few indirect outage costs are incurred. In this instance, total outage costs will be relatively high if the actual reliability level is low, and these costs will be smaller if actual reliability is high. ESTIMATION OF OUTAGE COSTS 47 The effects that the relation between expected and actual reliability has on outage costs is demonstrated graphically in figure 4.1. Consider a field of curves, each of which is a graph of total outage costs against the actual level of reliability, but parametrized by a given level of ex- pected reliability. In general, at a given level of actual reliability, outage costs are higher when the difference between actual and expected relia- bility is greater. Also, outage costs will typically decrease with increasing reliability for any given level of expected reliability. These relations are depicted in the figure. Overall, total outage costs are likely to be highest with high expected reliability and low actual reliability (RII*, Rr). Lower total outage costs are likely to occur in the case of low expected and actual reliability levels (RL*, RL), whereas total outage costs will be even lower when there is low expected and high actual reliability Figure 4.1. Relation between Total Outage Costs and the Levels of Actual and Expected Reliability D -- C - - 0 111 Expected reliability level A - - ----- - I I I 11 I 0 RL R Actual reliability level Note: R" = actual high reliability level; R = actual low reliability level; and R' = critical reliability level. R"* = expected high reliability level, and R'* expected low reliability level 48 THEORY (RL*, R"). Finally, total outage costs will be lowest of all when there is both high expected and actual levels of reliability (RH*, Rn). In reality, reliability expectations might lie anywhere between RL* and RH*, assuming that these are the limits. Thus, there will be many curves relating the reliability level to outage costs, one curve representing each level of reliability expectation. At each level of actual reliability, the curve that indicates the lowest possible outage costs is the one for which the actual and expected reliability levels are equal. Therefore it is pos- sible to draw an envelope curve indicating those outage costs which would result if individuals could anticipate correctly the actual level of reliability and would take rational steps to minimize the resulting outage costs. Such an envelope curve is represented by the bold line in figure 4.2. In practice, it will be difficult to determine how changes in actual reliability affect consumers' expectations of reliability. It may be neces- sary to estimate outage costs based on the assumption that expectations Figure 4.2. Envelope Curve of Total Outage Costs (Heavy Line) 0 0 0 RL* Expected reliability level R11* 0 Actual reliability level ESTIMATION OF OUTAGE COSTS 49 remain essentially unchanged over some range of actual reliability levels. With this simplified approach, adaptations to avert outage costs, such as purchasing a standby generating plant, would presumably occur only after the level of reliability falls below some critical value, which would vary for different consumers. For example, as shown in figure 4.1, if reliability level is reduced from R" to R", outage costs will appear to increase by AD, given the assumption that reliability expectations remain unchanged at the high level R"*. The increase in outage costs, however, may be only AC if consumers' expectations and their consequent be- havior adjusted to the lower level of reliability R". This would occur after the critical reliability level Re has been passed. Actually, expecta- tions would take time to adjust, and therefore the resulting increase in actual outage costs would lie somewhere between AC and AD. In conclusion, by ignoring possible feedback effects between changes in reliability and reliability expectations, some relatively small errors in outage cost estimation are likely to be introduced. Since little is known in advance about the extent of such feedback effects, however, sophis- ticated attempts to correct for them could easily result in even greater errors. Methods of Estimating Outage Costs In the recent economics literature, there are two schools of thought concerning how outage costs should be estimated. One approach is to estimate them on the basis of observed or estimated willingness-to-pay for planned electricity consumption.' The other approach, the one used in this book, estimates outage costs by the effects of outages on the pro- duction of various goods and services.2 1. See Gardner Brown Jr and M Bruce Johnson, "Public Utility Pricing and Output Under Risk," Ameiican Economic Review (March 1969), pp. 119-28; Michael A. Crew and Paul R. Kleindorfer, "Peak Load Pricing with a Diverse Technology," The Bell Jownal of Economics (Spring 1976), pp. 207-3 1; Roger Sherman and Michael Visscher, "Second Best Pricing with Stochastic Demand," Amencan Economic Review (March 1978), pp 41-53; and Michael A. Crew and Paul R. Kleindorfer, "Reliability and Public Utility Pricing," American Economic Review (March 1978), pp. 31-40. Crew and Kleindorfer also recognize that there are other costs associated with outages: that is, the rationing costs of determining how to shed loads at the lowest cost, but these costs are not well defined. 2. See Michael L. Telson, "The Economics of Alternative Levels of Reliability for Electric Generating Systems," The Bell Jownal of Economics, vol. 6 (Fall 50 THEORY As mentioned in chapter 3, Method of Optimizing Reliability, at- tempts to estimate outage costs according to willingness-to-pay are actu- ally part of a more general literature on optimal pricing for public utilities under conditions of uncertainty: that is, stochastic demand and supply. In this approach the variable to be maximized is net welfare, which is generally set equal to the expected area under the demand curve corresponding to planned electricity consumption, minus the sum of the expected costs of supplying electricity, plus any expected costs of rationing available electricity among consumers if an outage occurs. Thus, outage costs are measured by the expected reduction in net wel- fare or the amount those deprived of electricity would be willing to pay for it, minus the costs saved by not supplying it. Studies that estimate outage costs on the basis of willingness-to-pay assume that electricity provides direct satisfaction to its consumers. Outage costs are therefore estimated in terms of lost consumers' surplus. Other studies that estimate outage costs by the effect of outages on vari- ous types of production do not make this assumption. Instead, they treat electricity as an intermediate input used to produce various goods and services that provide consumers with satisfaction, rather than as a final good that provides satisfaction to consumers. Outage costs are therefore measured primarily by the costs to society of outputs not pro- duced because of outages. The studies that estimate outage costs on the basis of willingness-to- pay have several important shortcomings. (a) It seems clear that ob- served willingness-to-pay for planned electricity consumption is not an accurate indicator of what an individual would be willing to pay to avoid an unplanned outage.3 This type of outage is apt to disrupt activi- ties involving electricity consumption, and, therefore, actual outage costs 1975), pp. 679-94; Ralph Turvey and Dennis Anderson, Electricity Economics (Baltimore: Johns Hopkins University Press for the World Bank, 1977), chap. 14; Mohan Munasinghe, "Costs Incurred by Residential Electricity Consumers Due to Power Failures," Journal of Consumer Research (March 1980), and Mohan Munasinghe and Mark Gellerson, "Economic Criteria for Optimizing Power Sys- tem Reliability Levels," The Bell Journal of Economics, vol 10 (Spring 1979), pp. 353-65. 3. For example, Michael Webb, in "The Determination of Reserve Generating Capacity Criteria in Electricity Supply Systems," Applied Economics (March 1977), pp. 19-31, suggests using electricity tariffs as a lower bound on the esti- mate of outage costs. This is inappropriate because even at the margin, the cost of an unexpected interruption in the supply of electricity will exceed what con- sumers are willing to pay for the planned consumption of electricity. ESTIMATION OF OUTAGE COSTS 51 may be greatly in excess of observed (long-run) willingness-to-pay. (b) These studies measure losses of consumers' surplus on the basis of their assumption that load shedding takes place according to willingness- to-pay: that is, those with the lowest willingness-to-pay are the first to have their electricity cut off. Thus, with reference to figure 4.3, the mar- ginal consumers' surplus lost is the triangle-shaped area, ABC, defined by the downward sloping demand curve, DD, the horizontal line at the price, f, and the vertical line representing the quantity, QA, of elec- tricity supplied in spite of the outage. In many instances, however, it is not reasonable to assume that load shedding takes place according to willingness-to-pay. For example, if the outage is caused by a distribu- tion system failure rather than a generation system failure, the ability to carry out load shedding according to some predetermined order may be severely limited. If this is the case, the resulting loss in consumers' surplus is the trapezoid-shaped area, EFGH, defined by the demand curve, the price line, and the inframarginal units of electricity not sup- plied, AQ2. The implication of these arguments is that actual outage costs will exceed outage costs estimated on the basis of the marginal consum- Figure 4.3. Marginal and Inframarginal Consumer's Surplus Lost D E IH UI I II D 0 QA Q Quantity (kilowatt-hours) Note: ABC = consumer's surplus lost because of marginal energy lost, AQ,; EFGH = consumer's surplus lost because of inframarginal energy lost, AQ, 52 THEORY ers' surplus lost. Finally, with this approach, the empirical estimation of outage costs requires exact knowledge of various consumers' demand functions for electricity. Given the problems associated with empirically estimating these demand functions, it is likely that any estimates of outage costs obtained in this way will be subject to considerable error.4 Therefore, outage costs would be more appropriately measured in relation to the effects of outages on a variety of productive activities. A general methodology for estimating outage costs consistent with this conclusion is developed in this chapter, and attempts to estimate direct outage costs in relation to the effects of outages on production are reviewed. Production is a process in which capital and labor are combined with other inputs, such as raw materials and intermediate products, to pro- duce a stream of outputs over time. Under conditions approximating those of perfect competition, the net social benefit of a marginal unit of output in a given time period equals the value of the output minus the value of inputs. For inframarginal units of output, producers' and con- sumers' surpluses must be included when measuring the net benefits of production. When market distortions are present in the economy, appro- priate shadow prices must be used to value inputs and outputs (see chapter 9, Shadow Pricing, for details). The net social benefit resulting from a time stream of marginal outputs equals the present value of the resulting stream of net social benefits. Thus, the opportunity cost of sup- plying electricity with less-than-perfect reliability can be measured in terms of the resulting reduction in the present value of this stream of net social benefits. When an outage disrupts production, the net benefits derived from all activities that rely on electricity are reduced. Direct outage costs are incurred, since the costs of inputs are increased, and/or the value of out- puts is reduced. Specifically, an outage can cause raw materials, interme- diate products, or final outputs to spoil, and it can also result in idle productive factors The spoilage effect leads to an opportunity cost equal to the value of the final product not produced as a result of the outage, minus the value of additional inputs not used because the final output was not produced. If the value of the output is not easily determined, 4. See Lester D Taylor, "The Demand for Electricity: A Survey," The Bell Journal of Economics, vol. 6 (Spring 1975), pp. 74-110; and chapter 8, Power System Supply Costs. ESTIMATION OF OUTAGE COSTS 53 however, as in the case of household and public sector outputs that are not sold directly on the market, then it is necessary to use the cost of producing the spoiled product or output as a minimum estimate of the resulting cost of the outage. When productive factors become idle because of an outage, an oppor- tunity cost results. The magnitude of the opportunity cost depends on the nature of the production process and on the producer's decision whether or not to work overtime to make up the lost output. The idle factor cost when lost output is not recovered equals the foregone value- added: that is, the value of the lost output minus the value of materials and intermediate products involved in its production. Again, when the value of outputs cannot be easily determined, then this cost may be estimated by the cost of idle productive resources during the outage period, assuming that factor payments equal marginal revenue products. This measure of outage costs also ignores the losses of consumers' sur- plus, which is apt to be small because of the marginal reduction in output resulting from most outages. Any offsetting benefits realized during outage periods when production has stopped, such as workers' enjoyment of the forced idleness, is also neglected. Lost output might be made up in the short run by overtime produc- tion. An opportunity cost would result in this case, since output is pro- duced later in the time stream and factor costs, especially labor, increase. In practice, it is better to ignore the longer-term possibility that the pro- ductive life of capital might be extended by the length of the outage, since the capital is not used during this period. It would not be realistic to assume that lost output could be recovered during this "extra" pro- duction period at the end of the machines' lifetime, unless physical depre- ciation was strictly a function of usage. Instead, if depreciation were a function of time, technical change, or changing factor prices, then the life of the equipment would not be significantly extended. Even if the lost output were produced later, the present worth of the resulting net benefits would generally be small because of the effect of discounting. This approach for estimating outage costs can be simplified so that it can be applied when there are few details available about the response of various economic units to outages. In most cases an industrial user of electricity would not have an economic incentive to make up lost output with overtime. Similarly, electricity used in the home and for street lighting produces outputs that are integrally related to the time of production. Since these outputs are essentially consumed at the time of production, there is little likelihood of overtime production. 54 THEORY Review of Previous Studies Several previous studies have attempted to estimate outage costs.5 Given the preceding discussion of the general nature of outage costs, these studies are now briefly reviewed with respect to: (a) the actual measure of outage costs that they develop; (b) the way in which this measure is utilized to obtain outage cost estimates for various types of electricity consumers; and (c) the extent to which these studies investi- 5. The studies reviewed in this section are: Dahlin Lalander, "Memorandum Concerning Estimation of the Costs of the National Economy in the Event of a Loss of Supply" (Vattenfall, 1948); Swedish Joint Committee for the Electricity Council, "Cost of Interruptions in Electricity Supply" (Stockholm- September 1969); R Bruce Shipley, Alton D Patton, and John S. Denison, "Power Re- liability Cost vs Worth," IEEE Transactions on Power Apparatus and Systems, vol. PAS-91 (September/October 1972), pp. 2204-12; World Bank, EMENA Proj- ects Division, "Appraisal of the Istanbul Power Distribution Project, Istanbul Electricity, Tramway, and Tunnel Company (IETT), Turkey" (a restricted- circulation document) (Washington, D.C., April 1973, processed); Pablo Jaromillo and Esteban Skoknic, "Costo Social de las Restricciones Energia Elctrica," Ofi- cina de Planificaci6n, Chile (August 1973); Taiwan Power Company, "Evaluation of Generating Capacity Reserve for Taiwan Power Company"; Jamaica Public Service Company Plannig Department, "Reliability Dollar Value Analysis," and "The Selection of a Generation (Static) Reliability Criteria for the Jamaican Public Service Company, Ltd" (November 1975); Alvin Kaufman, "Reliability Criterion-A Cost-Benefit Analysis," Office of Research, New York State Public Service Commission (August 1975); Michael L. Telson, "The Economics of Alternative Levels of Reliability for Electric Generating Systems"; DeAnne S. Julius, "The Economic Cost of Power Outages: Methodology and Application to Jamaica," report no RES7 the World Bank, Energy, Water, and Telecommunica- tions Department (a restricted-circulation document) (Washington, D.C., August 1976, processed); Michael Webb, "Determination of Reserve Generating Capacity Criteria in Electricity Supply Systems", and D. Priestman, "The Cost of a Long Term Electrical Energy Shortage Due to Underplanning" (paper presented at the Eleventh Annual Pacific Northwest Regional Economic Conference, May 1977, Eugene, Oregon; processed. Other relevant studies include: H. Weber, "Evalua- tion of the Damage to the Economy Caused by Losses of Electricity Supply," Energetik, vol. 2 (1966), pp. 22-26; J. Fabres and A. Bonnardot, "The Cost of Energy Not Applied in Electrical Networks," Electrical Review (November 1971), pp 737-39; G. F. L. Dixon, "British and French Views on Security of Supply," Electricity Review (November 1971), pp. 735-37; S. Schulte, "Problems in the Evaluation of Costs Incurred Due to Electricity Supply Failures," Elek- trizitatswirtschaft, vol. 70, no. 23 (Nov. 1971), pp. 656-61; and L. Lundberg, Quality of Service from the Consumer's Point of View (report of the Group of Experts, no. 60/Dl. International Union of Producers and Distributors of Elec- trical Energy) (Paris: UNIPEDE, 1972). Further references are given in ap- pendix E. ESTIMATION OF OUTAGE COSTS 55 gate the relation between the duration of an outage and its resulting cost. For more specific details readers are referred to the original studies. Measurement of outage costs None of the studies reviewed in this section explicitly discusses the fact that there are two general types of outage-related costs: the direct costs of spoiled products and idle factors, as well as the indirect costs of obtaining standby sources of energy and of adopting less efficient production techniques. Since these studies did not attempt to measure indirect outage costs as defined earlier in this chapter, only their attempts to measure direct outage costs are discussed here. Previous attempts to measure the direct component of total outage costs were unsatisfactory because they did not recognize production as a process through which inputs are combined with raw materials and intermediate products to produce a stream of outputs over time. There- fore, these studies do not estimate the effects of outage costs on the stream of final outputs. The exception is the Jamaica study by Julius, which implicitly recognizes how these costs affect industrial consumers by allowing for the possibility of overtime production. This study also attempts to measure the effects of outages on industry on the basis of opportunity costs. Several studies use the simplistic assumption that outage costs are directly related to the average level of output per unit of time or elec- tricity. A major weakness of this approach is that such average measures cannot be used in general to estimate the marginal effect of an outage, as discussed at greater length in the section on the relation between outage cost and duration. In the Istanbul study, for instance, the average value added per hour of work day in 1971 was multiplied by the num- ber of hours of outages during work days in that year, to estimate the costs of outages in 1971. Similarly, in the study by Shipley and others, an estimate of outage costs per kilowatt-hour of electricity not consumed because of outages, was obtained by dividing the gross national product (GNP) in a given year by the kilowatt-hours consumed in that year. The studies in Taiwan and Chile as well as those by Kaufman, Telson, and Priestman also use estimates of either output or value added per megawatt-hour or kilowatt-hour to measure the costs of outages to in- dustrial consumers. The Taiwan study first determined production values per megawatt-hour for various industries, and then assumed that load 56 THEORY shedding would occur according to the value of production per megawatt- hour. Costs of outages of various durations were calculated based on the assumption that load shedding occurred strictly in accordance with priority: that is, the supply of electricity to the industry with the lowest output per megawatt-hour would be curtailed first. For example, given a shortage of generating capacity, the electric energy made available to the industry with the lowest output per megawatt-hour would be cut off first, and so on. The product of megawatt-hours curtailed times the value of lost production per megawatt-hour over all the industries af- fected provided an estimate of the cost of a particular outage. In many cases it may be inappropriate to use ratios of output or value added per kilowatt-hour to compare the losses among industries. Given an electricity-intensive industry and a nonelectricity-intensive industry, the former would have a lower production value per kilowatt-hour than the latter. It cannot necessarily be concluded from this alone, however, that electric energy is more important to the low-electricity-intensive industry than to the high-intensive one. Industry production functions and the availability of electricity substitutes would actually determine the importance of electricity. Thus, load shedding strictly according to the ratio of value added per unit of electricity might not minimize the value of reduced production.6 Furthermore, load shedding according to some fixed order may be difficult to accomplish when outages are re- lated to transmission or distribution: that is, when the nature of the system failure determines which consumers are not supplied with elec- tricity. The Chilean study estimates costs per kilowatt-hour of outage for twenty industrial users of electricity by employing an input-output ap- proach. More specifically, a vector of input-output coefficients, b,,, which indicates the reduction of electricity consumption in sector j, given a US$1.00 reduction in final demand for the output of sector i, is determined. If the output of sector j is not an input to sector i, then bj = 0. Thus, (bi, X C,), where C, = electricity consumption in sector j, measures the total reduction in electricity consumption in sector j re- sulting from a US$1.00 reduction of output in sector i, whereas the reciprocal of this measure is an estimate of the value of lost production in sector i, resulting from a 1 kilowatt-hour reduction in the electrical energy supplied to sector j. Similarly, the Priestman study uses a regional- 6. This point is emphasized in: Michael L. Telson, "The Economics of Alterna- tive Levels of Reliability for Electric Generating Systems," p. 688. ESTIMATION OF OUTAGE COSTS 57 ized input-output model to estimate shortage costs for each kilowatt-hour of electricity not supplied. Kaufman estimates outage cost for New York State in value added for each dollar of electric utility revenues in 1972. He first estimated the state utilities' lost revenues and then multiplied this figure by the ratio of value added to electric utility revenues. Such outage costs are calculated on a yearly basis for 1974 to 1985. This assumes that the value of production for each dollar of revenues would be increased 2 percent annually to account for the expected growth of electricity inputs. Finally, Telson suggests two upper-bound estimates of the costs per megawatt-hour of outages. The first of these is the large upper-bound estimate, which is defined as the ratio of the gross product of an area to the electric energy consumed by commercial and industrial users in the area. The small upper-bound estimate is the ratio of wages and salaries in a given area to the electric energy consumed by commercial and in- dustrial users. The Swedish and Jamaican Public Service Company studies use a more sophisticated approach to determine outage costs. Both employed interviews and questionnaires to determine the effect of electric power outages on industrial output. In the Swedish study, estimates of outage costs for industrial consumers of electricity were obtained from ques- tionnaires completed by approximately seventy firms, which account for 28 percent of total industrial consumption. Total costs for the indus- trial sector were calculated as weighted averages of the costs in the twelve industries considered; the weights were the levels of electric en- ergy consumption of each industry in 1965. These costs were estimated for outages of various durations and were measured in value-added terms, to avoid double-counting when aggregating across sectors. The study by the Jamaican Public Service Company initially calcu- lated the amount of gross domestic product (GDP) in value-added terms accounted for by each sector, and then the sensitivity of each sector to electricity outages: that is, the percent by which production would be reduced as a result of an outage was determined by averaging the esti- mates of three experts. The product of GDP for each sector times the sector's sensitivity to outages provided an estimate of the cost of an outage to each sector, based on the so-called "dollar value effect." The empirical results obtained should be viewed with caution, since the sen- sitivity estimates used assumed an outage of undetermined length, rather than of 1 megawatt-hour, as suggested in the report. By summing the above costs across all sectors and dividing by the total megawatt-hours 58 THEORY of electricity consumption in Jamaica, a weighted measure of the value of production per megawatt-hour was obtained. This served as an esti- mate of the cost to society of each megawatt-hour of electricity not sup- plied, and is called the "reliability dollar value." The estimate of the value of production per megawatt-hour is biased downward, since resi- dential electric consumption was included in the denominator, whereas the value of household production was excluded from the numerator. Finally, this study measured the opportunity costs of outages caused by ruined and idle productive resources of industrial consumers. In some cases this cost might be roughly equivalent to the financial cost of out- ages, particularly when prices reflect opportunity costs, and there is neither slack productive capacity nor overtime production. If some pro- duction is recovered, however, either by using existing productive ca- pacity more intensively after the outage or by overtime production, then the opportunity cost and financial cost measures may differ, and the former would provide a better estimate of the economic resource cost. In summary, this review makes clear that most studies estimate outage costs as the value of production foregone during an outage. This lost production is assumed, in most cases, to be proportional to either the total length of outages or to the total amount of electricity not supplied. Such an approach leads to overestimates of outage costs if there is (a) some possibility of substituting other energy sources for electricity in production processes; (b) some production processes that either do not use electricity at all, or use it for noncritical aspects of production; (c) excess production capacity; or (d) sufficient inventories to cover lost production together with some excess capacity that allows lost produq- tion to be recovered eventually. Conversely, this approach could lead to an underestimate of outage costs if production cannot restart imme- diately after the supply of electricity is restored, or if materials are spoiled because of outages. The use of direct questionnaires or expert estimates would reduce the possibility of such over- or under-estimates. Treatment of electricity consumers by category Applying the general techniques of estimating outage costs described in the previous section to the specific types of electricity consumer af- fected by outages is particularly relevant. Many studies only consider the cost of outages that affect industrial users of electricity, including those focusing on Istanbul, Taiwan, and Jamaica (Julius), and those by Kaufman and Telson. The work on Sweden and Chile, and the Ja- ESTIMATION OF OUTAGE COSTS 59 maica Public Service Company and Priestman studies, attempt to esti- mate the costs that outages impose on residential as well as on industrial consumers. The Swedish study estimates outage costs for "typical" resi- dential consumers. These costs include expenses associated with alter- native energy sources needed, reduced efficiency of domestic work, interference with food preparation, and restrictions on leisure activities. The procedures used to obtain these specific cost estimates, however, are not described in detail. The Chilean study uses a fundamentally different approach to estimate the costs that outages impose on residential consumers of electricity. In this study, such costs are estimated in terms of two components: (a) the per-kilowatt-hour tariff based on the assumption that consumers value the electricity they use, or want to use, but cannot obtain because of outages, at least as much as they pay for it; and (b) the implicit cost of temporarily useless appliances. This latter cost is determined by dis- tributing the annuitized purchase price and operating cost of the appli- ances over their useful lifetimes, and then dividing this annual cost by the appliances' annual usage of kilowatt-hours. The result is an estimate of the implied appliance cost per kilowatt-hour of outage. The method used in the Jamaica Public Service Company's study to estimate outage costs for residential consumers is similar to the technique used in the Chilean study. Although the implicit capital cost of temporarily useless appli- ances is calculated in the same way in both studies, the kilowatt-hour tariff was not included in the estimated outage cost because these elec- tricity charges are not incurred during the outage. Outage costs will be less than those estimated by this approach to the extent that (a) some of the appliances considered will not be in use at the time of the outage, (b) the outage will not affect the quality of service provided by some appliances, such as refrigerators when the outage is relatively short, or (c) the use of some of the appliances can be rescheduled without incon- venience. Other more fundamental problems with this approach are discussed later. Finally, the study by Priestman uses the lost consumers' surplus approach to measure residential outage costs, which would un- derestimate these costs significantly, as discussed previously in this chapter. Only the Swedish study attempts to estimate outage costs for those other than industrial and residential consumers. Specifically, an attempt is made to estimate these costs for agricultural consumers. These esti- mated costs are determined on the basis of a hypothetical "average" farm. In this case, outage costs result from less productive labor for hand milking, other milk production, and animal husbandry; loss of some 60 THEORY egg and poultry production; interference with food preparation and do- mestic work; and restricted leisure activities. In summary, it is evident that one of the shortcomings of the studies reviewed here is their failure to consider the costs that outages impose on various types of electricity consumers other than industrial users. A few studies attempt to estimate these costs for residential consumers, but, as discussed earlier, these efforts have serious weaknesses. More general weaknesses of the previous analyses are that they fail to view the household as a productive unit and, more specifically, that they ignore the possibility that an outage may make productive household labor idle. This indicates that any study that considers only the cost of idle appliances may underestimate the costs that outages impose on residen- tial consumers. Therefore, an alternative method of measuring outage costs for residential consumers is developed in chapter 5, Residential Outage Costs. Relation between outage costs and outage duration One of the most important issues arising from the estimation of out- age costs is the relation between outage duration and the resulting cost. If total outage costs are not linearly related to total outage duration, then the studies estimating outage costs as a linear function of total hours or kilowatt-hours of outages-that is, those in Istanbul, Taiwan, Jamaica (Julius), and Chile and those by Kaufman, Priestman, Shipley and others, and Telson-will obtain inaccurate cost estimates. The study in Sweden is one of the few that explicitly considers the relation between outage cost and duration. Outage costs for industrial, residential, agricultural, rural, and urban users of electricity are divided into fixed and variable components. This study shows that fixed costs are incurred as soon as the outage occurs and are independent of the length of an outage. Variable costs, however, increase with the duration of an outage. Yet, some estimates of fixed costs for outages longer than one- half hour actually consist of the sum of the fixed cost and variable cost components of the shorter outages. In this sense they do not meas- ure truly fixed costs.7 7. For example, the fixed costs of an outage between one-half and one hour for the total industrial sector was estimated to be $0 21. This cost actually repre- sents the fixed cost of shorter outages, $0 08, plus the (linearly) variable cost of shorter outages, $0.27/hour X 0.5 hour = $0.13. ESTIMATION OF OUTAGE COSTS 61 Conclusion This review indicates that most previous attempts to estimate outage costs have failed to develop an adequate conceptual framework within which to analyze outage effects and, consequently, outage costs. The costs of purchasing standby sources of energy are ignored, and even the attempts to measure direct outage costs are inadequate. In general, pro- duction is not viewed as a process that occurs over several periods. As a result, most existing outage cost estimates come closer to measuring the financial cost of an outage, rather than its true economic cost. Also, most studies fail to consider the costs that outages impose on other types of electricity users besides the commercial-industrial group. Even those that estimate outage costs for residential consumers ignore the oppor- tunity costs of idle time inputs in households affected by outages. Finally, little attention is given to the relation between outage cost and outage duration. These weaknesses in the existing methodology of the esti- mation of outage costs are discussed further in the following chapters that develop methods of estimating outage costs for different types of electricity consumers. Specific methods of estimating outage costs for various types of consumers should be micro-oriented and consumer-specific. Their ap- plicability would depend on the availability of detailed information concerning levels of economic activity and the effects of outages. As indicated in the case study analyzed in Part Two, practical experience shows, however, that it may be possible to develop "shortcuts" that would also allow outage costs to be estimated roughly on a regional, provincial, or national basis. This would limit the field work required at the micro-level. For example, the value added for each kilowatt-hour in certain industries may be a good proxy for mean outage costs for each kilowatt-hour lost. Therefore, any macro-economic input-output data relating electricity inputs to industrial outputs by sector could be uti- lized to estimate outage costs In other cases, the production process for a given activity may be similar enough in different countries for more readily available outage cost estimates from another country to be used. By using such estimates and also by adopting efficient sampling tech- niques, the number of field surveys necessary to estimate outage costs for macro-level studies of reliability could be reduced. Chapter 5 Residential Outage Costs A household is a productive unit combining resources such as house- hold members' time, electricity, and other inputs to produce outputs, the enjoyment or consumption of which increase the welfare of the mem- bers of the household.' In the absence of external effects, the value of resources normally used in household production that are ruined or become idle because of an unforeseen outage could serve as an estimate of the welfare loss resulting from the outage. The unpredictability as- sumption is important because if exact times of outages were known beforehand, consumers would be able to adjust their schedules to mini- mize outage costs. As discussed in chapter 4, Estimation of Outage Costs, the short-run costs associated with a kilowatt-hour lost because of unexpected outages will, in general, exceed the maximum amount ra- tional consumers would be willing to pay for the same kilowatt-hour, on the basis of their longer-run demand curve for planned electricity con- sumption. 1. See Gary Becker, "A Theory of the Allocation of Time," Economic Journal, vol. 75 (September 1965), pp. 493-517; Kevin Lancaster, "A New Approach to Consumer Behavior," Journal of Political Economy, vol 74 (April 1966), pp 132-57; and Reuben Gronau, "The Intra-Family Allocation of Time: The Value of the Housewives' Time," American Economic Review, vol. 63 (September 1973), pp 634-51; for a more complete discussion of household production theory 62 RESIDENTIAL OUTAGE COSTS 63 Household Activities Although the household can be viewed logically as a productive unit, the measurement of residential outage costs is not straightforward. This is because most of the "outputs," such as leisure, are consumed within the household and are not valued in the market. Also, the value of inputs into this production process, especially household members' time, is often not determined in the market. The most important household out- puts that use electricity as a principal market input are housekeeping, nutrition, and leisure. Of particular relevance to housekeeping activities is the possible flexi- bility of rescheduling household chores, thereby minimizing outage costs. Interruptions in electricity supply usually affect the functioning of house- hold electrical appliances used for ironing, washing, vacuuming, and other chores. Sometimes, however, it is possible that housekeeping ac- tivities which do not require electricity may be substituted for those that do. In addition, during any period, nonhousekeeping activities may be substituted for those involving housekeeping activities. Therefore, the outage costs resulting from idle resources used for housekeeping usually will be small. In general, the costs will not be zero because of the psy- chological costs of disruptions in the normal routine, assuming that household producers rationally allocate their time to various kinds of production before the outage. Nutrition, defined here as an economic activity, could be hampered by outages occurring when food is being prepared or consumed, par- ticularly in homes that rely on electric cooking appliances or lighting. For interruptions of relatively short duration, the outage costs may in- volve only the inconvenience of a delayed meal, but during lengthy interruptions, which are much less frequent, meals may have to be pur- chased, resulting in an unexpected expense. In areas where outage expectation is high, households may incur additional indirect outage- associated expenses by purchasing nonelectric appliances, such as small kerosene stoves for emergencies. When other fuels such as kerosene, gas, or firewood are used exclusively for cooking, outage costs are likely to be small. If the expenses associated with nonelectric cooking facilities exceeded the costs of purchasing and using an electric stove, and if the former was preferred to the latter specifically because of the low relia- bility of electricity supply, then the difference in costs between the two alternatives would also constitute an indirect outage cost. 64 THEORY Leisure differs from the housekeeping and nutrition activities in ways that make the associated outage costs more important. First, the pro- duction and enjoyment of leisure in most households is limited, particu- larly for wage earners, to a relatively fixed period of time, usually in the evening. It is assumed that housewives are not limited to enjoy leisure only during the evening hours and, therefore, that their outage costs are small. Thus, it is possible to avoid complications arising from having to estimate the value of housewives' time.2 Second, those leisure activities, such as television viewing and reading at night, which would require elec- tricity have limited substitution possibilities for nonelectricity-using ac- tivities during an outage, at least in the short run. Since the loss of leisure activities is likely to be the most significant component of resi- dential outage costs, a model of household activity based on the con- sumer's labor-leisure choice is developed to estimate the loss of welfare associated with interruptions in electricity supply. Clearly, many other household activities and outputs-other than the three categories of housekeeping, nutrition, and leisure-depend on at least the partial use of electricity. For example, power outages also will affect the operation of major appliances including refrigerators, air con- ditioners, and heaters, which are only partially associated with the dis- ruptions of household activities discussed previously. In these cases, the effects of the disruption would be significant only for outages of several hours, which generally occur far less frequently. In addition to the loss of services from such equipment, the damage to and reduced life span of motors and equipment resulting from voltage variations would have to be considered. Households may also incur indirect outage costs by purchasing emergency items such as standby generators, storage bat- teries, and kerosene lamps. In this respect, the consequences of outages may be inequitably distributed, because wealthier consumers will be better able to afford voltage-boosting devices and alternative energy sources, thereby reducing direct outage costs. Poorer users, however, may be less dependent on electricity and, therefore, less susceptible to outages. 2 See Reuben Gronau, "The Intra-Family Allocation of Time: The Value of the Housewives' Time." The low outage cost does not imply that the activity of housewives is valueless It reflects the assumption that housewives have greater flexibility in scheduling their leisure, so that the inconvenience imposed by leisure loss resulting from evening outages is less severe than for wage earners. RESIDENTIAL OUTAGE COSTS 65 Value of Foregone Leisure Consider a typical household that maximizes utility over some period of time (D days). Utility U is expressed as a function of leisure type S that cannot be enjoyed without electricity, leisure type V that is elec- tricity independent, and income I (net of expenses incurred to enjoy the leisure), which represents all other consumption: (5.1) U = U(S, V, I). Next, leisure type S is specified as a function of the inputs: time t (hours), electricity consumption e (kilowatt-hours), flow of services z from the stock of electricity using equipment (TV), and other inputs represented by x: (5.2a) S = S(t, e, z, x). Similarly, leisure type V is a function of time 0 and other inputs rep- resented by m: (5.2b) V = V(0, m). Furthermore, e and z may be written as functions of the stock of electricity using capital k, the value of appliances annuitized over their useful life, and of time t which is a measure of intensivity of use. There- fore, e = e(k, t) and z = z(k, t). The household budget constraint may be written: (5.3) I= w(H-t-0)-p*e-b.k-c.x-rr-m where w = effective hourly net income earning rate; H = maximum feasible number of hours of work in the time period; p = mean price for each kilowatt-hour of electric energy; b = equivalent income fore- gone for each unit of k in the time period; c = cost for each unit of other inputs x used; and r = cost for each unit of other inputs i used. First, the longer-term situation, a period of one year, is examined. Maximizing utility subject to the linear budget constraint is equivalent to unconstrained maximization of the expression: 66 THEORY (5.4) L = U(S, V, I) -. X. [H - t -0- (I+ pe + b.k + c-x + r-m)]. w The following equations indicate the first-order (necessary) conditions. aL aU FS aS ase OS azi pBel (5.5a) a + + L + X*l + 0 at as at ae at az at W at (5.5b) a=ala-ae+ O---z + *[p.a- + b]= 0 ( k aS ae ak az ak w Ak aL aU as X (5.5c) - =- + --c = 0 ax as ax w aL aU X (5.5d) =- + - = 0 aI HI W aL aU aV (5.5e) - + x = 0 aoL auv aL aU aY X (5.5f) - - + --r =0 am aV am W aL (5.5g) -= -[H - t - 0 - (I+ pe + b.k + c-x + r-m)] =0. Multiplying equations (5.5a), (5.5b), and (5.5c) by dt, dk, and dx respectively, summing the three resulting equations, and rearranging terms yields: a Uas as ae aS.Lzd (S e as az A as -I-+ .--+-.- .dt± +±* + j-.dk±+--dxI aS at + e at az at ae ak az ak/ Ox O e ( e + w + p.- *dt + p.- + b).dk + c.dx] = 0. w at ak RESIDENTIAL OUTAGE COSTS 67 Simplifying further: au (5.6) -*dS + -- (w.dt + p*de + b-dk + c.dx) = 0. as I Dividing equation (5.6) by equation (5.5d) yields an expression involving the marginal rate of substitution of income for electricity- dependent leisure, keeping utility constant as derived from the consumer's long-run decision: (5.7) MRSr,s-dS = w-dt + p-de + b-dk + c-dx where 8 U 8 U dl1 MRSr,s - j as ai dS aUlaU Iconstant by definition. MRSr.s measures the marginal monetary value of elec- tricity-dependent leisure: that is, it is the income increase that will compensate the consumer just enough for this leisure foregone at the margin to remain on the same indifference curve.' Consider the effect of an unexpected outage during the evening when the family is enjoying leisure type S. During the outage, that is, in the short-run, it can be argued that e and z depend only on t. This assumes a putty-clay type of relation between k, e, and z. For example, in the short run, electricity use may be linearly proportional to time. There- fore, it is possible to write: e = (t). Using the above expressions to evaluate equation (5.7), and replacing dS by AS, and so on: (5.8) MRSrs- AS IV + P- At + c-Ax + b*Ak. 3. See Robert D. Willig, "Consumers' Surplus Without Apology," American Economic Review, vol. 66 (September 1976), pp. 589-97. 68 THEORY Thus, the left side of equation (5.8) represents the overall welfare decrease because of an incremental loss of leisure AS resulting from the unexpected outage of duration At; the right side measures the value of the inputs necessary to produce the leisure. The term (b.Ak) is interpreted as representing the value of the input of electricity-using equipment that is foregone during the outage. If the income foregone in each period (bk) is uniformly distributed over the leisure period (t) during which the equipment is used, then the average value of appli- ance input for every unit of leisure time is bk/t, and therefore b-Ak - b-(k/t)-At. The household's electricity bill, however, will also be reduced by the amount p.(aT/at)* At from kilowatt-hours not used during the outage. Therefore, the net incremental welfare loss or outage cost may be written: (5.9) OCR = MRSI.s.AS - p--*At = iv*At + c*Ax + b-Ak. at Extreme differences that could occur between outage costs estimated for very rich and very poor consumers of electricity, especially in coun- tries where the income distribution is highly inequitable, may not be realistic. As discussed in chapter 9, Shadow Pricing, if there is dimin- ishing marginal utility of income and consumption, then it is possible to weight the outage costs, depending on the average income level of the household. The use of such social weights, which should reflect na- tional income distributional goals, would tend to reduce the disparity between the disutility of outages to low- and to high-income households. Finally, an expression is derived for the marginal value of electricity- independent leisure. Multiplying equations (5.5e) and (5.5f) by dO and dm, respectively, summing the two resulting equations, and rearrang- ing terms as before, yields: au /av av x - - dO + --dm + Xd + -*r.dm = 0. av 0ao am w This may be rewritten: (5.10) --dV + w-dO + = 0. aV W( RESIDENTIAL OUTAGE COSTS 69 Dividing equation (5.10) by equation (5.5d) allows the marginal rate of substitution of income for electricity-independent leisure, keeping utility constant (MRS,,), to be determined: (5.11) MRSrv*AV = wAO + r-Am: where AV has been used instead of dV, and so on. Equation (5.11) is analogous to equation (5.8). It measures the welfare change caused by an incremental change in the availability of electricity-independent leisure AV, in terms of the value of the inputs: that is, time At and other input Am, which are required to produce this leisure. The relevance of equation (5.11) to outage cost estimation is discussed in the next section. Empirical Estimation As mentioned in the earlier discussion dealing with the theoretical model, the empirical estimation of residential outage costs is particularly difficult because of the nonmarketable nature of the household outputs produced by using electricity. From a practical viewpoint, data on wages and income are far easier to obtain than information on the use of appliances and other inputs. Fortunately in most instances the dominant term in equation (5.9) would be the wage element. Take, for example, a television set, one of the more expensive items of electrical equipment commonly used for leisure. Assuming a purchase price of US$250 and a six-year lifetime (independent of usage and outages) and a discount rate of 10 percent, the annuitized value is US$57.50 a year. For a set that is used four hours a day on the average, the corresponding value of b - Ak is US$ 04 an hour of outage, which is likely to be a negligible amount, even compared with minimum income earning rates for rela- tively poor households using electricity. Similarly, the term c - Ax is also likely to be relatively insignificant. For example, it could represent a snack being eaten while watching television. An outage would interrupt the snack. If the food is wasted, there will be a small welfare loss, but if it is eaten later, there would be no loss. It may be concluded that the difficulties of obtaining data on owner- ship of electrical appliances or other inputs used during leisure time will usually far outweigh any resulting refinement to the basic estimate of outage costs that is derived purely on the basis of more readily avail- 70 THEORY able income data. Therefore, in practice the following expression may be used as a good approximation to equation (5.9): AOCR (5.12) At - V. Arguing, analogously, that the wage term is likely to dominate the second term on the right side of equation (5.11), it is possible to derive another approximate relation: AV (5.13) MRSI,v- ~ iv. Therefore, the incremental monetary values of both electricity-dependent and -independent types of leisure per time unit are roughly equal to the wage or income earning rate. In practical terms, the theoretically derived link between the two types of leisure and the income earning rate summarized in equations (5.12) and (5.13) is intuitively reassuring, because electricity-dependent leisure and actual working hours may not be direct physical substitutes for each other. For example, the normal workday could extend from 9:00 A.M. to 5:00 P.M., whereas electricity-dependent leisure may begin only after 7:00 P.M. Therefore, the marginal tradeoff between electricity- dependent leisure and Qxtended working hours may have to occur by adjusting the intervening electricity-independent leisure period. As discussed earlier, a principal practical advantage of using fore- gone leisure to estimate the outage costs of residential consumers is the availability of easy-to-obtain income data. Often a good correlation between family income and kilowatt-hours of electricity consumption could be obtained for a typical sample of residential consumers from the utility company's billing records and from household budget surveys. The income levels of households that use electricity could then be estimated. Since the method of estimating residential consumers' outage costs may sometimes lead to incorrect estimates, the discussion must be fur- ther clarified. (a) It is assumed that workers can vary their work hours to equate their wages with the marginal value of their leisure time. Traditional work practices such as the forty-hour week, union restrictions on hours worked, or insufficient employment alternatives might prevent this. If RESIDENTIAL OUTAGE COSTS 71 workers are unable to work as much as they wish, then their wage will overestimate the value of lost leisure. A related point is that the day- time wage rate may not be a good proxy for the value of leisure. The marginal wage rate corresponding to the leisure hours may be more appropriate, and in some cases this may be the overtime rate of pay. (b) The cost to nonwage-earning members of the family is effectively ignored by allowing only the wage earner to represent the household as an income-earning unit. For example, the value of the housewife's time may be estimated as the average earning rate of women who work out- side the home, although the corresponding outage cost may not be accurate, because of the greater work-leisure substitution possibilities for housewives as well as differences between the productivity of house- wives and women who work outside the home. (c) Residential consumers may develop outage expectations, presum- ably because of the frequency of such occurrences in the past, so that the possibility of interruptions in electricity supply will be considered when labor-leisure decisions are made. This indicates that the cost of the out- age will be less than when no outages are expected. (d) If some leisure is enjoyed outside the household that is affected by the outage, then ideally, this case should be treated separately. (e) Finally, in unusual situations outages may provide some con- sumption benefits to residential consumers-perhaps the enjoyment of a novel situation. These difficulties indicate that the estimate of outage costs inferred from consumers' labor-leisure choices should be independently verified. As noted earlier, the short-run outage cost is likely to exceed the maxi- mum willingness to pay for the lost kilowatt-hours, based on the house- hold's longer-run demand curve. Therefore, empirical verification of equation (5.12) must depend on the determination of the consumer's willingness to pay in the short run to avoid an unexpected outage. Any household survey to test this hypothesis must be carefully worded and administered (see the case study for details). Chapter 6 Industrial Outage Costs A method of estimating the outage costs incurred by electricity users who produce a marketable output is developed in this chapter. Although the chapter focuses on industrial users, the technique described could be applied to a much wider class of commercial consumers whose pro- ductive activities may be analyzed within the same general framework. The method proposed for measuring the economic costs of random out- ages affecting such users of electricity is based on the application of the notion of short-run opportunity costs. Types of Outage Costs The effects and direct costs of outages to industries during working hours are classified into two main categories: (a) spoiled material in the process of being produced or in storage and (b) reduced production during the outage and the following restart period: that is, after elec- tricity is restored but before full production resumes.' The estimated 1. Links could be developed between this framework for outage cost analysis and the recent work on physically based electricity demand models developed to analyze large industrial loads With the latter technique, the usage patterns of individual items of equipment and the output flow and storage structure of indi- 72 INDUSTRIAL OUTAGE COSTS 73 outage costs resulting from these effects are discussed in the next section, using the most convenient data as parameters: that is, the average fre- quency and duration of outages in a given service area. If the reliability level of usual electricity service is poor, certain in- dustrial consumers, especially those who are sensitive to outages, may wish to improve the security of supply by installing standby generators or by reinforcing their links with the public grid. They may also attempt to modify their production processes to reduce outage costs by sched- uling critical outage-sensitive operations during the hours of the day when interruptions would be least likely to occur, or by adopting en- tirely different production techniques. All additional expenses connected to any new facilities or modifications to normal operating procedures would be indirect outage costs as defined in chapter 3. To use this information effectively in the analysis, however, it would be necessary to determine not only the magnitude of such expenditures, but also the exact level of reliability at which industrial consumers would consider additional costs economically justified. In summary, for industrial and commercial firms, the indirect outage cost of adopting less efficient pro- duction techniques at a given level of reliability can be measured by determining how much lower production costs would have been if elec- tric power reliability were not a concern Yet information on indirect outage costs is not always readily avail- able from the affected firm Furthermore, although useful data may be gathered from similar firms, it is difficult to ensure that any observed production cost differentials result from a response to observed relia- bility, rather than to differences in technologies and capital vintage. The costs of obtaining a standby energy source are easier to determine and sometimes provide insights into the magnitude of direct outage costs as well. A consumer's decision to purchase a standby energy source, which for simplicity is assumed to reduce direct outage costs to zero, would depend on whether or not its cost were greater or less than those of the direct outage costs that could have been expected during the lifetime of the back-up source. Thus, the cost of a standby energy source that was already purchased would serve as a lower limit on the estimate of direct outage costs, whereas if the source had not been purchased, its cost would provide an upper limit on the estimate of direct outage costs. vidual productive processes are analyzed to determine the hourly kilowatt load of a given firm. See, for example, Y. Manichaikul and F. C. Schweppe, "Physically Based Industrial Load," IEEE Transactions on Power Apparatus and Systems, vol. PAS-98 (July/August 1979), pp. 1439-45 74 THEORY Spoiled Product Cost The economic value of spoiled product depends on the extent to which it has been processed and must include the value of all embodied inputs used in its production. Typically, some raw materials and other inputs that are transformed into finished output by the factors of pro- duction might be considered. The outage cost should include the value of the raw material and other inputs ruined, as well as the value-added embodied or included in the spoiled output, resulting from partial or complete processing by the primary factors. In some industries, output will be ruined instantly when an outage occurs; in others the outage would have to be of a certain critical duration before any product would be spoiled. Thus, in the first case the value of spoiled product cost (SPC) over a given time interval is a function only of outage frequency, whereas in the second case the cost depends on both outage frequency and dura- tion. For interruptions shorter than the critical duration, no product would be spoiled, but for outages exceeding the critical duration, the value of SPC could be an increasing function of duration. For any specific firm over a given year, the economic value of spoiled output can be written: f Q SCP = F 0(d,)- h where Q = total annual value added; h = number of hours of plant operation in the bench mark year; f = frequency of outages per year; d. = duration of the i'^ outage in hours; and 0(d,) = value of spoiled product for an outage of duration d, as a fraction of average tetal value added per hour, Q/h. Note that / = o if d, < a, where a = critical duration of outage beyond which the output is spoiled, and aOl/d > 0 in general. fl itself may be further broken down as follows: fl(d,) = [v (d.) + m (d,)] where v (d,) = the lost value added (from capital and labor), which is already included in the spoiled product; and m (d,) = the value of other inputs lost, such as raw materials. Both v and m are given as frac- tions of total average hourly value added. When only raw material inputs in stock are spoiled because of the outage, then v (d) = 0, and INDUSTRIAL OUTAGE COSTS 75 conversely, if finished product was ruined, then 0 (d) = value of finished output that was spoiled at product prices. Idle Factor Cost During the outage period, a certain fraction e (where 0 < e < 1) of normal output will not be produced. There will be no idle resources and, therefore, no reduction in output if the firm does not use electricity in the production process or if managers can substitute those aspects of the production process that do not use electricity for those that do. This same fraction also measures the fraction of time during the outage when productive resources (capital and labor) are idle. Furthermore, even after the supply of electricity is restored, a certain fraction of normal output Z (where 0 < Z < ) may not be produced in some firms during a restart period. For instance, motors must be turned on, furnaces reheated, or equipment cleaned before production can resume. Once again there is an opportunity cost in the form of idle resources. For firms that have restart periods, this cost could de- pend on: (a) the frequency of outages only; (b) both outage frequency and duration, where duration must exceed a "critical" length of time to result in a positive restart time; and (c) both frequency and duration, where restart time is related in a positive, continuous manner to outage duration. Thus, the annual opportunity cost of slack factors of production or idle factor cost (IFC) during the time of the outage and the subsequent restart period is given by: f Q IFC = d [*d, + i*y(d,)].- h where y(d,) = restart time for an outage of duration d,. Note that -y = 0 if d. < 5, where 6 = critical duration of outage beyond which restart time becomes necessary, and ay/ad > 0 in general. Some firms may have a certain amount of built-in slack productive capacity during normal operation. Because of the fixed capital stock, and the possibility of wide fluctuations in the desired level of output, a firm might have excess capital in the short run. Conversely, since labor is usually viewed as a variable input even in the short run, the reason for 76 THEORY any excess available labor might be questioned. The notion that firms invest in workers through on-the-job training is one plausible explana- tion of why it may be economically rational for the firm to maintain excess labor in the short run.2 In these cases, the opportunity cost of the outage can be reduced by more intensive utilization of resources during normal working hours after the supply of electricity is restored to meet a production target. This more intensive utilization would, in effect, reduce the net amount of idle resources that results from outages. It is assumed that on average a certain fraction of the opportunity cost of the idle resources, A, during outage and restart periods can be recov- ered by this more intensive post-outage utilization of resources. More generally, A should be allowed to vary according to the length of the outage and the time of its occurrence. Knowledge of the average duration of outages and their distribution over time would allow an average value of A to be determined. This reduction in outage costs over a year's time or the recovered cost (RC) may be written: RC = X-IFC. Thus, allowing for the possibility of excess capacity, the total basic outage cost (OCB) for a particular firm during a given year will be: QIJ OCB = SPC + JFC - RC --E {10(d,) + [d, + y(d,)](l - X).E) h s where, for convenience, E = e is assumed. Alternatively, OCR may be split into nonfactor (NFC) and factor cost (FC) components as fol- lows: OCB = NFC + FC where NFC = Q/h.y m(d,), and f FC = Q/h.E {v(d1) + [d, + y(d,)](l - X)e). 2. See, for instance, Walter Oi, "Labor as a Quasi-Fixed Factor," Journal of Political Economy (December 1962), pp. 538-55. INDUSTRIAL OUTAGE COSTS 77 Overtime Production Cost For firms that operate twenty-four hours a day and cannot work over- time to make up the production lost because of outages, or for firms that decide not to work overtime, ocl: is an appropriate estimate of the costs that result from outages. Other firms, however, might decide to make up some of their lost production by working overtime. Whether this overtime production occurs on the day of the outage or later does not significantly affect the resulting production costs, assuming that overtime wage rates remain the same. In theory, the firm's decision to work overtime would be based on a comparison of the marginal private costs and benefits of overtime production. The sizes of available inven- tories or contractual obligations would be important factors in this decision. The constraints imposed by contractors could easily be in- cluded in the model by introducing a penalty, such as a fine, for an un- met deadline. Under conditions approaching perfect competition, it is unlikely that firms would have an economic incentive to make up any lost produc- tion. Exceptions might occur because of contractual obligations or be- cause of some kind of previously existing production constraint, such as a shortage of materials, that prevented the firms from producing a profit-maximizing level of output. Firms with some market power, such as monopolies, might also have an incentive to work overtime if they could pass on the extra costs to the consumer. Ultimately, firms might make up all lost production by using overtime, but the question of whether or not a firm decides to work overtime is important, since it has a direct effect on outage costs. To discuss further how the decision to produce overtime affects the costs of outages, the concept of the opportunity cost of using productive resources must be considered in greater detail. Within the short-run production period being considered, labor has alternative uses in mar- ket or household production (see chapter 5, Residential Outage Costs). Thus, even if the lost product of labor during the outage and restart periods is recovered by employing labor for overtime production, an opportunity cost still will result from the outage that can be measured as the foregone leisure of overtime workers, rather than the foregone output of the firm (IFC) Within the same short-run framework, suppose that the net lost production of capital caused by the outage is recovered by an equal amount of overtime production using machines outside of 78 THEORY normal working hours. Then there will be no cost associated with capital made idle during the outage, assuming that capital is not already used twenty-four hours a day, that depreciation is a function of the actual hours of usage, and that the additional maintenance and other costs for capital incurred during overtime are negligible. No alternative produc- tive use of capital is foregone because of this overtime production, and, thus, there is no net opportunity cost with respect to capital (see also chapter 4, Estimation of Outage Costs). If a firm wishes to recover a fraction of the output lost because of the outage, then the period of overtime, he, during which the primary factors must be employed is defined by the expression: (Q/h)ho = p*FC. Therefore, f h. = p I [v(d.) + I(d, + y(d,)) (1I Xe where p = fraction of FC that is recovered (0 p < 1). The value of lost nonfactor inputs does not appear in this expression because that loss is permanent and cannot be recouped by overtime. The term h, may be interpreted as a measure of the effective lost hours of production resulting from the outage. The resource cost of such overtime work can be written in the follow- ing form: where viv/w = effective wage ratio, which is assumed to reflect the opportunity cost of overtime labor relative to normal labor, and L = the labor component of annual value added. Since overtime wage rates are often institutionally determined, the actual wage ratio may not be the appropriate measure for w/w. In case of severe distortions in the labor market, shadow wage rates would have to be used to represent the opportunity cost of labor, both during normal and overtime work- ing hours (see chapter 9). The general expression for outage cost, including the overtime case, is given by: INDUSTRIAL OUTAGE COSTS 79 wL - Z I {m(d,) + [I - p(1 - ---)] [v(d.) + {d, + -y(d,)}(1 - I)e]}. h IVQ The two extreme cases may be examined by the following equations. Case I. No lost output is made up; therefore, p = 0, and OCI = OCB. Case II. All lost output is made up;' therefore, p = 1, and OC"I = OCB + -.-- I FC. Clearly, then, OC" < OCI as - <- (WQ wV L The intuitive explanation of this equation is that the more labor intensive the production process, that is, the smaller the ratio of total value added to labor costs, Q/L, the more likely an increase in opportunity cost, because overtime wages will be greater than the opportunity cost reduction resulting from the decrease in the period during which capi- tal is idle. In summary, a range of values for the costs incurred by industrial consumers resulting from outages may be estimated. For a firm that does not produce twenty-four hours a day, if v/w < Q/L, then OC" and OC' are minimum and maximum estimates, respectively, of outage costs. Conversely, if ip/w > Q/L, then OC" and OCI are mini- mum and maximum estimates, respectively. For firms producing twenty-four hours a day, the resulting opportunity cost of an outage can be estimated as OCI. In many cases, however, X = 0 and p = 0 so that: f OC = (Q/h) E [m(d,) + v(d,) + {d, + y(d.)} -E]. t=1 3. The case when available hours of overtime are not sufficient to allow all lost production to be recovered is not considered here but may be derived quite easily. Given typical outage durations, these instances are apt to be rare. Chapter 7 Other Outage Costs Outage costs incurred by consumers other than in the residential and industrial categories are described in this chapter. They are commercial, public services, special institutions, and rural users. Much of the dis- cussion that follows refers to outages of less than a few hours duration, especially when making up disrupted activity at a later time is consid- ered. The more widespread effects of prolonged outages are discussed in the final section. Commercial The commercial consumer category covers a variety of electricity users. Outage costs suffered by such consumers generally may be ana- lyzed within a framework similar to that described in chapter 6, Industrial Outage Costs. Since much of the commercial activity in this category could be classified in the tertiary or services sector-for example, shops, restaurants, offices, and small businesses-the possibility of making up work interrupted by outages is much greater by using existing manpower and capacity more intensively during normal working hours. Generally, the more commercial consumers rely on electricity-using equipment, the larger the corresponding outage costs would tend to be. For example, offices where only the lighting is affected may be able to function normally. If electricity-dependent facilities such as reproducing 80 OTHER OUTAGE COSTS 81 machines, desk calculators, and computer systems are used extensively, work is more likely to be interrupted. In particular, the erasure or loss of stored computer data could have serious longer-term consequences. Similarly, the higher floors of tall buildings may be inaccessible without electricity-using elevators, although staircases may be used to serve the lower floors and also shorter buildings. Electrical heating and air- conditioning, especially in large buildings, however, will only be affected by relatively long outages of several hours. Considerable flexibility may also be built into the usual office routine, enabling employees to finish an interrupted activity without overtime work. For instance, workers may take their tea or coffee break or have their daily chat during an outage-induced work stoppage, instead of at the usual times. Shops and stores will be similarly affected. Often, sales activity can continue during the day, especially in smaller shops Even if volume is reduced, it could often be made up during normal hours, after the electricity supply had been restored. Using equipment such as electronic cash registers and demonstrating electrical appliances to potential cus- tomers would, however, be severely curtailed. Commercial firms engaged in small-scale production activities not large enough to fall into the industrial category, such as artisans' workshops and family businesses, could be analyzed in terms of the disruption of production and the spoilage of materials. Again, considerable flexibility and slack is likely to be present, and workers, especially self-employed persons, could work more intensively to recoup outage-related losses. Spoilage costs resulting from outages are likely to be most important to commercial users such as supermarkets, restaurants, and hotels, who use refrigeration to store perishable items. These costs will tend to be small, however, except during lengthy outages, typically lasting several hours. Customers might even enjoy the novelty value of the new situa- tion, for example, dining by candlelight at a restaurant in spite of po- tentially delayed service. Commercial establishments that are open at night, such as late-closing shopping centers, movie theatres, and night-clubs, would have to close if the outages were relatively long. Transacting business during outages would be more difficult, and theft and security problems are more likely to arise. In summary, the outage costs of the large variety of commercial elec- tricity consumers must be examined on a case-by-case basis, especially when considering the recovery of lost activity during normal working hours by using existing slack capacity more intensively. 82 THEORY Public Services The costs society incurs as a result of electric power outages affecting public sector services are especially difficult to estimate, since no directly related consumption charges exist. Public illumination is seriously af- fected by electric power outages, because there is little possibility of substituting this output between different hours of the day, or of using nonelectrical inputs to provide the service at short notice. Generally the decision concerning the marginal investment on public illumination is unlikely to be made on the basis of an explicit cost-benefit analysis. Yet, if street lighting is either inadequate, resulting in reduced security for citizens at night, or too extensive, leading to increased costs and munici- pal taxes, then the public would pressure the local government to change the situation. Therefore, in the absence of a detailed knowledge of the benefits of public illumination, it may be argued that a community has invested in street lighting to the point where the marginal costs and benefits of such lighting are roughly equal. An outage affecting street lighting will clearly reduce community wel- fare. From the preceding analysis, it may be deduced that one estimate of this welfare loss would be the value of the capital equipment used for public illumination, annuitized over the total lifetime hours of usage and prorated during the outage period, plus the cost of routine mainte- nance, which is unaffected by outages. Electricity charges not paid dur- ing the outage would be netted out This estimate of welfare loss would generally be minimal, since the public illumination benefits lost may not be at the margin, thus raising the question of consumers' surplus. (This assumes that the community demand curve for public illumination is downward sloping.) Therefore, as noted, the short-run costs imposed on citizens-by an unexpected outage, such as the sudden loss of security, are likely to exceed the willingness-to-pay for public illumination in the longer term. If data are available, the increase in street crimes resulting from decreased street lighting may be used to measure outage costs. The increased risk or incidence of accidents as well as the time wasted because of traffic congestion resulting from nonfunctioning traf- fic lights could be used to estimate outage costs for this specific type of interruption. Typical examples of other public sector outputs likely to be disrupted by power outages include sewage and water treatment plants, telephone and mass transport services, and radio and television. An appropriate OTHER OUTAGE COSTS 83 measure of outage costs may be used for each case, such as foregone output, idle productive capacity, or citizens' willingness to pay more to avoid the effects of outages. Generalized services in urban centers, such as those provided by the police, fire, and sanitation departments, are likely to be affected by out- ages to the extent that they depend on electricity for lighting, commu- nications, pumping, transport, and so on. Any consequent loss of security and safety or breakdown of public order will be extremely dif- ficult to estimate in economic terms before the outage. In a given situa- tion, the duration and geographic extent of a blackout may have to exceed certain critical values before such society-wide effects become significant. Beyond this critical point, however, economic and social losses are likely to rise sharply, especially if social conditions, time, and weather combine to aggravate the situation and if the public au- thorities are unprepared and unable to cope with the crisis. (See the section on secondary effects at the end of this chapter for a discussion of the New York City power failure during the hot summer night of July 13, 1977.) Special Institutions Specialized institutions, such as hospitals, health clinics, universities, schools, places of worship, orphanages, and homes for the elderly, are discussed in this section. The economic costs of outages for hospitals are significant enough to merit detailed treatment. Although a hospital essentially provides health services, this output is difficult to measure and furthermore, since little is known about the specific production process, several difficulties arise in estimating outage costs. If there are no standby facilities, some intermediate products in hos- pitals, including medicines and blood, will spoil during a long outage, and the value of the spoiled products would be one component of the direct outage costs. Obviously, electrical instruments and equipment are useless without electricity. In some cases, the decrease in the delivery of health services will depend on the time of the outage, for example, the need for lights. In other cases time would not be important, for example, when an artificial respirator is required. If this lost health service cannot be made up easily through more intensive use of such facilities at other times, the annuitized value of the idle equipment would 84 THEORY provide a minimum estimate of the outage cost. It is also possible that nonelectric equipment may be useless during an outage, because it is used in a situation that requires electricity as a complementary input; surgical equipment would be one example. The opportunity cost of this idle equipment should also be included. Another related result of an outage is the loss of human life-an ex- tremely crucial cost. Although the personal, psychological cost to family and friends is likely to be immeasurable, one estimate of the social cost could be the expected earnings or foregone net future output of the deceased person. In general, estimating such costs would be a com- plex task. Contingencies involving risk to human life, however, are likely to be associated with certain critical facilities, such as operating rooms and intensive care equipment, which will normally have back-up power, for example, batteries. Often, the hospital may have a standby gen- erator, in some cases to meet legal requirements imposed by the com- munity. Whether to impute corresponding, indirect outage costs will depend to some extent on how the need for a back-up source was deter- mined. If the decision to install the equipment had been made only to meet legal requirements and was not made on an economic basis, it would be difficult to infer the corresponding indirect outage cost. The effectiveness of labor inputs also will be reduced by an outage: that is, some labor may be made idle. The extent of this idle labor and, therefore, the resulting opportunity cost will vary with the time the out- age occurred and is likely to be particularly significant during the night. The effect of outages on hospital auxiliary facilities such as kitchens, laundries, heating, and air-conditioning should also be considered. Many of the outage costs incurred by health clinics are likely to be similar to those experienced by hospitals, although there are differences in the type and scale of operations, such as the lack of inpatients and less electric equipment. The effect of power failures on educational insti- tutions will vary with their dependence on electricity. For example, the activity in night schools and universities with extensive laboratory facili- ties will be disrupted more than work in day schools and ordinary classrooms. In periods of heavy rain, however, lighting may be essential even during the day. The nature of religious institutions would tend to minimize the costs imposed by outages, unless there is heavy dependence on electric lighting and heating during hours of worship. Electricity inter- ruptions restrict activities in orphanages and homes for the elderly, and, in the latter, increased health risks could be significant. OTHER OUTAGE COSTS 85 Rural This section focuses on outage costs of rural electricity consumers in the agricultural sector. Consumers in small urban areas, often classified in the rural category for other purposes such as billing, can be treated like the various other urban users described earlier. The distinguishing characteristics of rural grid-supplied electricity sys- tems are the relatively low customer densities and the correspondingly high capital costs of supply. Consequently, supply networks will be weaker and less reliable. Rural electricity users, however, are more likely to compensate for these conditions than their urban counterparts by having alternative or standby sources of power and by generally relying less on electricity. Thus, indirect outage costs may be more sig- nificant for rural consumers. The outage costs of large agro-industries may be analyzed in the same way as industrial electricity consumers. Seasonal availability of agri- cultural produce for processing and of the rural labor supply has to be considered. Large mechanized farms could also be treated analogously. The drying, milling, extracting, preserving, and storage of vegetables and grain may be affected by outages. Electric motors used to pump water will not function during outages, but adequate water storage fa- cilities could minimize the associated outage costs. In the livestock sec- tor, outages could disrupt milking, egg laying, hatching, ventilation, water supply, feeding, and waste removal, as well as produce refrigera- tion and storage. Since the living quarters of farm owners and workers are usually con- nected to the same electricity supply as the farm's productive facilities, the outage costs to households, as described in chapter 5, Residential Outage Costs, must be added to the foregone output and spoilage costs discussed above. On electrified small farms the household component of outage costs is likely to be in proportion to the disruption of produc- tive activities. In determining income earning rates for such consumers, however, the value of auto-consumption should not be overlooked. Secondary Effects In the analysis of outage costs presented thus far, the main emphasis has been on tracing the effect of electricity supply failures on the im- 86 THEORY mediate consumers. In certain instances, however, more widespread effects must be considered. The disruption of public services could lead to external costs. For example, stopping sanitation services or water and sewerage treatment may have external health diseconomies, such as greater incidence of bowel diseases or susceptibility to epidemics The outage-delayed pro- duction of an industrial firm could be an intermediate input for a second firm at a different time and location. Therefore, secondary costs could be imposed on the latter. That may seem quite unrelated to the original outage. Finally, as discussed earlier, lengthy and widespread outages may lead to a breakdown of law and order, which could have far-reaching consequences and economic costs. The New York City blackout of July 13, 1977, which lasted twenty- five hours and affected nine million people, is the best documented case of an extensive and long-lasting power failure.' The total outage costs have been conservatively estimated at US$350 million, of which about US$155 million was incurred by damaged or looted businesses. Prac- tically all social agencies, including the law enforcement and criminal justice authorities, were reported to have been totally unprepared for the effect of the blackout. There was much uncontrolled looting and collective arson by people without previous arrest records and with higher employment status than experienced criminals. The cascading nature of secondary effects is best exemplified by the outage costs of the New York City Metropolitan Transportation Authority (MTA). The MTA suffered a direct revenue loss of US$2.6 million, outage-related vandalism, and overtime payment losses of US$6.5 million, and recently was forced to initiate a US$11 million program for new equipment to prevent major disruptions caused by future blackouts. I See Systems Control Inc., "Impact Assessment of the 1977 New York City Blackout" (U.S Department of Energy Report), no. HCP T5103-01, Arlington, Virginia, July 1978, processed, Robert Sugarman, "New York City's Blackout: A $350 Million Drain," IEEE Spectrum (November 1978), pp. 44-46; G. L. Wilson and P Zarakas, "Anatomy of a Blackout," IEEE Spectium (February 1978), pp 39-46- and "Blackout '77: Once More with Looting," Time, vol. 110 (July 25, 1977), pp 12-26. For an analysis of the central Illinois power failure of March 1978, which lasted several days, see Gregory C. Kohm, "A Survey of Disruption and Consumer Costs Resulting from a Major Residential Power Out- age," Argonne National Laboratory, report no. ANL/EES-TM-29, Argonne, Illinois. June 1978, and Gregory C. Kohm, "Costs of Interruptions of Electrical Service in the Commercial Sector," Argonne National Laboratory, report no. ANL/EES-TM-30, Argonne, Illinois, September 1978. Chapter 8 Power System Planning and Supply Costs The effective application of the reliability level optimization and plan- ning model presented in chapter 3 requires prior estimation of two cost categories: outage costs and electricity supply costs. Since outage costs have been treated in detail in chapters 4 to 7, this chapter analyzes sup- ply costs in depth. First, however, the rationale underlying investment decisions in the energy sector should be discussed, as well as how the new reliability optimization procedure changes the conventional phi- losophy of power system planning. The Investment Decision In chapter 2, Introduction to Reliability, the purpose of a power system was defined simply in relation to its capability to deliver elec- tricity from the source to the consumer. Well before the decision is made to invest in electric power, however, broader issues must be faced involving the total future energy needs, availability of supply, and the optimal mix of different sources to be developed. Although the entire range of national energy sector investment and pricing policies is best analyzed and determined within an explicit economic framework, in practice such decisions are often made by policymakers on an arbitrary or judgmental basis. Today's societies require increasing amounts of energy for a variety of uses in homes, industries, and businesses as well as for agriculture 87 88 THEORY and transport. Arrayed against these energy needs are the short-term, depletable, fossil fuel supplies-petroleum, coal, and natural gas-in addition to the longer-run energy sources-water, nuclear, solar, geo- thermal, wind, tidal power, and biomass (that is, organic and often noncommercial fuels such as wood and animal waste.)1 At this stage, two basic decisions are required. First, the appropriate level of demand for energy that must be served to achieve social goals such as economic development and growth and basic human needs should be determined. Then, a mix of energy sources must be estab- lished that will meet the desired demand, based on several national objectives, such as minimum cost, independence from foreign sources, conservation of resources, environmental considerations, and price sta- bility.2 The analysis is complicated by uncertainties regarding the future evolution of demand and supply, relative costs and prices, and the lack of compatibility of the different energy sources with all the various en- ergy uses. Furthermore, closely associated with the investment decision is the pricing policy, which will be based on criteria such as economic efficiency in resource allocation, economic second-best considerations, sector financial requirements, social equity considerations, and other political constraints.3 Pricing decisions may also have feedback effects on investment decisions through demand. (See chapter 3, Method of Opti- mizing Reliability.) The electric power sector is usually one of the most important elements within the broader energy framework. Once the major decisions regard- ing energy policy have been made at the national level, the power sector authorities must perform a similar but more detailed analysis. More specifically, the demand for electricity must be forecast, preferably dis- aggregated by geographic region and customer category. Then alternative 1. Short-term and long-term energy sources are also called renewable and non- renewable, but the distinction is not strictly correct because the second law of thermodynamics forbids isolated, self-regenerating energy sources 2 See Mohan Munasinghe and Colin J. Warren, "Rural Electrification, Energy Economics, and National Policy in the Developing Countries," IEE International Conference on Future Energy Concepts, London, January-Feb nuary 1979, IEE Conference Publication no. 171. 3 See Mohan Munasinghe and Jeremy J. Warford, "Shadow Pricing and Power Tariff Policy," Marginal Costing and Pricing of Electrical Energy, Pro- ceedings of the State-of-the-Art International Conference, Montreal, May 1978, pp. 159-80. POWER SYSTEM PLANNING AND SUPPLY COSTS 89 methods of physically meeting these requirements and their correspond- ing costs must be determined. These steps, which result in the deter- mination of power system costs, are detailed in the following sections. Again, the procedure involved in selecting an optimal plan and relia- bility level, described fully in chapter 3, adds an extra dimension to the conventional technique of system expansion planning in which the target reliability level is arbitrarily determined. This method considers as variables, first, the reliability level and, subsequently, if necessary, also the demand forecast by an iterative technique. Load Forecast The major elements of load forecasting that are relevant to the sys- tem planning process are reviewed in this section. For greater detail, the reader is referred to the notes cited in the text.4 Unlike in the tradi- tional engineering context, where demand is synonymous with capacity or power, the terms demand and load forecast are used interchangeably to denote the magnitude as well as the structure of the requirements of both electrical power and energy (kilowatt and kilowatt-hour, respec- tively) except when the appropriate distinction is necessary. The struc- ture of demand includes disaggregation by geographic area, by consumer category, and over time, as well as load and diversity factors and system losses. A knowledge of loads at the disaggregate level is important, because the demand characteristics vary by consumer type, by geographic area, and with time. Therefore, the properties of the aggregate demand, for example, at the system level, may be quite different from the character- istics of individual loads. Disaggregate loads are important in the system planning process. For generation planning, the system may be modeled as one source feeding a single lumped load but, in designing transmis- sion networks, the characteristics of demand by region and by major load center, such as a city, become important. Ultimately, for distribu- 4. See, for example, Federal Power Commission, The Methodology of Load Forecasting, 1970 National Power Survey (Washington, D.C, 1970); Robert L. Sullivan, Power System Planning (New York: McGraw-Hill International, 1977), chap 2; and G E. Huck, "Load Forecast Bibliography-Phase I," Pro- ceedings of the IEEE Power Engineering Society Summei Meeting, Vancouver, July 1979, paper no. F7950-3. 90 THEORY tion grid planning, a detailed knowledge of demand at each load center is required, as discussed in the next section. Furthermore, the sum of many disaggregate demand forecasts, estimated by using several inde- pendent techniques, often can serve as a useful check on an independ- ently made global forecast for the same region. A discussion of the basic relation between power and energy might be helpful at this point. The commonly used unit of energy in heavy current electricity applications is the kilowatt-hour. The rate of energy flow per unit of time is called power or capacity, which is measured in kilowatts. Therefore, it follows that energy in kilowatt-hours is the product of power in kilowatts and time in hours. More accurately, energy is the integral of instantaneous power flow, over time. The distinction between power and energy is important because the same amount of energy may be delivered quickly at a relatively high rate of power flow or more slowly at a lower power level. This point is best exemplified in nuclear fission by contrasting the practically instantaneous explosion of an atomic bomb with the controlled release of power from a nuclear reactor. The load factor (LF), which is the ratio of average to maximum, or peak, kilowatts during a given interval may be specified at various levels of aggregation. The LF may be determined for a single customer or for an entire system on a daily or annual basis, and so on. It is important, because the size and, therefore, the cost of power system components are determined to a great extent by their capability to handle peak power flows. Since most customers require their maximum kilowatts only during a relatively short peak period during the day, the LF is also a measure of the utilization of capacity. (See also the discussion of the load duration curve in the next section.) A load forecast could be made either in units of peak power or of total energy consumed during a given period. The LF may be used to convert from one unit to the other, and also to check for mutual consistency when both types of forecasts have been made independently. In general, the kilowatt peaks of different customers do not occur simultaneously. The diversity factor (DF) of a group of consumers is the ratio of the sum of the individual peak demands to their combined or simultaneous peak demand. Therefore, the DF is a number greater than or equal to unity. It measures the divergence or spreading of indi- vidual peak loads over time, and enables a coincident peak load to be computed for the group from the disaggregate peak values. The total amount of both kilowatt and kilowatt-hours generated at source will be POWER SYSTEM PLANNING AND SUPPLY COSTS 91 greater than the corresponding values consumed because of power and energy losses in the system. Generation losses are usually of the station- use type: that is, involving use of auxiliary equipment at the power plant. Transmission and distribution network losses are basically technical losses, including transformer losses. Theft is a common loss in some countries and must be considered in the demand forecast. Since it is also a type of electricity consumption, ideally, the corresponding user benefits, and outage costs should also be considered in the optimizing process. In practice, this would be extremely difficult to do, because little is likely to be known about these consumers. Load forecasts are made for different periods.' Very short-term de- mand projections are made on a daily or weekly basis, typically for optimizing system operation and scheduling of hydro units. Short-run forecasts ranging between one and three years are used in hydro-reservoir management, distribution system planning, and so on. The horizon for medium-term demand projections is about four to eight years, which corresponds to the lead times generally required for major transmission and generation projects. These forecasts, therefore, are especially useful in determining the timing and sequencing of such facilities. Some nuclear power stations may, however, take more than ten years to complete. Long-range demand projections, usually of ten to thirty-five years, are extremely important in long-run system expansion planning. Since they are most relevant to the topic addressed in this study, these forecasting methods are discussed next. In general, such long-range demand pro- jections may be developed at various levels of disaggregation, ranging from national forecasts to projections for specific groups of consumers in localized areas. The earliest approach to long-term load forecasting basically involved trend-line extrapolation. More specifically, a time series of past demand for electricity was analyzed as a function of time, using a variety of techniques ranging from simple graphing to sophisticated mathematical curve fitting. The resulting trend, sometimes expressed as a compound growth rate, was extended into the future. Because this method implicitly assumes that present growth patterns will remain essentially unchanged 5. See Frank D Galiana, "Short Term Load Forecasting," Systems Engineer- ing for Power. Status and Piospects, Henniker, New Hampshire, A ugust 1975, NTIS no CONF-750867, pp 105-14; and K N. Stanton, "Medium Range, Weekly, and Seasonal Peak Demand Forecasting by Probability Methods," IEEE Tyansactions on Powet Apparatus and Systems, vol. PAS 71 (May 1971), pp. 1183-89. 92 THEORY into the future, it is often acceptable where stable socioeconomic condi- tions permit electricity demand to increase steadily for many years. Adjustments based on expert judgment may be made to the trend-line estimates if significant changes are expected in the overall environment, such as economic and demographic shifts, and weather changes. Sys- tematically enumerating and summing of individual loads after consid- ering the effects of diversity is another simple technique that has been used effectively, especially with large consumers, to develop the overall forecast. Correlation methods of forecasting are more sophisticated than the trend line techniques. The basic rationale underlying the correlation ap- proach is that regional or national electricity load growth could be fore- cast indirectly by linking it to several other variables whose future evolution would be easier to predict than the demand for electricity itself. The simplest methods include the correlation of electricity demand to some measure of economic activity, for example, per capita gross na- tional or regional product, personal disposal income, or industrial or commercial value added. Demand may also be correlated with electricity price through the price elasticity of demand.6 Then, projected values of income and price could be used in the estimated equations to forecast future load growth. Both the extrapolation and the correlation ap- proaches require some knowledge of historical data on electricity de- mand specific to the consumer group and the area or country under consideration. When this information is unavailable, techniques that use appropriate data from other comparable regions may be necessary.7 More complex multiple correlation techniques consider several addi- tional variables, such as prices of competing fuels and energy sources, temperature and weather, land usage, and population shifts. These meth- ods often involve fitting nonlinear demand functions. Such econometric methods that explicitly consider the price of electricity as an explanatory 6. The elasticity of the dependent variable y with respect to the independent variable x is given by: E, a l a)x X 7 See for example H. Aoki, "New Method of Long Range or Very Long Range Demand Forecast of Energy, Including Electricity, Viewed from a World- wide Standpoint," Electric Power Development Company Ltd., Tokyo, Japan, 1974; in which an attempt is made to correlate the growth rate and the level of per capita gross national product (GNP) and per capita kilowatt-hour electricity consumption for 111 countries. POWER SYSTEM PLANNING AND SUPPLY COSTS 93 variable are particularly relevant to this analysis, because in the op- timization model presented in chapter 3, price is included in the speci- fication of demand. This allows potential variation in the load forecast to occur through the iterative price feedback loop depicted in figure 1.1 of chapter 1. In a recent review of the topic, it was pointed out that problems encountered to date have been mainly conceptual.8 These include the difficulties of: (a) modeling multipart (for example, fixed and variable charges) and multiblock (that is, varying prices for different consumption blocks) tariffs, as well as discontinuities in the demand function; (b) distinguishing between short- versus long-term, and static versus dynamic adjustments; and (c) incorporating the resulting changes in the prices of competing fuels. The recent resurgence of interest in marginal cost pricing has resulted in the continued development of econometric models that emphasize isolating the effects of electricity price on the demand level.' All the models discussed so far have been mathematically determinis- tic, since the uncertainty in the load projections usually is accounted for by parametric shifts in the forecasts to test for sensitivity. Recently, more sophisticated techniques have been developed involving matrix methods, such as input-output matrices that capture the relations between productive sectors, and stochastic processes, such as those representing sectoral growth probabilities in terms of a Markov model. Such methods enable researchers to consider probabilistic effects explicitly.10 The re- sulting long-range demand forecasts are still deterministic, however. Again, for sensitivity testing, the basic assumptions may be varied to provide low-, medium-, and high-demand forecasts, covering a range of load growth rates. To summarize, no single, universally superior approach to load fore- casting exists In general, it is better to use several independent long- 8. See Lester D. Taylor, "The Demand for Electricity: A Survey," The Bell Joutnal of Economics, vol 6 (Spring 1975), pp. 74-110. 9. See several papers that recently appeared in Maiginal Costing and Pricing of Electric Eneigy, Proceedings of the State-of-the-Art International Confelence, Montreal, May 1978 10. See, for example, IAEA, Nuclear Power Planning Study for Indonesia (Vi- enna, 1976); N R Prasad, John M Perkins, and G Nesgos, "A Markov Process Applied to Forecasting Part I-Economic Development," Pioceedings of the IEEE Power Engineering Society Suinme Meeting, Vancouver, July 1973; and N R. Prasad, John M Perkins, and G Nesgos, "A Markov Process Applied to Fore- casting. Part II-The Demand for Electricity," Pioceedings of the IEEE Power Engineering Society Winter Meeting, New Yoik, January 1974. 94 THEORY range forecasting methods to cross-check the results and to obtain a probable range within which the demand projection will fall. The more sophisticated techniques tend to obscure the basic methodological as- sumptions as well as weaknesses in the data, and, therefore, the simpler techniques may be more appropriate if the available information is considered unreliable. The determinants of demand must be selected carefully, because they vary from case to case, and the level of disag- gregation chosen should depend on the data, as well as on the ultimate purpose of the projection. Demand forecasting is a dynamic process in the sense that the procedure must be repeated often, in light of improved information and techniques of analysis. Establishing a reliable data bank is invaluable for this constant revision of the demand forecast. Finally, in some cases institutionally imposed constraints that reduce demand, such as peak suppression or not connecting customers, as well as the existence of privately owned or captive generation, may lead to a sub- stantial gap between the potential and the achievable demand. System Design and Planning The reliability optimization procedure described in chapter 3 was developed in accordance with alternative power system expansion plans that were designed to meet the projected demand at various levels of reliability. This section deals with the principles by which such alterna- tive systems are designed. Since a very rigorous and highly mathematical treatment of power system design and planning is unnecessary here, the presentation is generally descriptive and focuses on the economic as- pects of the various tradeoffs involved." In particular, any references to cost minimization in this section imply that such costs may be readily determined, as described in the next section on costing. Ideally, the planning of the whole system should be carried out on an integrated basis, as implied in the optimization model described in chapter 3. To make the practical problems of system design tractable, however, it is convenient to break the procedure down into parts asso- ciated with the main subsystems: generation, transmission, and distribu- 11. See, for example, Robert L. Sullivan, Power System Planning; and Upton G. Knight, Power System Engineeting and Mathematics (New York: Pergamon Press, 1972). POWER SYSTEM PLANNING AND SUPPLY COSTS 95 tion. This type of hierarchical decomposition is logical from several points of view.'2 First, as mentioned in the previous section on load forecasting, various completion times are associated with the discrete projects that comprise a long-range system expansion plan. These range from five to ten years for the design and construction of a large nuclear generating plant, to one to two years for distribution schemes. Second, the problems and design philosophies associated with the different parts of the total power system are inherently dissimilar. For example, distribution system plan- ners require detailed knowledge of localized geographic areas and, as the case study indicates, must be familiar with thousands of small com- ponents, such as distribution transformers, switches, and reclosers, al- though their analysis may be relatively simple. At the other extreme, however, generation planning is carried out at a more aggregate, system- wide level, and is concerned with several relatively large generating units, generally having modes of interaction that are more complex to analyze. Consequently, the models and criteria currently used to design the vari- ous subsystems are also different. These are reviewed briefly here nonmathematically. Although the discussion is cast in the context of traditional system expansion planning, that is, essentially choosing the design that minimizes only system costs while meeting given load and reliability requirements, the basic ideas involved may be readily adapted to the new method in which the reliability level is treated as a parameter to be varied. Early approaches to system design and planning were rather intuitive and relied heavily on the designer's past experience. In contrast, the more advanced mathematical methods currently used by some utility com- panies rely on optimization models. The goal is the minimization of an objective function, usually the present discounted value of system costs, subject to constraints, such as meeting the load and reliability targets, and not violating technical and operating requirements.13 (See, also, chapter 3, Method of Optimizing Reliability.) 12 See David A Wismer, Optimization Methods for Large Scale Systems (New York: McGraw-Hill, 1971) 13. For a more detailed and mathematical treatment, see IEEE, Application of Optimization Methods in Power System Engineering, IEEE Tutorial Course Text no. 76CH1107-2-PWR (New York, 1976), and Robert Fischl, "Optimal Sys- tem Expansion Planning: A Critical Review," Systems Engineering for Power- Status and Piospects, USERDA Conference, Henniker, New Hampshire, August 1975. NTIS no. CONF-750867, pp. 233-60. 96 THEORY From a general point of view, if the problem is deterministic and the objective function and constraints are known, then some definitive nominal design may be found. An example of a known objective func- tion would be the best estimates of plant costs, load, and demand in generation planning. Given uncertainty, flexible design strategies are required, such as the worst case concept, in which upper and lower design limits are determined that correspond to maximum and minimum values of the objective function and constraints. Another strategy uses the statistical concept where, given a probabilistic distribution of values of the objective function and constraints, the average design configura- tion that emerges from among the allowed design variations is found The specific solution techniques for the optimization problem may be considered under three categories: programming, search, and other special procedures. The mathematical programming approaches, includ- ing linear, nonlinear, integer, mixed-integer, and dynamic programming versions, are most useful when the objective function is simple and well defined. They rely on explicit, computerized algorithms that are used to find the solution after a finite number of steps. Search techniques, used when programming methods would be difficult to apply, for example, with poorly defined, complex, or implicit objective functions, are gen- erally easier to implement. They do not guarantee convergence to the solution within a reasonable time, however. Special procedures are often elegant but, generally, they are applicable only to particular problems.'4 The basic questions in generation system design relate to the size, timing, type (or mix), and location of generating plants. The economic aspects of each of the choices involved are clarified in the following discussion. The problem of size and timing resulting from the growth of peak megawatt demand over time in a typical capacity-limited system, is depicted in figure 8.1.15 The installed capacity of existing generating plant (MWo) will be sufficient to meet the demand in two years' time, after allowing for a suitable reserve margin (see also, chapter 2, Intro- duction to Reliability.) Two expansion alternatives, which meet all the constraints, are to be considered: in the first one, two medium-sized generating plants will come on-stream in the second and fourth years of the system plan, whereas in the second option, a small plant will be 14. See, for example, Lester R. Ford and Delbert R. Fulkerson, Flows in Net- works (Princeton: Princeton University Press, 1962). 15. 1 megawatt = 10' kilowatts = 10' watts. POWER SYSTEM PLANNING AND SUPPLY COSTS 97 Figure 8.1. Size and Timing of Generation Additions to Meet Peak Demand for Power Alteynative 2 Alternative I Peak megawatt demand MWo I I II 0 2 4 6 8 Years Note. MW= capacity of existing generating plant commissioned in the second year, followed by a large power station in the sixth year. The system planner must choose the cheaper alternative. Generally, in a real system the two expansion paths would be compared over a longer period, but in this example, the alternative plans have been made roughly equivalent after the sixth year to highlight the nature of the choice of size and timing of the next two generation additions. Moreover, in predominantly hydroelectric systems, shortages of energy because of limited reservoir storage capability may precede any capacity or power constraints. The selection of an appropriate plant mix is best discussed in the context of the system's annual load duration curve (LDc). A typical LDC for a given year is shown in the lower half of figure 8.2, a graph of the hourly system megawatt demand plotted against the number of hours in the year during which this demand level is equaled or exceeded. The peak demand (MW) occurs only over a short period and, since the average level of megawatt demand (that is, the total energy in megawatt- hours or area under the LDC curve divided by 8,760 hours) is less than 98 THEORY Figure 8.2. Types (or Mix) of Generating Plant Required to Meet the Annual Load Duration Curve (LDC) Gas turbines, slope b, O 0~ U aH Base lad steam plant, slope b 4S *0 IH Hours a year of plant operation CI 0 H 8,760 Hours a year during which the given level of demand is equaled or exceeded Note: Top, cost characteristics of typical thermal plants, bottom, system annual load duration curve. POWER SYSTEM PLANNING AND SUPPLY COSTS 99 MW, the load factor will be less than unity. (See the preceding section on load forecast.) For simplicity, only two kinds of generating units are considered: gas turbines and base load steam plants; the relevant characteristics of both are depicted in the upper part of figure 8.2. The figure is a graph of the total average cost per megawatt of installed capacity, that is, capital cost plus operating cost, plotted as a function of the numbers of hours of operation. Gas turbines have lower capital costs (represented by the intercept a1, which is the investment cost per megawatt, annuitized over the lifetime of the machine), but higher fuel costs (as indicated by the slope b, of the operating cost curve) than the steam plant. The cost characteristics of these units have been simplified for convenience of analysis by assuming fixed values of a,, a., b, and b2. This will not, however, affect the logic of the discussion that follows. Usually, for a given type of generator, the capacity cost for each megawatt installed decreases as the machine size increases, and for a given machine, the operating cost need not increase linearly with hours of usage. As the upper diagram shows, from the economic point of view gas turbines are more expensive than base load units if they are to be used more than H hours a year and vice versa. This essentially static picture is only illustrative because, actually, the relevant streams of present dis- counted investment, plus operating costs of the machines, would have to be compared for many years. Pursuing this simplified logic further, how- ever, the lower diagram indicates that it would be economical to serve the bottom X megawatts of load (that is, the base load) with steam units and the upper X, megawatts of load (that is, the peak load) with gas turbines,,where X, + X, = MW. A reserve margin may be included, if necessary. In practice, many kinds of generating units including nuclear, coal- and oil-fired steam, gas turbine, conventional and pumped-storage hydro, and, more recently, geothermal, tidal, and wind powered units that have characteristics varying by type and by size, would have to be taken into account. When generation additions are being considered to meet future load growth, however, the basic principle of selecting units with lower capital costs but higher operating costs for peaking purposes, and vice versa, generally holds true. Usually, the choice of generator location affects the design of the transmission system and, therefore, both these problems should be ana- lyzed within a common framework. Transmission planning typically in- volves the solution of a dynamic network-type problem, in which the 100 THEORY basic objective is to select at least cost the type, timing, and location of line additions that would connect the various sources or generating stations to the different sinks or load centers. In addition, the require- ments imposed by load, reliability level, technical, and other constraints must be satisfied. A commonly used network model is the dc-load flow model, which may be used in either a linear or nonlinear framework.16 In the single- step, essentially static concept, the design optimization procedure is repeated at various points in time when generation and load levels are specified, for example, in the last year of the planning horizon. This is done to provide instantaneous snapshots of the system's evolution. In dynamic methods, large computing times are required to handle trans- mission line variations over both space and time, as in the analysis of a large interconnected area during each year of the planning period. The time problem may be simplified by preselecting several expansion alternatives according to certain performance criteria. None of these techniques can guarantee a definitive solution, however, given the size of the problem and limits on calculating times. Transmission system performance criteria, against which the system model is judged, are of two general types: steady state and transient.17 Steady state performance of the system consists basically of verifying that line and transformer design limits are not exceeded under normal loading and operating conditions or with single contingencies, such as loss of a single line, transformer, or generator. Transient performance criteria are used to test the system model for stability in a variety of situations. One group of tests involves the ability of an interconnected system to maintain steady state stability under normal and contingency conditiots when perturbed by a small disturbance, such as the switching on of a minor load. Verifying a system's dynamic stability is also very important. This involves the degree of damping of high amplitude oscil- lations induced by a large fault, such as failure of a major line resulting from a three-phase fault to ground or loss of a block of generators. Having examined the transmission system design and planning prob- lem, it is appropriate now to return to the question of generator loca- 16. See B. Stott, "Review of Load-Flow Calculation Methods," Proceedings of the IEEE, vol 62 (July 1974), pp. 916-29. 17. For a more detailed discussion of transmission design criteria, see: Canadian International Development Agency, Regional Power Systems Engineering Seminar, Kathmandu, Nepal. February-March 1977. POWER SYSTEM PLANNING AND SUPPLY COSTS 101 tion. As discussed in chapter 2, Introduction to Reliability, the reliability analysis of combined generation and transmission system models raises formidable problems. Similar problems arise in system planning and, therefore, although the generation and transmission subsystems are in- timately related, separate models are generally used to design each subsystem. More specifically, a typical large computerized generation planning model would yield the appropriate plant mix, size, and timing. Some- times the formulation includes a limited, but not very accurate, repre- sentation of the transmission network.'8 Then the optimum locations would be chosen from among a variety of potential sites to supply the specific load centers, within the framework of a more detailed trans- mission planning model. Sometimes, however, site selection is so com- plicated that it tends to dominate the transmission model. In practice it would be necessary to iterate between the models to converge to the best mutually consistent solution. Although generation and transmission system planning is an inter- related process, in principle, the distribution grid serving a localized geographic area or load center can be designed independently. Recently, computerized methods have been developed to determine the optimum size, timing, and location of distribution substations and primary feed- ers, as well as the planning of secondary networks."' Sophisticated models and computerized algorithms are not as widely used in distribution sys- tem design as in generation and transmission work, however. In the more conventional approach, forecast loads are imposed on the existing distribution system at specific future times, and the network is systematically strengthened to meet these loads adequately. Meeting consumer demand within acceptable voltage limits would determine the location of new substations and primary feeders and the upgrading of 18 See, for example, Dennis Anderson, "Models for Determining Least Cost Investments in Electricity Supply." The Bell Journal of Economics and Manage- ment Science, vol 3 (Spring 1972), pp 267-301. 19 See Stewart B. Holt, Jr and Dale M Crawford, "Distribution Substation Planning Using Optimization Methods," Application of Optimization Methods in Power System Engineering, IEEE Tutorial Course Text no. 76CH1107-2-PWR (New York, 1976), pp 69-76, D. L Wall, G L. Thompson, and J. E. D. N. Green, "An Optimization Model for Planning Radial Distribution Networks, IEEE Transactions on Power Apparatus and Systems, vol PAS-98 (May/June 1979), pp 1061-68; and Yngve Backlund and Janis A Bubenko, "Computer-Aided Dis- tribution System Planning," Electrical Power and Energy Systems, vol. 1 (April 1979), pp. 35-45. 102 THEORY existing ones. Loading under normal and emergency (or fault) condi- tions, as well as during peak and off-peak periods, would be examined. Flexibility in design would be an important consideration. For example, this would facilitate isolation of faulted sections of feeders and would enable customers to be switched from faulted to functioning feeders. Often, because of the large numbers of customers and components such as line sections, switches, distribution transformers and so on, only certain representative feeders or circuits would be analyzed in detail to establish general criteria such as maximum kilovolt-amp for a circuit. These criteria could then be applied to other feeders without further study. In general, the larger and more complex the service area, the greater would be the advantage of using even simple computerized tech- niques for circuit-by-circuit analysis. The distribution system design problem is examined more closely in the case study, chapter 11, Long Range Distribution System Planning. Costing The process of costing or estimating the power system supply costs may be broken down into two steps. The first stage involves determining the appropriate model of the physical system to be costed; this could be done in two ways. One obvious candidate, which would correspond very closely to the real physical system, is the model or combination of sub- models used in the system design stage described in the previous section. Recently, several researchers have attempted to take the alternative approach of estimating neoclassical, long-run production functions of electric power systems to determine the cost structure, economies of scale, technical progress, factor substitution possibilities, and so on.20 These researchers have used the Cobb-Douglas constant elasticity of substitution (CES) and translogarithmic formulations. 20. See, for example, Phoebus J Dhrymes and Mordecai Kurtz, "Technology and Scale in Electricity Generation," Econometrica, vol. 32 (July 1965), pp 287- 315; M Galatin, Economies of Scale and Technical Change in Thermal Power Generation (Amsterdam: North-Holland, 1968); Fred McCoy, "The Production Function Method I," Marginal Costing and Pricing of Electric Energy, Pioceed- ings of the State-of-the Art International Conference, Mont,eal, May 1978; and Laurits Christensen, "The Production Function Method II," Marginal Costing and Pricing of Electric Energy, pp. 107-13. POWER SYSTEM PLANNING AND SUPPLY COSTS 103 The system design discussed earlier encompasses these issues, how- ever. Furthermore, no generalized production model derived from neo- classical economic theory could hope to capture the detailed information regarding the physical system that is included in an engineering planning model. In particular, sector-wide production functions based on cross- section or pooled-that is, cross-section and time series-data are gen- erally appropriate to determine historical trends in the economics of power sector evolution, rather than to represent a given system accu- rately. Production functions estimated for a single system using time series data are more specific, but they still remain oriented in the past rather than the future. To summarize, an engineering model used in the design and planning of a system is far more appropriate than an eco- nomic production function model for estimating future system supply costs when the reliability level is to be optimized. Once the model of the physical system has been identified, the next step in estimating the supply costs is to determine the items to be costed and their valuation. Again, two methods are possible. In the first method, commonly used in the United States, the financial viewpoint of a private electric power utility is adopted.2' The items in the costing exercise are based primarily on accounting concepts. They include physical assets, services, depreciation, interest, and taxes that may be affected by regu- latory requirements. The values placed on them are the private financial costs incurred by the utility. These include the purchase cost of assets and services, financing charges, and the cost of raising capital based on the debt-equity mix. The second method is basically economic and more appropriate in the context of the national economy or society as a whole. The goods and services used as physical inputs to the electric power system, such as labor, land, physical capital, and materials, are con- sidered scarce economic resources that could be used in alternative production and valued accordingly. This approach is particularly appro- priate where the utility is publicly owned, which frequently occurs in the developing countries. Since the principal economic criterion for optimizing system relia- bility is the maximization of the net benefit accruing to society as a whole, rather than to the power utility alone, the second approach dis- cussed above is more relevant to this discussion. The identification and 21 See James Suelflow, Public Utility Accounting: Theory and Application (East Lansing: Michigan State University, 1973). 104 THEORY shadow pricing of real economic resources used as inputs into the elec- tric power sector are discussed in detail in the next chapter. In conclusion, it should be noted that the process of system planning and determining electricity supply costs is usually complicated by sev- eral practical difficulties. These include uncertainties in the demand projections as discussed earlier, errors in the cost estimates, techno- logical changes, construction delays, and environmental constraints. Often these problems cannot be analyzed in a general framework and have to be treated on an individual basis. In some cases the uncertain- ties inherent in load forecasts, cost estimates, and so on may be asso- ciated with appropriate probability distributions, permitting statistical decision theory to be applied to long-range system planning.22 With unreliable data, greater flexibility in system planning is possible by adopt- ing an approach in which several distinct scenarios are simulated to provide the decisionmaker with a range of alternative choices. Most recently, it has been proposed that the theory of fuzzy sets be combined with the criteria used for decisionmaking in long-range system expansion planning; in this type of analysis uncertainties such as demand shifts are represented by unpredictable system states (creating a "fuzzy" en- vironment).23 22. See, for example, R. Schlaifer, Analysis of Decision Under Uncertainty (New York: McGraw-Hill, 1969); and H. Raiffa, Decision Analysis: Introductory Lectures on Choices Under Uncertainty (Reading, Mass.: Addison-Wesley, 1970). 23. S. B. Dhar, "Power System Long-Range Decision Analysis Under Fuzzy Environment," IEEE Transactions on Power Apparatus and Systems, vol PAS-98 (March/April 1979), pp. 585-96. Chapter 9 Shadow Pricing This chapter offers a brief introduction to the use of shadow prices that would be relevant to the electricity sector. The discussion on valuing inputs and outputs is developed in the context of a national economy, rather than from the viewpoint of a private power utility company, and, therefore, it is particularly relevant to the developing countries. Gen- erally, when market imperfections occur, shadow prices may be used instead of the distorted market prices to represent the true economic opportunity costs of various goods and services in the economy. Such shadow prices have their roots in the theory of welfare economics and cost-benefit analysis. General Principles In the idealized world of perfect competition, the interaction of atom- istic profit-maximizing producers and atomistic utility-maximizing con- sumers yields a situation that is called pareto-optimal. In this state, prices reflect the true marginal social costs, scarce resources are effi- ciently allocated, and for a given income distribution, no one person can be made better off without making someone else worse off I 1. See Francis J. Bator, "General Equilibrium, Welfare, and Allocation," American Economic Review (March 1957), pp. 22-59; and Ezra J. Mishan, Cost Benefit Analysis (New York: Praeger, 1976), part vii. 105 106 THEORY Conditions are likely to be far from ideal in the real world, however. Distortions resulting from monopoly practices, external economies and diseconomies not internalized in the private market, interventions in the market process through taxes, duties, and subsidies result in market prices for goods and services that may diverge substantially from their shadow prices or true economic values. Moreover, if there are large income disparities, the passive acceptance of the existing skewed income distribution, which is implied by the reliance on strict efficiency criteria for determining economic welfare, may be socially and politically un- acceptable. These considerations suggest the use of appropriate shadow prices instead of market prices for economic analysis, especially in the developing countries where market distortions are more prevalent.2 The relevance of shadow prices is illustrated in figure 9.1, which is derived from figure 3.3. The curves of marginal supply costs (MSC..) and negative outage costs (-MOC..) without shadow pricing, yield the apparent "optimal" reliability level R'n. But this result is inappro- priate, because both system and outage costs have been valued in terms of the nominal private financial costs incurred by the utility and consumers. The corresponding shadow-priced marginal supply and negative outage costs (MSC, and -MOC,) intersect at the reliability level R", which is the correct optimal value from the national view- point. In general, R' and R' will not coincide, because each of the two shadow-priced marginal cost curves may lie above or below the corresponding nonshadow-priced curves, depending on the distortions in the economy. Consider a general equilibrium model of the economy in which the national goal is embodied in some acceptable objective function such as aggregate consumption. Consumption is to be maximized subject to con- straints such as limits on resource availabilities and distortions in the economy.3 Then the shadow price of a given scarce economic resource represents the change in the value of the objective function caused by a marginal change in the availability of that resource.4 In the more specific context of a mathematical programming macroeconomic model, the op- 2. For a discussion of the limitations of shadow pricing see: Richard S. Weck- stein, "Shadow Prices and Project Evaluation in Less Developed Countries," Eco- nomic Development and Cultural Change (April 1972), pp. 474-94. 3. See Stephen A. Marglin, Public Investment Criteria (London: George, Allen, and Unwin, 1967). 4. See Partha Dasgupta and Joseph Stightz, "Benefit Cost Analysis and Trade Policies," Journal of Political Economy, vol. 82 (January-February 1974), pp. SHADOW PRICING 107 Figure 9.1. Effect of Shadow Pricing on the Optimal Reliability Level -Mocss -MOCS I MSCS - I - I MSC ~ i 0 Rs"' Rs "'I Global reliability index (R) Note: MSC,., -MOCNs, and Rh"' are, respectively, the marginal supply costs, negative marginal outage costs, and apparent optimal reliability level without shadow pricing MSCs, -MOCs, and Rs" are the corresponding shadow-priced quantities timal values of the dual variables that correspond to the binding resource availability constraints in the primal problem have the dimensions of price and could be interpreted as shadow prices.' Two basic types of shadow prices may be distinguished, which involve a society's concern with or indifference to income distributional con- siderations. To illustrate this point, consider the simple national goal of maximizing the present value of aggregate consumption over a given period. If the consumption of different individuals is added directly with- out considering their income levels, then the shadow prices desirable 1-33, and Peter Warr, "On the Shadow Pricing of Traded Commodities," Journal of Political Economy, vol. 85 (1977), pp. 865-72. 5. See David G. Luenberger, Introduction to Linear and Non-Linear Pro- gramming (Reading: Addison-Wesley, 1973), chap 4; and Peter G. Sassone, "Shadow Pricing in CBA Mathematical Programming and Economic Theory," The Engineering Economist, vol. 22 (Spring 1977), pp. 219-33. 108 THEORY from such a model are called efficiency prices because they reflect the pure efficiency of resource allocation. When the consumption of the lower income groups is given a greater weight in evaluating aggregate consumption, however, the resultant model yields the set of shadow prices called social prices.6 Two practical difficulties are worth discussing First, there is an ob- jection to using social pricing in project work on the grounds that the weighting of consumption benefits by income category is necessarily quite arbitrary, and that income redistributional goals are better realized through fiscal and other policy instruments rather than by biasing in- vestment decisions. Acceptance of efficiency prices, however, implies that equal weights are attached, also arbitrarily, to benefits accruing to all individuals.7 Also in many countries few practical policy tools may be available to the government to influence the existing income distribu- tion.8 In practice, the use of social versus efficiency prices depends on factors such as data availability and the commitment of the government to income distributional goals. Second, in actually estimating shadow prices, it is rarely possible to use the full-fledged general equilibrium approach referred to in the theory. Many countries do not have the requisite data, and it would be wasteful and time-consuming to reanalyze such a large model whenever new investment decisions were required. Instead, partial equilibrium techniques are used to evaluate the effect of the change in the availability of a given resource by its effect on a few key areas, rather than throughout the economy. The partial equilibrium method has been criticized on the basis of nonmarginality, for its lack of simultaneity, and because of the judg- mental element involved in choosing which linkages will be analyzed when the effect of some disturbance is to be evaluated. In principle, however, these objections can be overcome by using an iterative process of successive, convergent approximations and by considering a suffi- cient number of linkages, so that the partial equilibrium shadow prices closely approximate the corresponding general equilibrium values. 6. See Lyn Squire and Herman G van der Tak, Economic Analysis of Projects (Baltimore- Johns Hopkins University Press for the World Bank, 1975), chap. 6. 7. However, Ezra J. Mishan, Cost Benefit Analysis, chap. 61, argues that the only implication is that of a potential pareto improvement rather than uniform weighting of benefits. 8. See Partha Dasgupta, Amartya Sen, and Stephen Marglin, Guidelines for Project Evaluation (UNIDO) (New York: United Nations, 1972), chap. 7; and Ian M D. Little and Jan A. Mirrlees, Project Appraisal and Planning for Devel- oping Countries (New York: Basic Books, 1974), chap. 4. SHADOW PRICING 109 Numeraire To derive a consistent set of economic prices for goods and services it is necessary to adopt a common yardstick or numeraire to measure value, as the following example illustrates If bananas are to be compared with pineapples, it may be argued that the equivalent units should be either one banana for one pineapple or 1 kilo of bananas for 1 kilo of pineapples. In the first case the com- mon yardstick is one fruit; in the second it is the unit of weight. Clearly, if the weights of the two types of fruits are not identical, the result of the comparison will depend on the yardstick used. Unfortunately, the situation is more complicated with a unit of ac- count, or numeraire for economic value, because the same nominal unit of currency may have a different value depending on the economic circumstances in which it is used. For example, a rupee's or a dollar's worth of a certain good purchased in a duty-free shop is likely to be more than the physical quantity of the same good obtained for one rupee or one dollar from a retail store, after import duties and taxes have been levied. Therefore, it is possible to distinguish intuitively be- tween a border-priced rupee used in international markets free of im- port tariffs and a domestic-priced rupee used in the domestic market subject to various distortions. A more sophisticated example of the value differences of a currency unit in various uses often arises in countries where there is inadequate aggregate savings and investment, and therefore the rate of economic growth is low. In this case, a rupee of savings, which could be invested to increase the level of future con- sumption, may be considered more valuable than a rupee devoted to current consumption. The choice of the numeraire, like the choice of a currency unit, should not influence the economic criteria for decisionmaking except in mag- nitude, provided the same consistent framework and assumptions are used in the analysis.9 For example, only one difference exists between two studies using as units rupees and rupiyal (ten rupees). All monetary quantities in rupees will be numerically ten times as large as those in 9 For a discussion of the different assumptions used in various approaches to shadow pricing, see Hugh Schwartz and Richard Berney (eds ), Social and Eco- nomic Dimensions of Project Evaluation (Washington, D C.: Inter-American Development Bank, 1977); and Deepak Lal, Methods of Project Analysis, World Bank Staff Occasional Papers, no 16 (Baltimore: Johns Hopkins University Press, 1974). 110 THEORY rupiyal. Therefore, one numeraire may be selected instead of another because it is easier to apply. One numeraire that has proved to be most appropriate in many in- stances is a unit of uncommitted public income at border prices. This is essentially the same as freely disposable foreign exchange available to the government, but is expressed in units of local currency converted at the official exchange rate.10 The discussion in the next section uses this particular yardstick of value. The border-priced numeraire is par- ticularly relevant for the foreign-exchange-scarce developing countries, and represents the set of opportunities available to a country to pur- chase goods and services on the international market. Unless otherwise specified, all values referred to in the following discussions are in real terms: that is, net of inflation. Application of Shadow Prices The estimation and use of shadow prices is facilitated by dividing economic resources into tradable and nontradable items The values of directly imported or exported goods and services are already known in border prices: that is, the foreign exchange costs converted at the offi- cial exchange rate. Locally purchased items whose values are known only in domestic market prices, however, must be converted to border prices by multiplying the domestic prices by appropriate conversion factors (CF). Therefore, the treatment of tradables and nontradables is somewhat different, as the following discussion indicates. When tradables with infinite elasticities are involved, the cost, insur- ance, and freight (c.i.f.) border price for imports and the free-on-board (f.o.b.) border price for exports may be used with a suitable adjust- ment for the marketing margin." If the relevant elasticities are finite, then the change in import costs or export revenues, which will be the dominant component, as well as any shifts in other domestic consump- 10. See Ian M D. Little and Jan A. Mirrlees, Project Appraisal and Planning for Developing Countries, chap 9, and Lyn Squire and Herman van der Tak, Economic Analysis of Projects, chap. 3. A numeraire based on private consump- tion is advocated in Partha Dasgupta, Amartya Sen, and Stephen Marghn, Guide- lines foi Project Evaluation (UNIDO). 11. Infinite elasticities of world supply for imports, and world demand for exports. SHADOW PRICING 111 tion and production, and income transfers should be considered. (See appendix B for details.) The free trade assumption is not required to justify the use of border prices, since domestic price distortions are ad- justed, in effect, by subtracting all taxes, duties, and subsidies. The discussion may be clarified by the following example. Imagine a household in which a child is given an allowance of ten rupees a month as pocket money. The youngster may purchase a bag of candy from the grocery store for two rupees. Since the parents want to discourage con- sumption of sweets, however, they impose a fine of one rupee on each bag of candy. The fine is exactly like an import duty, and the child must surrender three rupees for every bag of candy (valued at its domestic price, inside the household). From the point of view of the whole family unit, however, the total external payment for the item is only two rupees because the one rupee fine is a net transfer within the household. There- fore, the true economic cost, or shadow price, of the bag of candy (val- ued at its border price) is two rupees, when the effect of the fine on the distribution of income between parent and child is ignored. Next, nontradable economic resources are considered. This category includes both the conventional definition of a nontradable as a com- modity whose domestic supply price over some given range of output lies between the f o.b. and c.i.f. prices for export and import, respec- tively, and also items that are not traded at the margin because of pro- hibitive trade barriers, such as bans or rigid quotas. If the increased demand for a given nontradable good or service is met by the expansion of domestic supply or imports, then the associated border-priced mar- ginal social cost (Msc) of this increased supply is the relevant resource cost. If the input is supplied through the decreased consumption of other domestic or foreign users, then the border-priced marginal social bene- fit (MsB) of this foregone domestic consumption, or reduced export earnings, would be a more appropriate measure of social costs. The socially optimal level of total consumption for the given input (Q,,t) would be at the point where the curves of Msc and MSB intersect. The differences between MSB and Msc arise from price and other distortions that lead to nonoptimal levels of consumption Q -4- Qo,. More generally, if both effects are present, a weighted average of Msc and MSB should be used. The MSB would tend to dominate in the short-run, supply- constrained situation, and the Msc should be more important in the longer run, when expansion of output is possible (see appendix B). A correspondingly similar analysis may be used when the supply of a nontradable is increased. The Msc of composite goods may be deter- 112 THEORY mined by successively decomposing the nontradable into its constituent inputs. This should be done until only the ultimate tradable inputs, which can be valued at border prices, and nontraded primary factors, such as labor and land, remain. The MSB for intermediate and final consumption should be evaluated by the foregone social profit and con- sumers' surplus, respectively; the income transfer effects of any price changes should be added to these. In practice the Msc is often used instead of the MSB because of data constraints. As noted earlier, the Msc of nontradable goods and services from many sectors can be determined through appropriate decomposition. For example, suppose one rupee's worth, in domestic prices, of the out- put of the domestic construction sector may be broken down successively into n components, such as capital, labor, and materials. These are valued at rupees a1, a2, . . ., a,,, in border prices. Since the conversion factor of any good is defined as the ratio of the border price to the domestic price, the construction conversion factor equals 5 ai. With nontradables that are not important enough to merit individual attention or that lack sufficient data, the standard conversion factor (SCF) may be used. The SCF is equal to the official exchange rate (OER) divided by the more familiar shadow exchange rate (SER). Conversion of domestic-priced values into border price equivalents by application of the SCF to the former is conceptually the opposite of the traditional practice of multiplying foreign currency costs by the SER to convert to the domestic price equivalent. A convenient approximation to the standard conversion factor is the ratio of the official exchange rate to the free trade exchange rate (FTER), when the country is moving toward a freer trade regime:12 OER ex + 7M SCF= - = FTER eX(1 - t ) + nM (1 + t,,,) where X = f.o.b. value of exports; M = c.i.f. value of imports; E = elasticity of export supply; 77 = elasticity of import demand; t. = 12. For a more detailed discussion of alternative interpretations of the SCF and SER, see Lyn Squire and Herman G. van der Tak, Economic Analysis of Projects, and Bela Balassa, "Estimating the Shadow Price of Foreign Exchange in Project Appraisal," Oxford Economic Papers, vol. 26 (July 1974), pp. 147-68. SHADOW PRICING 113 average tax rate on exports (negative for subsidy); and t,,= average tax rate on imports. The most important tradable inputs used in the electric power sector are capital goods and petroleum-based fuels; world market prices may be used for both where appropriate. In some countries fuels, such as coal, are available that have no clear-cut alternative uses. In these cases the Msc of production may be used. The most important nontradable primary factor inputs are labor and land, which complete the discussion on shadow price applications. In particular, the procedure outlined for estimating the shadow wage rate (SWR) also illustrates the effect of income distributional considerations. Other important nontradable in- puts, such as the services of the domestic construction sector, may be broken down into tradables and primary factors, as discussed earlier. Consider a typical case of unskilled labor in a labor surplus country, for example, rural workers employed for dam construction. The fore- gone output of workers used in the electric power sector is the domi- nant component of the SWR. Complications arise because the original income earned may not reflect the marginal product of agricultural labor and, furthermore, for every new job created, more than one rural worker may give up former employment." Allowance must also be made for seasonal activities such as harvesting. In theory, if the laborer has to work harder in a new job than before, then the disutility of fore- gone leisure should be included in the SWR, but in practice this com- ponent is ignored. Overhead costs, such as transport expenses, should also be considered. These concepts may be summarized by the following basic equation for the efficiency shadow wage rate (in efficiency prices): ESWR = a*n + c*u where m and u are the foregone marginal output and overhead costs of labor in domestic prices, and a and c are corresponding conversion fac- tors to convert these values into border prices. The effect of these changes on consumption patterns is important to consider. Suppose a worker receives a wage W,, in a new job and that the income foregone is Wo, both in domestic prices; W, may not necessarily be equal to the marginal product foregone m. It could be assumed, quite 13. See John R. Harris and Michael P. Todaro, "Migration, Unemployment, and Development," Ameiican Economic Review, vol. 60 (March 1970), pp. 126-42. 114 THEORY plausibly, that low-income workers consume all their increase in income (W,, - W.). Then this increase in consumption will result in a resource cost to the economy of b -(W,, - W,), where b is the border-priced Msc of increasing private consumption, in domestic prices, by one unit. The increased consumption also provides a benefit given by w - (W, - Wo), where w represents the MSB, in border prices, of increasing domestic- priced private sector consumption by one unit. Therefore: SWR = a*m + c*u + (b - w)(W. - Wo). The consumption term (b - w) disappears if at the margin (a) so- ciety is indifferent to the distribution of income or consumption, so that everyone's consumption has equivalent value; and (b) private con- sumption is considered to be as socially valuable as uncommitted public savings, the numeraire. (See appendix B for a more detailed explanation of b and w). Regarding land, the appropriate shadow value placed on this primary factor depends on its location. In most cases, the market price of urban land is assumed to be a good indicator of its economic value in domestic prices, and the application of an appropriate conversion factor, the sCF, to this domestic price will yield the border-priced cost of urban land inputs. Rural land that can be used for agriculture may be valued at its opportunity cost: that is, the net benefit of foregone agricultural output. The marginal social cost of other rural land is usually assumed to be negligible, unless there is a specific reason to the contrary. If a hydroelectric dam floods virgin jungle, however, loss of valuable timber or spoilage of a recreational area with commercial potential might be involved. The shadow price of capital is usually reflected in the discount rate or accounting rate of interest (A RI), which is defined as the rate of decline in the value of the numeraire over time. Although there has been much discussion concerning the choice of an appropriate discount rate, in practice the opportunity cost of capital (OCC) may be used as a proxy for the ARI, in the pure efficiency price regime.'4 The OCC is defined as the expected value of the annual stream of consumption in border prices, 14. See, for example, Stephen A. Marglin, "The Social Rate of Discount and the Optimal Rate of Investment," Quarterly Journal of Economics (1963); Ezra J. Mishan, Cost Benefit Analysis, chap. 31-34; and Arnold C. Harberger, Project Evaluation (London: Macmillan and Co., 1972). SHADOW PRICING 115 net of replacement, which is yielded by the investment of one unit of public income at the margin. A simple formula for ARI, which also in- cludes consumption effects, is: ARI = OCC [s + (1 - s)w/b] where s is the fraction of the yield from the original investment that will be saved and reinvested.'5 The objective of this section has been to facilitate the application of shadow pricing in power sector economic analysis. A word of caution is necessary, however. Although the principles underlying the use of shadow prices are relatively straightforward, usually the estimation of shadow prices on a rigorous basis is a long and complex task.'6 There- fore, the electric power sector analyst is advised to use shadow prices that have already been calculated by other specialists. Alternatively, per- haps the analyst could make simple estimates of a few important items, such as the standard conversion factor, opportunity cost of capital, and shadow wage rate. When the data are not precise enough, sensitivity studies may be necessary over a range of values of such key national parameters. 15. Lyn Squire and Herman G. van der Tak, Economic Analysis of Projects, chap. 10. 16 See Colin Bruce, "Social Cost-Benefit Analysis: A Guide for Country and Project Economists to the Derivation and Application of Economic and Social Accounting Prices," World Bank Staff Working Paper, no. 239 (Washington, D.C.: World Bank, August 1976).  Part Two Case Study The objective of the case study is to test and to evaluate the reliability and system optimization theory developed in Part One. The parameters of this study were determined on the basis of the following three criteria. First, the study was implemented in a developing country because the World Bank is particularly concerned with the needs of the Third World for economic development. In a developing country, the application of the theoretical methodology can be examined critically under conditions of data scarcity compared with the industrialized countries. In this con- text, shadow pricing concepts must also be applied. Second, a distribution study was selected because it afforded greater opportunities for advancing the state-of-the-art in engineering. This sup- ply side consideration paralleled the major demand side effort in eco- nomics to measure outage costs. The engineering component is especially relevant, because generation and transmission system models and plan- ning techniques tend to be much more sophisticated and better in- vestigated than those generally used in distribution network studies, although usually distribution failures account for most consumer out- ages.' (See chapter 8, Power System Supply Costs.) Furthermore, it is possible to compute load-point outage frequency and duration indexes, 1 See, for example, R. N. Allan, E N. Dialynas, and I. R. Homer, "Modelling and Evaluating the Reliability of Distribution Systems," IEEE Transactions on Power Apparatus and Systems, vol. PAS-98 (May-June 1979). 117 118 CASE STUDY which are appropriate for estimating consumer outage costs more accu- rately for distribution systems than for generation and transmission sys- tems. Third, the choice of Cascavel, in southern Brazil, as the city for study was influenced by the need to collaborate with a local electric power utility that was willing and able to assist in the study.2 Other considerations that affected the decision included the importance of having a representative mix of consumer types, as described in chapter 10, and the requirement of implementing the methodology within a rea- sonably compact, medium-sized urban area, for example, a population of 100,000. The techniques described in Part One were applied in a relatively straightforward fashion, by following the sequence of steps summarized in the flow chart depicted in figure 1.1 of chapter 1. A highly disaggregate load forecast was prepared using correlation techniques in conjunction with urban land use and socioeconomic data. The design and costing of alternative distribution system expansion paths was detailed and de- veloped over a longer period than is common in most distribution plan- ning studies. Expected outage frequency and average duration indexes were computed at the point of consumption using a relatively simple technique. Outage costs were estimated by using information on local economic activity, as well as several consumer surveys that were based on the theoretical models developed earlier. Finally, the cost-benefit analysis and fine-tuning of the system optimization procedure led to the innovative step of designing so-called "hybrid" distribution net- works or grids. The reliability level of these hybrid grids was varied in different neighborhoods, depending on their sensitivity to outages. The methodology was implemented primarily by employing three coiputerized models that were used specifically to determine the de- mand forecast, the alternative distribution system designs, and the outage costs and system costs. Despite their potential complexity and size, these computer programs were adapted especially to be implemented on com- pact mini-micro-computer systems. 2. Compania Paranaense de Energia El6ctrica (COPEL), Parana, Brazil. Chapter 10 Demand Forecast The load forecast developed in this chapter is specifically for the purpose of long-range distribution system planning. Therefore, as discussed in chapter 8, Power System Planning and Supply Costs, a computerized approach was used to make these demand projections, which are both long term and highly disaggregate:' (a) by type of consumer-twenty- four categories; (b) geographically-247 cells, each 500 X 500 meters square; and (c) in time-annually over twenty years. Straightforward correlation techniques were combined with land use and socioeconomic information to obtain the desired results. First, the intensity of energy consumption by consumer category was estimated by relating the kilowatt-hour use to convenient measures of customer magnitude, for example, kilowatt-hours for each household, each unit of industrial value added, each hospital bed, and so on, in any given year. Then, land use, demographic, and other socioeconomic data were used to determine the customer magnitudes incident in each geographic cell and over time. For example, the number of households, total indus- trial value added, and number of hospital beds in each cell were exam- ined for each year. The product of the intensity of energy use and the customer magnitude yielded the total disaggregate energy demand by consumer category, by 1. Details of the computation are provided in appendix C. 119 120 CASE STUDY geographic cell, and by year. Throughout the analysis a neutral price assumption was used: that is, the price of electricity would be constant in real terms. This pricing assumption was the most safe and reasonable choice, since the Brazilian federal government, which regulates electricity tariffs, has adopted a policy of nominal price increases equal to the an- nual rate of inflation during the past few years. Electricity consumers were divided into six major categories to deter- mine the demand forecast and to estimate outage costs. Each major category was also divided into the following subcategories: (1) Residential-lower, lower-middle, upper-middle, and upper in- come groups; (2) Main industrial-metallurgy and mechanical,2 nonmetallic min- erals, wood, vegetable oils, food and beverages, and other; (3) Service industrial-telephone, water and sewage treatment, met- allurgy and mechanical, and other; (4) Commercial-light, medium, and heavy; (5) Public illumination-express, important, main, normal, and sec- ondary roads; (6) Special institutions-hospitals and schools. Land Use and Occupancy by Geographic Cell The future geographic distribution of the various consumers was based upon the long-range urban development plan adopted by the Cascavel city authorities.3 This plan included a map, figure 10.1, detailing the location of the following land classifications: ZR1-Residential area surrounding the core of the business district, an area predominantly occupied by families in the upper and upper-middle income groups; ZR2-Inner suburban area for families in the upper-middle and lower- middle income groups; ZR3-Outer suburban area for families in the lower income group; 2. The output of this type of industry was divided equally between the main and service industrial sectors. 3. Prefeitura Municipal de Cascavel, Plano Diretor de Desenvolvimento (Parana, Brazil, 1975). DEMAND FORECAST 121 ZC and ZCR-Heavy commercial area and high-rise apartments for upper and upper-middle income families in the center of the city; SC and SL-Medium commercial area and medium-sized apartment buildings for upper-middle and lower-middle income families; ZI-Main industrial area where no residential buildings are permitted; SI-Service industrial area along the main highways and some resi- dential buildings for lower income families; SV-Green areas for recreation; ZM-Military area. A comprehensive set of zoning regulations describes the uses per- mitted for each class of land, the amount of land that may be occupied, the ratio of floor area to land area, minimum lot sizes, setback from lot lines, and so on. These regulations were used to determine future occu- pancy levels in dwelling units, population, and commercial floor space. For example, in ZR3, only single-story residences will be permitted on a minimum lot size of 450 square meters. Streets, walkways, and play- grounds will require about 15 percent of the land. An additional 10 percent will be required for service commercial establishments, such as groceries, laundry, and drugstores. Therefore, for a typical square kilometer of ZR3 land, the following mix might be found: Streets = 15 percent of 1 square kilometer = 0.15 square kilometer Commercial = 10 percent of 1 square kilometer = 0.10 square kilometer Residential = 75 percent of 1 square kilometer = 0.75 square kilometer Number of houses = 750,000 square meters per square kilometer/ 450 square meters per home = 1,666 homes per square kilometer Assuming five persons in each family, one square kilometer of ZR3 could contain a maximum of 8,333 people if it were 100-percent satu- rated and each family had a house on a minimum-sized lot. Since distribution planning requires a knowledge of loads by small geographic areas to locate future substations and primary feeders advan- tageously, the individual load areas or cells should be sized so that the maximum demand is well within planning limitations. A load of 5,000 122 CASE STUDY Fgure lo"1 Casca vel Urba, Zonng Classification 0 N SV L x ZR2 SV, SC Z R 2 S L ZRi SP .. ZR ZR 3R sC D÷ ýR2 c ZR2 . ¥.•::......,. NOle Z R 7 residentiai 9 10 denial(uPermidle nd upper and uPPer-middle income),. ZR2 resi det'l(uPr-idl adlower-middle incomresi- 'ncoffe); ZC E3ZCR R3 - hev c nom) ZR3 @=residential (o. n come ); Scrn C R ; S heavy commerclal and residential (upper and wpper_ - medium commercial nd esidential (Upper- DEMAND FORECAST 123 :: -- - - --- - - S P SP * ....::: "NZR3nI ZR1 ZR2 ZR1 ::l,an ZM ~ mlitar zone. ,S Z . .. SL P\ \\\X\\.\ ZR2~~~~ \Z'\\\o\<<' R, n M = iar oe 124 CASE STUDY kilowatts would be appropriate when planning 15-kilovolt primary sys- tems, for example. This usually results in cell sizes ranging from 0.1 square kilometer for the centers of large cities to 1.0 square kilometer for rural areas. For this study, a single cell size of 0.25 square kilometer (500 meters X 500 meters) was selected. The location of the cells corresponded to COPEL'S coordinate system, which simplified the correlation of existing load levels with forecast demands. The selected grid was superimposed onto a map containing the various land classifications. As an illustration, a similar but larger 1-kilometer square grid is shown in figure 10.2. The fractional area, in square meters, of each cell within the various zoning classifications was derived from the map and entered into a com- puterized data base used for load forecasting.4 The future land use was then used to compute the probable mix of consumers for each cell. For example, a cell might contain 0.15 square kilometer of ZR3 land and 0.1 square kilometer of recreation land (SV). Maintaining the same assumptions as in the earlier numerical example, the land uses within this cell would be: Residential area = 0.75 X 0.150 = 0.1125 square kilometer Maximum number of houses = 1660 X 0.1125 = 250 homes Street area = 0.15 X 0.150 = 0.0225 square kilometer Light commercial area =0.10 X 0.150 =0.0150 square kilometer Recreational area = 1.0 X 0.100 = 0.100 square kilometer Residential Electricity Consumption The basic unit for analyzing residential consumption was the average household of five persons. This mean household size of five persons was approximately constant over all income classes and was also assumed 4. See Walter G. Scott, "Computer Model Forecasts Future Loads," Electrical World (September 15, 1972), pp. 114-16. DEMAND FORECAST 125 to remain unchanged in the future. Using COPEL's billing data, as well as income and other data from a 1975-76 household survey, it was possible to plot the curve of average annual household kilowatt-hour consumption against income net of taxes (by income class), as figure 10.3 shows.r Assuming that this relation between kilowatt-hours and real income remains unchanged in the future, and estimating the average annual rate of growth of gross household income in real terms to be 4 percent on the basis of past growth rates and long-run economic projec- tions, the corresponding future annual kilowatt-hour consumption of households in each income class could be determined, as summarized in table 10.1. It was also assumed that the real electricity price and the tax structure with resepect to real income would remain essentially the same. Next, a forecast was made of overall population, as well as the frac- tion of population served with electricity, on the basis of the most recent demographic information and discussions with city planners, as shown in table 10.1. The distribution of population by income class was 20 percent lower, 45 percent lower-middle, 27 percent upper-middle, and 8 percent upper in 1976, and it was estimated that this income structure would remain basically unchanged during the forecast period. The mean real income level of each income class, however, was assumed to grow at 4 percent annually, as previously mentioned. The forecast population was distributed throughout the city as fol- lows: the 1976 distribution of residential consumers by level of kilowatt- hour consumption, and therefore by income class, was known on a cell-by-cell basis from COPEL billing records. For the future years, the city was divided into the three saturation regions-high, medium, and low-based on population density, as shown in figure 10.2. A 100- percent saturation level implied that the land was carrying the maximum residential population permitted under the applicable zoning regulations. The forecast population by income class was allocated across the resi- dential zones on the basis of reasonable estimates of saturation factors and numbers of single and multifamily dwellings per cell. (See appendix C for details.) Kilowatt-hour consumption figures for each residential class may be obtained on a cell-by-cell basis from the forecast of the number of households and each household's kilowatt-hour consumption. 5. cuRA, "Pesquisa Fisico-Socio-Economica" (prepared for the Cascavel City Government) (1975-76). 126 CASE STUDY Figure 10.2. Cascavel Cell Grid, Saturations 1, 2, 3, and Layout of Principal Roads 0 N M L1 K I H I- G F E D C B 1 2 3 4 5 6 7 8 9 10 1 DEMAND FORECAST 127 12 13 14 15 16 17 18 19 20 21 22 128 CASE STUDY Table 10.1. Forecast of the Cascavel Urban Population, Electricity Service, Electricity Consumption, and Income 1976 1980 1984 1988 1992 1998 Population (thousands of persons) 90 146 214 281 341 399 Average annual growth rate (percentage) 18 13 10 7 5 4 Percent- age of total Percentage of income class Income group population served by electricity Lower 20 25 40 50 60 70 80 Lower-middle 45 50 60 70 80 90 90 Upper-middle 27 75 85 90 95 100 100 Upper 8 100 100 100 100 100 100 Total 55.8 66.0 73.8 81.7 89.5 91.5 Total annual electricity consumption (gigawatt-hour) Lower 0.3 0.8 1.8 2.9 5.5 8.6 Lower-middle 3.5 8.1 16.2 25.7 38.2 50.7 Upper-middle 5.9 12.0 21.2 32.8 47.6 61.7 Upper 4.4 8.0 12.8 17.9 24.1 30.8 Total 14.1 28.9 52.0 79.3 115.4 151.8 Average annual household electricity consumption (kilowatt-hour) Lower 307 360 430 500 580 680 Lower-middle 794 910 1,060 1,210 1,380 1,570 Upper-middle 1,631 1,840 2,060 2,310 2,580 2,860 Upper 3,283 3,520 3,760 4,040 4,400 4,820 Average annual household net income (1976 Cr$ x 103)a Lower 18.4 21.5 25.2 29.5 34.5 40.3 Lower-middle 47.7 54.3 62.3 71.6 82.3 94.7 Upper-middle 97.5 111.8 128.0 146.8 167.8 191.1 Upper 228.6 249.7 269.5 301.6 341.2 386.3 a. US$1 = Cr$12.35 (end 1976). DEMAND FORECAST 129 Figure 10.3. Relation between Average Electricity Consumption and Net Income of Households, by Income Class, 1976 5000- 5 ' 4000- 2 3000- z 2000- U-o 1000- 0 100 200 300 400 Net income (10 cruzeiros a year) Industrial Electricity Consumption The growth of value added in each of the six main industrial sectors was forecast for the 1976-96 period, based on the most recent data on industrial activity and discussions with local firms, government offi- cials, and so on. Past data on value added for each kilowatt-hour con- sumed were analyzed for each type of industry. These data made it possible to estimate future industrial loads. Electricity consumption for telephone service and water and sewage treatment in the service industrial group could be forecast by analyzing population growth and from information obtained from public officials. Other service industrial needs were determined by estimating energy usage per square meter of land for this kind of activity, chiefly on the basis of trends in their past relation with population. The industrial load forecast is summarized in table 10.2. The industrial loads were known on a cell-by-cell basis for 1976 from COPEL billing data. These loads were allowed to grow in their existing locations at the given rates until 1980, after which they were gradually Table 10.2. Industrial Electricity Consumption Value Average added annual (1976 growth Cr$) rate per Load Annual megawatt-hour consumption over 20 Sector kWh factor 1976 1980 1984 1988 1992 1996 years Main industrial Metallurgy and mechanical 23.5 0.15 255 446 780 1,364 2,386 4,173 15 Nonmetallic minerals 14.9 0.123 804 1,407 2,460 4,303 7,525 13,162 15 Wood 32.3 0.204 4,338 5,477 6,914 8,729 11,020 13,913 6 Vegetable oils 19.6 0.435 5,420 8,529 13,419 21,117 33,227 52,283 12 0 Food and beverages 19.9 0.183 3,267 5,141 8,089 12,729 20,029 31,515 12 Other 14.1 0.46 1,239 1,949 3,067 4,825 7,593 11,948 12 Subtotal 22.6 0.25 15,323 22,949 34,729 53,067 81,780 126,994 11.15 Service industrial Telephone 25.5 0.46 470 767 1,251 2,039 3,324 5,420 13 Water and sewage treatment 5.1 0.25 2,800 4,251 6,453 9,756 14,871 22,574 11 Metallurgy and mechanical 23.5 0.15 255 446 780 1,364 2,386 4,173 15 Other - 0.24 3,500 6,121 10,707 18,726 32,752 57,283 15 Subtotal - 0.25 7,025 11,585 19,191 31,885 53,333 89,450 13.56 Total - 0.25 22,348 34,534 53,920 84,952 135,113 216,444 12.02 DEMAND FORECAST 131 allocated to the main industrial (ZI) and service industrial (SI) areas. By 1984, all industrial activity would be confined to ZI and SI zones, as the urban authorities planned. Other Electricity Consumption For commercial electricity use, a survey was made to determine the floor area and electrical equipment in a variety of commercial estab- lishments. The survey results and recent data on the growth of energy consumption were used to determine the future energy requirements for light, medium, and heavy commercial consumers. These projections were adjusted to correlate commercial load growth with population in- creases in each area. For street lighting, energy requirements were based on five types of streets and their associated lighting standards: that is, express, important, main, normal, and secondary. The street lighting load was increased with the growing population, industrial, and commercial saturation of each zone. For schools, energy requirements during the forecast period were based on recent trends of energy use: that is, averaging approximately 4 kilowatt-hours for each student year. Also, it was assumed that the percentage of students in the population would increase steadily from about 9 percent in 1976 to 20 percent in 1996. For hospitals, future energy requirements were based on recent trends in energy use for each hospital bed: that is, approximately 1,000 kilowatt-hours for a bed annually. A constant ratio of six beds to every 1,000 persons was assumed based on information provided by local authorities on future hospital construction. Summary of Demand Forecast The demand for electric energy was estimated annually over the entire twenty-year forecast period, in each of the 247 geographic cells, and for each of the twenty-four consumer categories by using a variety of Table 10.3. Summary of Demand Forecast Consumer 1976 1980 1984 1988 1992 1996 Load category GWh MW GWh MW GWh MW GWh MW GWh MW GWh MW facto?- Residential 14.1 4.4 28.9 8.9 51.0 15.7 80.2 24.7 115.9 35.8 152.1 46.9 0.37 Main industrial 15.3 7.0 23.0 10.5 34.7 15.8 53.1 24.2 81.8 37.4 127.0 58.2 0.25 Service industrial 7.0 3.2 11.6 5.3 19.2 8.8 31.9 14.6 53.3 24.3 89.5 40.9 0.25 N.) Commercial 13.5 4.8 28.3 10.1 51.4 18.3 82.8 29.5 122.5 43.7 164.5 58.7 0.32 Public lighting 3.0 0.8 4.9 1.3 7.2 2.0 9.4 2.6 11.5 3.1 13.5 3.7 0.42 Hospitals and schools 0.6 0.1 1.0 0.3 1.4 0.4 1.9 0.5 2.4 0.6 2.8 0.7 0.46 Total 53.5 20.3 97.6 36.4 164.9 61.0 259.3 96.1 387.4 144.9 549.3 209.1 Note: GWh = gigawatt-hour; MW = megawatt. a. The load factor for each consumer category is a weighted average that includes the effect of diversity. DEMAND FORECAST 133 correlation techniques, in conjunction with land use, saturation, and socioeconomic data. Electricity consumption data were examined by consumer category, for the period 1970 to 1975 inclusive, to determine the evolution of the load factor( LF). With this information, appropriate constant values of LF were estimated for the forecast period, incorporating the effects of diversity among consumers. These values were used to project the disaggregate demand for power on the basis of the corresponding kilo- watt-hour load forecast made earlier. The global demand forecast for the entire city at four-year intervals and by major consumer categories is summarized in table 10.3. Chapter 1 1 Long-Range Distribution System Planning This chapter is concerned with the development of alternative system plans that were designed to achieve different levels of reliability. Again, the main purpose of the illustrative case study, described in part 2, was to test the new methodology of optimizing power system reliability levels, with special emphasis on the empirical estimation of outage costs. A com- prehensive distribution system planning study was not intended. There- fore each of the alternative system designs is based upon the same voltage criteria and constructed with similar materials and equipment in accordance with the same engineering standards. In this study the reliability level among the different expansion alternatives usually was varied by providing different substation and feeder capacities, as well as several interconnection possibilities between distribution circuits. In addition, this adjustment made it possible to limit the innumerable and time-consuming variations in system design that could have been gen- erated by minor alterations in the types of equipment and configurations used. The points at which such further fine-tuning of the system design could be carried out are indicated in the text. Stages of Distribution System Development Before examining the system design criteria, it is pertinent to discuss the three basic engineering stages in the development of a distribution system: the design of equipment and components; the determination 134 LONG-RANGE DISTRIBUTION SYSTEM PLANNING 135 of general construction standards based on the available equipment and components; and the selection of the types of construction standards to be applied in a specific situation. Manufacturers have the major responsibility for the first stage, the design of distribution equipment and components such as transformers, insulators, and switches. Overall, the efficiency, dependability, and com- pactness of these components have steadily improved. Since most of them have been standardized for use in the industrialized countries, the developing countries could lower costs by adapting component designs to local conditions, especially for rural electrification. Utility or consulting engineers are largely responsible for the second stage: the development of general construction standards. Usually these consist of drawings and materials lists to accomplish specific functions, such as a pole with a cross arm, insulators, and hardware to support a three-phase primary line. In general, construction design standards in the industrialized countries have reflected successfully the increases in con- struction labor costs and advances in equipment design. Again, devel- oping countries that accept these design standards without modification could be using their scarce resources inefficiently. In the third stage, engineers select and merge construction standards to build facilities to carry out specific tasks. For example, a substation may be built to serve an area, or primary lines laid to serve a factory or a residential area. This final stage, which predominantly involves planning, is most relevant to the case study. In many countries where capital is in short supply, it is not unusual to find similar facilities being constructed to serve all classes of con- sumers. When this happens, customers are rarely satisfied. A uniformly low service level probably will not provide industries with the quality of service they require to be competitive with manufacturers from neigh- boring countries. Remote farmers and villagers will be dissatisfied with the high electricity tariffs associated with a service level above their simple needs. Therefore, the principle of varying the reliability level according to the needs of specific groups of consumers should be con- sidered whenever possible. Definitions and Design Criteria This section defines and describes distribution systems and their volt- age standards, reliability criteria, and construction design criteria. 136 CASE STUDY Distribution systems As described in chapter 2, Introduction to Reliability, an electric power system may be broken down into three segments: generation, transmission, and distribution. Transmission and distribution facilities, both of which help to transport power from the generating source to the ultimate user, are usually distinguished from one another on the basis of their operating voltage. Installations operated at voltages higher than 45 kilovolts may be considered definitely transmission whereas lines operated at voltages lower than 25 kilovolts are distribution related. Facilities operating in the intervening range are more difficult to classify. For example, it is common to find a 34.5-kilovolt line being used to transmit power from a central station to many small towns where the voltage is stepped down to 12 or 6 kilovolts. This is definitely a trans- mission function. The same line, however, may serve several small in- dustrial consumers and even some farms along the way, which may be considered a distribution function. For this study, primary feeders were designed to operate only at 13.8 kilovolts, to keep the variability in the design within practical limits. It may well be more economical to serve certain parts of the city at 34.5 kilovolts in the future although such fine-tuning of the system was not considered to be within the scope of this study. The major components of the Cascavel network, a typical distribu- tion system, are shown in figure 11.1 and are described below. (a) The distribution substation includes the transformer, which steps down the transmission voltage from 138 kilovolts to the distri- bution primary voltage of 13.8 kilovolts, and other facilities such as switch gear, busses, and fuses. (b) The distribution primary system, that is, circuits or feeders, con- sist of the conductors and associated facilities that carry elec- tricity from the substations to the distribution transformers. (c) The distribution transformer reduces the voltage from the primary level-for example 13.8 kilovolts-to the utilization level. (d) The secondary system and service line consist of conductors and associated hardware to deliver power to the consumer's service inlet. (e) The service inlet receives power from the secondary system, con- nects the supplier and the user, and measures electricity use. LONG-RANGE DISTRIBUTION SYSTEM PLANNING 137 Figure 11.1. Major Components of a Typical Distribution Network Transmission line 138 kilovolts r -- ---- --- ------------ -I Breaker Station transformer Distribution Breaker substation Busbar Breaker Breaker \hkilovolts Distribution primary feeders Distribution transformer 207/120 volts Customer service Secondary lines inlets and meters 207/120 volts Distribution transformer Voltage standards for distribution systems All power distribution systems experience voltage drops caused by the flow of current. If the delivered voltage is too low, equipment perform- ance will be poor; if it is too high, equipment may fail prematurely. Therefore, an acceptable range of supply voltage must be established, and the voltage ratings of customer equipment must be standardized to correspond to the supply voltage. In general, frequency variations are not as serious as voltage fluctuations, but they can still affect electric 138 CASE STUDY timing devices, synchronous motors, and other mechanisms. Since fre- quency changes result from overloading of generation rather than dis- tribution, however, this aspect is ignored in this case study involving a distribution system. Although voltage standards vary in different countries, the principles used in matching equipment ratings to supply voltage levels are uni- versal. In Brazil, there is no national standard, but many individual utilities use voltage criteria patterned after the ones established by the American National Standards Institute (ANSI).1 Therefore ANSI stand- ards were used in this analysis, although any other internationally ac- cepted set of standards could also have been adopted. In brief, with the ANSI standards for standard or nominal 120-volt service, the power supplier is obligated to provide voltage at the consumer's service inlet within the favorable voltage ranging from 114 to 126 volts under nor- mal operating conditions. These conditions are somewhat relaxed in the tolerable voltage ranging from 110 to 127 volts, which is applicable under fault or emergency conditions. The consumer's equipment should perform satisfactorily from 110 to 126 volts and acceptably within the wider limits of from 106 to 127 volts. In both the favorable and tolerable ranges, the minimum voltages for equipment use are 4 volts lower than the corresponding values for the supply voltage at the service inlet to allow for additional voltage drops in the consumer's internal wiring. The supply voltage variations allowed by the ANSI criteria-12 volts for the favorable range and 17 volts for the tolerable range-must be allocated among the major components of the distribution system. De- termining the optimal division of voltage drops for the various distribu- tion system components could become a major study in itself, because it is the basis for the sizing of conductors, loading of transformers, choosing lengths of secondaries, placement of capacitors, and to on.2 For the purposes of this study, however, the following allocation of voltage variations was selected, based on existing COPEL criteria and on engineering judgment. (a) Service line. A 1-volt drop can be expected under normal con- ditions. (b) Secondary system. Analysis of the COPEL secondary system indi- 1. See ANSI, Publication no. C84.1, 1970, and appendix C for further details. 2. For details, see, for example, Westinghouse Distribution Systems Reference Book (East Pittsburgh: Westinghouse Corp., 1959) LONG-RANGE DISTRIBUTION SYSTEM PLANNING 139 cated that the voltage drop varies from 1 to 3 volts, and there- fore an average value of 2 volts was used in the study. (c) Distribution transformer. COPEL distribution transformers have an average loading of approximately 60 percent, with a conse- quent drop of about 2 volts. (d) Station regulator. A 2-volt band width spread is the normally accepted value. (e) Primary system. The primary system was allocated the remainder of the voltage ranges. Favorable voltage range: 12 - (2 + 1 + 2 + 2) = 5 volts Tolerable voltage range: 17 - (2 + 1 + 2 + 2) = 10 volts These results are summarized in table 11.1. Reliability criteria for distribution systems As stated previously, the reliability standards traditionally used in de- signing electric power systems do not appear to have been derived from explicit cost-benefit studies but, instead, have been based on rule-of- thumb, general desirability, and affordability. In reliability modeling, some sophisticated distribution reliability models have been proposed only recently (see chapter 2, Introduction to Reliability). Traditionally, the main emphasis has been on analysis of generation and transmission systems. Although many utilities gather outage statistics, however, these Table 11.1. Division of Voltage Variation over the Distribution System Components Favorable range Tolerable range Percentage Percentage Components Volts nominal Volts nominal Station regulator band width 2.0 1.67 2.0 1.67 Primary system 5.0 4.17 10.0 8.33 Distribution transformers 2.0 1.67 2.0 1.67 Secondary system 2.0 1.67 2.0 1.67 Service line 1.0 0.82 1.0 0.82 Total distribution system 12.0 10.00 17.0 14.16 Note: Based on nominal 120-volt service. Table 11.2. Alternative Distribution System Characteristics High-reliability system Medium-reliability system Low-reliability system Service under normal Voltage within favorable Voltage within favorable Voltage within tolerable conditions range during peak hours range during peak hours range during peak hours Service under emergency Substation A, circuit Al, and Substation A, circuit Al, and None, no interconnec- conditions, for exam- interconnection have suffi- interconnection have suffi- tion provided ple, with circuit BJ cient capacity to pick up all cient capacity to pick up all faulted (see schematic loads of circuit B1 during loads of circuit Bi only dur- below)" peak hours and to deliver ing off-peak hours and to power within the tolerable deliver power within the 0voltage range. tolerable voltage range. Design considerations Emergency conditions Normal conditions Normal conditions and costs dictated by Outage duration deter- Time to switch Time to repair during peak Time to repair mined by hours, and time to switch during off-peak hours Circuit AN Circuit B I Substation A Substation B C D E F G a. Corresponding reasoning applies if circuit Al is undergoing an outage. LONG-RANGE DISTRIBUTION SYSTEM PLANNING 141 data are rarely analyzed fully, translated into meaningful probabilities, and used systematically to improve system performance.3 The system in Cascavel is currently designed with sufficient capacity to withstand the loss of a station transformer or a feeder at peak load. For this study the system was considered highly reliable. In addition, medium- and low-reliability systems were defined and modeled for the study, as described below and summarized in table 11.2 and in the ac- companying circuit diagram. (1) High-reliability system. Under normal conditions, the system will have sufficient capacity to deliver power at peak load within the favor- able voltage range. In emergencies, the system will have sufficient ca- pacity and interconnections between circuits to pick up the load of a faulted circuit during the peak, after appropriate switching to isolate the fault, and to deliver power within the tolerable voltage range. The dura- tion of an outage will be determined by the time it takes to despatch a trouble lineman to the area, locate the problem, isolate the fault, and restore service by appropriate switching. The design and costs of a high-reliability system are basically dictated by the system's emergency capabilities. (2) Medium-reliability system. Under normal conditions, the system will have sufficient capacity to deliver power at peak load within the favorable voltage range. Interconnections between circuits are provided so that loads can be picked up from a faulted circuit under off-peak load conditions and so that power can be delivered within the tolerable voltage range. The duration of an outage will vary between the corre- sponding values for the high- and low-reliability systems, depending on the loading. System design and costs are basically dictated by capabili- ties under normal conditions: that is, favorable supply voltage at peak. 3. In practice, the design of most distribution systems is based on one or more of the following rules-of-thumb. (a) Sufficient capacity to withstand the loss of a specific portion of the system, such as a substation transformer, at peak; (b) Limiting the load on a circuit (for example, 5,000 kilovolt-amps on a 13.8 kilovolt feeder); (c) Limiting the length of primary mains (for example, 5.0 kilometers for a 13.8 kilovolt feeder); (d) Installation of reclosers based upon length of line or connected kilovolt-amps or number of customers, and so on, (e) Installation of fuses at every branch point; and (f) Installation of remote-controlled, motor-operated switches. 142 CASE STUDY (3) Low-reliability system. Under normal conditions, the system will have sufficient capacity to deliver power at peak load within the tolerable voltage range. No connections between circuits are provided for this system. The duration of an outage will be determined by the time it takes to despatch a trouble lineman to the area, locate the problem, isolate the fault, and restore service. Service is restored by switching or repair, depending on the location of the fault, as well as the switches. Again, the design and costs of the system are basically dictated by its capa- bilities under normal conditions; in this instance, tolerable supply volt- age at peak. A large number of variations of these three basic designs could have been generated by selecting different system components, configurations, and operating practices. These would include, for example, covered, in- sulated, or underground primary conductors, reclosers, switches, standby crews, more frequent maintenance, and so on. As discussed at the begin- ning of this chapter, however, these variations were not considered, since they were not relevant to the study. Even without using these additional components and configurations, it would have been possible to design other basic system configurations with higher and lower reliability levels than those considered. The physical characteristics of Cascavel, however, made this unnecessary. For example, a spot network system with automatic or centrally dis- patched switvhing might have been justified for the downtown area of a much larger city. In many small towns or rural areas, however, it would have been more sensible to build a distribution network that did not have sufficient capacity to meet all peak period requirements. For exam- ple, a system that relied on planned and rotating power cuts during the peak may have been more appropriate. Construction design criteria for distribution systems Several engineering considerations were included in the planning and design of the alternative distribution primary systems. The systems each were designed to meet a distinct level of reliability; they differed in regard to normal and emergency conductor loading and voltage regulation. Each plan, however, had the same final year substation configuration, quantity and location of substations, and standard overhead primary conductors. Differences in costs and losses among the systems arose from the variations in the capacity and number of circuits, as well as the timing of these investments in each plan. LONG-RANGE DISTRIBUTION SYSTEM PLANNING 143 COPEL's distribution design criteria were reviewed, and in general they were found to be reasonably adequate and convenient. A more compre- hensive distribution system planning study may have included an ex- tensive evaluation of such criteria, requiring a major effort beyond the scope of this study. The basic COPEL distribution substation layout used in the study are shown in figure 11.2. These substations had ring main busbars on the high voltage sides (138 kilovolts), Y (138 kilovolts) to delta (13.8- kilovolt) transformers, main-transfer busbars on the low voltage sides, and used oil or airblast circuit breakers depending on location and availability. The low- and medium-reliability systems modeled had 20-megavolt-amp transformers, whereas the high-reliability system used 10-megavolt-amp transformers. This was the least-cost solution imposed by the requirement that there must always be spare capacity equivalent to one transformer. COPEL distribution primaries were constructed with precast concrete poles and crossarms, 15-kilovolt class insulators, and the following bare all-aluminum conductors: sizes 2/0 AWG, 4/0 AWG, 336 McM, and 477 McM; having capacities of 7.08, 10.64, 12.9, and 16.66 megavolt amps, respectively, at 13.8 kilovolts.' Table 11.3 summarizes the main criteria used in designing the three systems. The conductor loadings for the low- and high-reliability systems were based on reserve requirements. Two different levels of maximum conductor loading were used to derive the two variants A and B of the basic medium-reliability system. In general, distribution transformers and secondary systems are de- signed at a minimum level of reliability. Unlike the primary feeders, secondary systems rarely contain interconnecting sections and surplus capacity for shifting loads. Also, they are constructed with covered or insulated wire to minimize faults-an acceptable practice at secondary voltage levels. An in-depth investigation of the transformer and sec- ondary system was not within the scope of this study, although this is an area for potential savings. Further studies could result in changes in construction practices, especially in electrifying areas of low consumer density. When an outage does occur on the secondary system, the consumers are without service until repairs are completed. The number of con- 4. AwG = American Wire Gauge; McM = thousands of circular mils; 1 circular mil = 0.7854 X 10' square inches. 144 CASE STUDY Figure 11.2. Typical Distribution Substation Layout Low- AND MEDIUM-RELIABILITY SYSTEMS: 40 MEGAVOLT-AMP SUBSTATION 138/13.8 kilovolts 20 megavolt-amps each 138 kilovolts 13.8 kilovolts 138 kilovolts HIGH-RELIABILITY SYSTEM: 40 MEGAVOLT-AMP SUBSTATION 138/13.8 kilovolts 10 megavolt-amps each 138 kilovolts [] [13.8 kilovolts 138 kilovolts Note: Substation components: O oil or air blast circuit breaker; trans- former-Y (center grounded) to delta. Table 11.3. System Reserve Requirements, Voltage Drops, and Conductor Loading Maximum conductor Maximum voltage drop loading (percentage Station transformer Circuit switching (percentage) of rated capacity) System plan reserve capacity reserve capacity Normal Switched Normal Switched Low-reliability None None 8.33 - 100 Medium-reliability None Off-peak 8.33 8.33 95 (type A) 100 switching only 65 (type B) High-reliability One transformer Switching at any 4.17 8.33 50 100 (10 megavolt-amps) time 146 CASE STUDY sumers out of service for any one outage is small, however, and outages are generally rare. For example, the failure rate of COPEL distribution transformers is approximately 3.4 percent a year. Although it appears high, an average consumer will face only one such failure every 29.4 years. Thus, the differences in the rate of secondary system failures between the three alternative system designs would be small compared with the differences in the primary system failure rate. Outage Parameters Outage records for the Cascavel distribution system were analyzed to determine outage statistics for the primary system, transformers, and secondaries. The load pattern for the system was also studied to deter- mine the relation between annual peak demand and demands during various periods. Analysis of past outage data In the subsequent analysis, outages refer to supply interruptions caused by faults in the distribution network, rather than at the generation or transmission level. For convenience, outages were divided into two cate- gories: temporary ones usually lasting less than five minutes and perma- nent outages, where field switching or repairs were required. Generally, the type of power system design, as well as the operating practices, would affect the characteristics of both temporary and per- manent outages. In this study, however, the basic design of the system has negligible influence on temporary outages: that is, the availability of interconnections between circuits and extra capacity in the substations does not affect the frequency or the duration of these faults. Thus, the effects of temporary faults, which will be small anyway, may be ignored, because they do not change with alternative system designs and there- fore do not affect the comparative analysis of outage costs. In contrast, the frequency and duration of permanent outages are greatly affected by the basic design of the system, as described earlier in the section on reliability criteria. Therefore, circuit interconnections and extra sub- station and feeder capacity limits the duration of permanent outages to only the isolation and switching time. With limited interconnections or LONG-RANGE DISTRIBUTION SYSTEM PLANNING 147 no interconnections, outage duration will be determined by both the switching and the repair times. Data on permanent outages in the Cascavel distribution grid in 1975 and 1976 were analyzed to determine outage frequency and duration during three specific intervals of the day: 0001 to 0800, 0801 to 1800, and 1801 to 2400 hours. These daily time intervals were chosen for convenience of analysis, as well as to distinguish among periods usually devoted to sleep, economic activity, and leisure, as well as between off- peak and peak periods. The results summarized in table 11.4 indicate that the percentages of total minutes of outage time during the three daily periods were quite stable during the two years, although there were greater variations in the annual outage frequencies and average dura- tions. These outage data were combined with the information on the physical characteristics of the distribution network. The data were used with the total length of primary feeders to derive both the average annual Table 11.4. Analysis of Permanent Faults during 1975 and 1976 Year and Annual Duration (minutes) Percentage daily period frequency Average Total of total 1975 0001-0800 24 72 1,732 46 0801-1800 45 23 1,013 27 1801-2400 24 43 1,043 27 All 24 hours 93 41 3,788 100 1976 0001-0800 89 39 3,572 45 0801-1800 245 8 2,632 33 1801-2400 131 12 1,767 22 All 24 hours 465 17 7,971 100 1975 and 1976 (Biannual totals and averages) 0001-0800 113 47 5,304 45 0801-1800 290 13 3,645 31 1801-2400 155 18 2,810 24 All 24 hours 558 21 11,759 100 148 CASE STUDY frequency and the average annual probability for each kilometer of feeder that an outage would occur during each of the three daily periods. Table 11.5 summarizes the exposure of feeder lines to random accidents, such as a car hitting a utility pole or a tree falling on a line. Load duration analysis A load duration analysis provides the relation between demand and energy that is vital to an in-depth study of the effect of outages on the system. The basic data for this analysis were the hourly demands during 1976 for the representative feeders 1 and 2, which served about 80 percent of the total Cascavel load. The 8,760 hourly demands on each feeder were analyzed monthly and annually by the three daily periods to provide the results presented in table 11.6. The Cascavel annual load duration information over all periods is summarized in table 11.7 and figure 11.3. The curves in the figure indi- cate the percentage of time during the year in which the given level of power demand is equaled or exceeded, and the energy supplied at or above that power level. For example, the generation and transmission facilities providing the top 10 percent of demand are only needed 1.45 percent, or 127 hours, of the year, although they supply only 0.08 per- cent of the total energy. Table 11.5. Outage Statistics Based on 1975-1976 Data Outage Outage frequencya Outage probability (frequency/ duration (probabihtyl kilometer/ (minutes! kilometer! Daily period year) outage) year)b 0001-0800 0.717 47 0.000192 0801-1800 1.840 13 0.000106 1801-2400 0.984 18 0.000136 All 24 hours 3.541 21 0.000142 a. Outage frequency = [(freq,5 + freq7e)/2 + (78 8 kilometer of pri- maries)]. b. Outage probability = [(total minutes-s + total minutes.) /2 (hours per year in the time period X 60 X kilometers of line)]. LONG-RANGE DISTRIBUTION SYSTEM PLANNING 149 Frequency and duration factors The past outage statistics and the results of the load duration analysis were used to determine the outage frequency and duration factors for the three systems. The average outage frequency for each kilometer of primary feeder given in table 11.5 was assumed to remain the same in the future for all the basic system designs. The present Cascavel system has the configuration and capacity to be considered a high-reliability system. Therefore the 1975-76 outage dura- tion factors (table 11.5) were used throughout the study to represent the time taken for a "trouble" lineman to be despatched, to locate and Table 11.6 Loading, by Period Demand Energy Feeder and Percent- Percent- daily time age of Megawatt- age of period Kilowatts peak hours total Feeder 1 (Serving predomi- nantly residential and commercial consumers) 0001-0800 2,700 67.5 3,971 23.3 0801-1800 3,750 93.8 7,377 43.3 1801-2400 4,000 100.0 5,688 33.4 Feeder 3 (Serving predomi- nantly residential and industrial consumers) 0001-0800 3,700 82.2 4,974 23.7 0801-1800 4,400 97.8 9,717 46.3 1801-2400 4,500 100.0 6,275 30.0 Feeders I and 3 (Serving about 80 percent of total city load)a 0001-0800 6,100 73.1 8,944 23.5 0801-1800 7,750 92.8 17,094 45.0 1801-2400 8,350 100.0 11,963 31.5 a. The loading of feeders 2 and 4, that represented the remaining 20 percent of the demand, was unavailable. 150 CASE STUDY Table 11.7. Load Duration Analysis Load as a Percentage of time given Percentage of energy percent- load is equaled or supplied above the age of exceeded for feeder given load for feeder peak 1 3 1+3 1 3 1+3 100.0 0.25 0.08 0.02 - - - 95.0 0.28 0.30 0.33 0.03 0.02 0.02 90.0 1.36 0.68 1.45 0.13 0.05 0.08 85.0 3.70 3.17 3.49 0.38 0.26 0.32 80.0 6.35 9.10 6.07 0.84 0.78 0.73 75.0 9.73 13.42 10.10 1.51 1.63 1.49 70.0 10.37 20.88 14.79 2.52 3.31 2.61 60.0 24.38 38.65 36.86 5.78 8.72 7.35 50.0 51.59 52.52 53.44 12.33 17.25 15.94 40.0 61.24 71.83 67.69 23.68 28.54 27.41 30.0 93.94 93.23 96.28 38.72 43.83 43.05 20.0 99.92 99.89 99.98 58.76 62.30 60.71 10.0 99.99 99.99 100.00 79.38 81.50 100.00a 0.0 100.00 100.00 100.00 100.00 100.00 100.00 Feeder Loss factor (percentage) Load factor (percentage) 1 26.24 48.48 3 31.22 53.03 1 + 3 30.23 52.44 a. Minimum demand was 18.18 percent of peak. isolate the fault, and to restore service by switching. This represented the high-reliability situation. For the low-reliability system, consumers are faced with the time it takes to despatch the lineman to locate the fault, isolate the problem, if possible, repair the damage, and restore service. All of the consumers on a circuit do not have to wait until repairs are completed if feeders are designed with a switch halfway between the substation and the end of a circuit. If the trouble is near the substation, the substation breaker is opened, and all consumers will be without service until repairs are made. If the problem is beyond the midpoint switch, then the trouble lineman can open the switch, and only the consumers on the further half will not have service until the damages are repaired. Assuming a uniform density of consumers, as well as a constant outage probability LONG-RANGE DISTRIBUTION SYSTEM PLANNING 151 Figure 11.3. Cascavel Distribution System: Load Duration Analysis Load as a percentage of peak 100 - 80 60O 40- 20 100 80 60 40 20 0 20 40 60 80 100 Percentage of energy supplied Percentage of time given load above given load is equaled or exceeded Note- For feeders I and 3, serving 80 percent of the urban load along the length of a feeder, the average percentage of waiting time during an outage may be estimated. For example, when the problem is in the first half of the feeder, all the consumers it serves will be without electricity the entire time of the outage. If the second half of the feeder is affected, only 50 percent of the customers will be without service until repairs are made. The average customer waiting period is, therefore, 75 percent of the average time needed to restore service. These data on the high- and low-reliability cases were combined with average repair times based on data supplied by COPEL to estimate the outage durations for the low-reliability system presented in table 11.8. The medium-reliability system incorporates aspects of both the low- and high-reliability designs. The system is designed to deliver power at peak load, at least within the tolerable voltage range. If an outage occurs when the actual load is less than some critical value, for example, x percent of the peak load, then the customers on the faulted line can be switched to another line and supplied within the tolerable voltage range. Customers must wait only until the fault is 152 CASE STUDY Table 11.8. Outage Durations for the Low-Reliability System Time required (minutes) by daily period Activity 0001-0800 0801-1800 1801-2400 Obtain crew 45 15 30 Repair damage 120 60 90 Restore service 30 - 15 Subtotal 195 75 135 Average time to repair faced by consumers (75 percent of subtotal) 146 57 101 Despatch lineman and locate and isolate fault 47 13 18 Total time 193 70 119 isolated and the appropriate switching is performed, a situation equiva- lent to the high-reliability case. If an outage occurs when the load is greater than x percent of the peak load, the other lines are incapable of picking up the faulted load, and these consumers must wait until the fault is isolated and repaired. This is equivalent to the low-reliability case. For a given medium- reliability system design, switching studies are performed to determine the percentage x. The load duration curve indicates the load level at any given time during the day, and these data may be used with the value of x to compute the average fault duration for the system for different periods of the day. The final parameters used to forecast the future frequencies and dura- tions of outages for the basic system design are summarized in table 11.9. System Design A computerized primary system model consisting of a digital data base and a package of analytical programs was used to design the alter- native systems." (See appendix C for details.) 5. See Walter G. Scott, "Rural System Engineering and Computer Models" (no. C76408-OIA) (paper presented at the IEEE National Rural Electric Conference, April 1976, Atlanta, Georgia; processed). LONG-RANGE DISTRIBUTION SYSTEM PLANNING 153 Table 11.9. Outage Frequency and Duration Parameters for the Three System Designs Mean outage duration (hours), by system Outage reliability level and period frequency Medium- (frequency/ High reliabilityd Low kilometer/ relia- Obq- relia- Daily period year)a bility" Peakb Peake bilitye 0001-0800 0.717 0.8 0.8 3.2 3.2 0801-1800 1.840 0.2 0.2 1.2 1.2 1801-2400 0.984 0.3 0.3 2.0 1.0 a Exposure factor is assumed to be the same as in 1975-76, see table 11.5. b. Switching time only, see table 11 5 c. Switching time plus 75 percent of repair time, see table 11.5. d. Forecast outage duration = (mean duration during off-peak X fraction of off-peak time) + (mean duration during peak X fraction of peak time). The data base contained all the pertinent physical and electrical char- acteristics of the distribution primary system, including the relations among the principal subdivisions of each feeder: that is, nodes, sec- tions, and branches. The major analytical programs computed the volt- age levels, conductor loadings, and line losses for any feeder. Other analytical programs estimated the fault currents and optimized the loca- tion of capacitors A third set of programs was used to simulate oper- ating conditions, such as the switching of loads between feeders, addition of new loads, and changing of load levels. The data bases of the load forecast and the primary system model were correlated through the coordinates placed in the node file.6 The 1996 loads were then imposed upon the existing system, and an analysis of the voltage, load, and loss was run. This pointed out where the exist- ing system would be weak in meeting 1996 load levels. The system was now expanded to alleviate the weaknesses pinpointed in the above analysis. For each alternative design, additions included new substations, primary branches, and interties in accordance with the corresponding target reliability level. As each group of additions was entered into the data base, the resultant circuits were analyzed for volt- age, conductor loading, and losses. This iterative process of making 6. See chapter 10 and appendix C. 154 CASE STUDY additions, analyzing, and making further changes was continued until the system met the desired reliability criteria within voltage and loading limits. The final product of this process was a primary system that could meet the end-year (1996) load levels within prescribed boundaries. This long-range plan became the guide or target for the interim four-year plans. During the development of the load forecast, load levels had also been established for the interim years (1980, 1984, 1988, and 1992), based on the growth of demand over the forecast period, 1976 to 1996. At each of these interim years, appropriate additions to the distribution network were determined by the iterative process described earlier. These additions enable the system to meet the load levels for that year within operating and design criteria. The above process was used to develop the three basic plans (low-, medium-, and high-reliability), as well as an additional alternative medium-reliability plan, Medium B, whose chief characteristics are summarized below. All the designs ultimately required the same seven substations shown in figure 11.4. The sequence and sizing of the substa- tions for the various plans are presented in table 11.10 and figure 11.5. The number of feeders and the length of line in service for the alterna- tive plans, for selected years, are shown in table 11.11. Reliability, Losses, and System Costs The expected long-range reliability levels, such as outage frequencies and durations for the alternative distribution system designs are estimated Table 11.10. Substation Capacities (megavolt-amps) Plan reliability level Study period Low and medium High (years) Additions Total Additions Total 1976-80 20 40 40 60 1981-84 40 80 20 80 1985-88 40 120 40 120 1989-92 80 200 70 190 1992-96 20 220 50 240 LONG-RANGE DISTRIBUTION SYSTEM PLANNING 155 in this section. Supply interruptions caused by failures at the generation and transmission level were assumed to be essentially the same for all the distribution network designs, and, therefore, their effects could be ignored in the comparative analysis of outage costs. In this case study, the out- age frequency for a distribution system was assumed to depend on the following factors: (a) exposure-length of primary feeders serving a consumer; (b) equipment and design-choice of overhead versus an under- ground system, or type of transformer, and so on; (c) placement-choice of installing lines along the street versus be- hind the property, for example; and (d) maintenance-effectiveness in patroling and repairing lines, checking transformers, and similar duties. Changing the exposure was the most clear-cut and convenient, but not necessarily the most cost-effective, method of generating the variations in outage frequency for this case study. The other factors could also have been varied and tested according to the proposed methodology, Table 11.11. Number of Feeders and Length of Lines Plan reliability level Medium Year Low (A and B) High Number of feeders 1976 4 4 4 1980 6 6 10 1984 10 10 13 1988 14 14 21 1992 20 20 25 1996 24 24 37 Length of line in service (kilometers) 1976 70.6 70.6 70.6 1980 91.0 92.15 95.2 1984 104.9 108.9 110.8 1988 124.8 136.6 138.4 1992 142.3 159.9 154.5 1996 157.2 181.8 179.7 156 CASE STUDY Figure 11.4. Substation Locations, 1996 0 N M L K MNorthwestern H G F Southwestern D c Southern 1 2 3 4 5 6 7 8 9 10 1fi LONG-RANGE DISTRIBUTION SYSTEM PLANNING 157 Northern - - KCntral KEastern ffSou theaster'n 12 13 14 15 16 17 18 19 20 21 22 158 CASE STUDY Figure 11.5. Substation Additions Low- AND MEDIUM-RELIABILITY SYSTEMS & 250 - E "5> 200-C-2 200 - HIERLIBLT SYSTEM SW- SE 150 - E-2 C- NW-1 100 -E- SW-1 50 - SE-1I 1976 1980 1985 1990 1995 Years HIGH-RELIABILITY SYSTEM Z250 -C2 E NW-2 1 SW-2 0200 - S-2 CO SE-2 N-1 150 - E-2 C-1 NW-1 100 - E-1 SE-11 50 - SW-1 E S-1 1: 0 I I I I lI I ll l- 1976 1980 1985 1990 1995 Years Note- The letters in both graphs indicate substation locations given in figure 11.4, and the numbers I or 2 refer to the first or second transformers. but the extra time and effort involved was not considered justifiable in the context of this study. The annual frequencies of outages for the different plans are given in table 11.12. (See appendix C for details.) LONG-RANGE DISTRIBUTION SYSTEM PLANNING 159 Table 11.12. Average Annual Frequency of Outages Plan reliability level Low and medium (A and B) High Daily period (hours) Daily period (hours) 0001- 0801- 1801- 0001- 0801- 1801- Year 0800 1800 2400 0800 1800 2400 1976 13 34 18 13 34 18 1980 11 29 16 7 18 10 1984 8 20 11 6 16 9 1988 7 17 9 5 12 6 1992 5 13 7 5 11 6 1996 5 12 6 4 9 5 Table 11.13. Maximum Outage Duration (hours) Daily period Plan reliability level (hours) Low Medium A Medium B High 0001-0800 3.2 1.0 0.8 0.8 0801-1800 1.2 0.7 0.2 0.2 1801-2400 2.0 1.3 0.6 0.3 For a given plan, the average number of outages on the system de- creased each year because the exposure, or average line length, decreased. The maximum outage duration was constant over the twenty years, how- ever, assuming that the present durations would be typical. Table 11.13 shows the maximum outage durations for the basic system plans. Loss levels are a measure of the efficiency of design and management of reactive volt-amps or VAR. High losses indicate that the system has been poorly designed because capacity is insufficient and VAR flows have been ignored. Very low losses also signal poor design because of excess capacity and perhaps too much VAR control. Overall kilowatt demand losses for the different system designs were determined at the time of system peak, using the primary system analysis program, whereas annual kilowatt-hour energy losses were estimated from the peak demand loss and annual loss factors (derived in the load duration analysis). These losses are summarized in table 11.14. 160 CASE STUDY Table 11.14. Energy and Demand Losses Plan reliability level Energy losses Demand losses (megawatt-hours) (kilowatts) Low Low and and me- Me- me- Me- dium dium dium dium Year A B High A B High 1976 1,480 1,480 1,480 560 560 560 1980 3,380 2,740 1,120 1,380 1,110 420 1984 3,870 3,130 1,950 1,460 1,180 740 1988 3,300 2,670 1,940 1,240 1,010 730 1992 4,680 3,790 3,460 1,760 1,430 1,310 1996 6,340 5,130 4,510 2,390 1,940 1,700 Table 11.15. Substation Construction Costs (Cr$ X 103) Adminis- Item Labor Materials tration Total High-reliability New 20 megavolt-amps 2,835 14,165 1,890 18,890 Additional 10 megavolt- amps 700 3,505 470 4,675 Low- and medium-reliability New 20 megavolt-amps 2,325 11,635 1,555 15,515 Additional 20 megavolt- amps 895 4,480 600 5,975 The construction and annual recurrent costs provided by COPEL were reviewed and compared with similar data from other utility companies, and in general they appeared to be reasonable. The basic items of ex- penditure used to estimate the alternative distribution system supply costs are summarized in tables 11.15 to 11.18. Recurrent annual expenses consisted of replacements, operation and maintenance (o&M), and administrative and general (A&G) costs. Re- placements are required for major components that fail and are not LONG-RANGE DISTRIBUTION SYSTEM PLANNING 161 Table 11.16. Line Construction Costs (Cr$ X 103) Cost per kilometer A dminis- Type Labor Materials tration Total New construction 2/0 AWG 55 95 15 165 4/0 AWG 60 110 20 190 336 McM 70 130 20 220 477 McM 85 145 25 255 Reconductoring 2/0 AWG 20 35 10 65 4/0 AWG 30 50 10 90 336 McM 40 75 15 130 477 McM 50 90 15 155 Note' AWG = American wire gauge, McM = thousands of circular mils. Table 11.17. Street Light Costs (Cr$) Type Cost per unit 400 watt sodium vapor (includes pole) 7,195 700 watt mercury vapor (includes pole) 6,320 400 watt mercury vapor (includes pole) 5,620 250 watt mercury vapor (pole not included) 1,575 125 watt mercury vapor (pole not included) 870 covered by routine operation and maintenance. Operation and mainte- nance costs generally are the labor and materials required to keep the system in good working order. Administrative and general costs include the managerial functions, buildings, and so on, associated with the operation and maintenance of the system. The annual costs for each plan consisted of the construction costs for that year plus the annual recurrent costs for the entire system. These costs were determined by system plan for each study year for the sub- stations, primary feeders, and street lights. Items that were common to the different plans, such as the 1976 existing plant, primary laterals, distribution transformers, secondaries, service inlets, and meters, have 162 CASE STUDY Table 11.18. Annual Recurrent Costs Item Substations Lines Replacements (percentage of investment) 0.6 0.20 Operation and maintenance 20 megavolt-amps substation (Cr$/kilovolt-amp) 19.5 - 30 megavolt-amps substation (Cr$/kilovolt-amp) 13.8 - 40 megavolt-amps substation (Cr$/kilovolt-amp) 13.8 - Lines (Cr$/kilometer) - 1,850 Administration and general (percent of o&M) 32.0 34.0 Table 11.19. Cumulative Annual Costs (Cr$ X 103) Plan reliability level Year Low Medium A Medium B High 1976 0 0 0 0 1980 4,390 4,640 4,640 28,670 1984 42,330 43,040 43,770 55,760 1988 85,080 87,100 87,970 109,100 1992 135,170 138,280 139,550 170,450 1996 161,090 165,570 167,030 219,400 Percentage of high- reliability plan costs 73.4 75.5 76.1 100 been excluded, because they would be effectively netted out in the analysis of comparative costs. The annual costs for the plans are summarized in table 11.19. (See appendix C for details.) Chapter 12 Outage Cost Measurement The empirical investigation of outage costs borne by Cascavel electricity consumers is described in this chapter. The theoretical concepts and models developed in chapters 5 to 7 were used as the bases for field surveys of different kinds of electricity consumers to estimate their outage costs. Residential and industrial consumer categories incurred the greatest outage costs, whereas these costs for the other types of con- sumers were relatively small. Residential Consumers A random sample of twenty-seven residential customers was selected from the 1976 list of approximately 9,000 electricity-using households in Cascavel. These consumers answered an in-depth survey designed to determine their opinion of the quality and value of electrical services, electricity consumption, income, leisure-time habit patterns, and the value they placed on foregone leisure during an outage. The complete questionnaire is given in appendix F. Unfortunately, the sample size was limited by the time and manpower resources available to carry out the survey. In view of the difficulty of obtaining meaningful answers to questions on outage costs involving hypothetical willingness to pay, considerable time had to be devoted to explaining the problem to consumers and putting them at ease. Care 163 164 CASE STUDY had to be taken also to avoid giving the impression that the interviewers wanted to increase or decrease their electric supply reliability, increase or decrease their electricity bill, obtain income information for tax pur- poses, and so on. At least two adult members of each home were required to be present to obtain replies that were representative of the household. Consequently, a team of three persons (including a translator) took one week to complete the twenty-seven interviews. All households in the sample indicated that electricity was an essen- tial service in their daily lives; in general, the poorer consumers felt that they were getting good value for money, whereas some of the higher income households thought that the price of electricity services was too great. A direct estimate of outage costs was obtained by asking con- sumers how much extra they would be willing to pay to avoid outages of different durations at various times during the day (questions 4 and 5). Customers indicated no willingness to pay extra to avoid daytime outages. The direct amounts that consumers were willing to pay to avoid evening outages was found to be linearly proportional to outage dura- tion, on average, over the range of three to eighty minutes, and the esti- mate of outage cost is based on values in this range. For outages of less than a few minutes many people indicated that they would sit out the inconvenience rather than pay, and for outages over one-and-a-half hours the outage cost for each time unit tended to also fall off quite rapidly, as households were unwilling to pay large sums of money: that is, the impact on income became important. Indirect estimates of outage costs were obtained by determining what additional amounts each household considered reasonable for payment to the utility com- pany if the current incidence of outages was halved and as a com- pensatory refund on their electricity bill if the existing outage rate was doubled (questions 3, 9, and 12).1 The evening time outage cost esti- mates given in table 12.1 are average values of the direct and the two indirect estimates for each household. Although related, questions 4, 9, and 12 were not asked consecutively. This reduced the possibility of consumers giving answers to a later question by merely extrapolating from one of the earlier questions. In fact, good agreement was obtained between the various estimates of outage costs for each household, and 1. The terms direct and indirect used in this chapter refer to the nature of the questions asked during the survey to estimate outage costs They have no relation to the direct and indirect outage costs discussed in chapter 4, Estimation of Outage Costs. OUTAGE COST MEASUREMENT 165 this was taken as an added sign of reliability of the estimates. As ex- pected, however, the indirect estimate of outage costs from question 9 generally tended to be lower than the estimate from question 12. These two estimates most often straddled the value of the direct estimate of outage costs. The daily leisure period during which electricity was considered essen- tial had a fairly uniform duration of about one-and-a-half hours (stand- ard error = twelve minutes) and occurred somewhere within the broader time interval of 1930 to 2230 hours. Approximately 60 percent of the latter interval was devoted to television watching, 25 percent to dining, and the remainder to other activities such as reading and conversing. The differences between households were minor; for example, the stand- ard error for the television watching period was only about 10 percent of the mean. Only one of the households in the sample did not possess a television set; however, in this case about 50 percent of their leisure time was spent listening to the radio, and special television programs such as football games were watched on the neighbor's set. Thus, these results confirmed the view expressed by local municipal authorities, that practically all electricity-using homes owned a television set. The mean household size was 5.1 persons, with a standard error of 1.4 persons, and the average time at which families went to sleep was about 2300 hours, with a standard error of forty-five minutes. After having verified the importance of the loss of leisure incurred by evening power supply interruptions, the survey data were used to test the following null hypothesis developed theoretically in chapter 5, Resi- dential Outage Costs (equation 5.12). Ho Outage cost per hour of electricity-dependent leisure = net income earning rate2 H: Ho untrue. The basic household data on outage costs are given in table 12.1, and are plotted against the net income earning rate in figure 12.1. The best- fit-ordinary-least-square ((OLSQ) regression line and the 45-degree line 2 Net income earning rate = gross earning rate minus income tax, estimated from known tax rates Total household income was, in most cases, the earnings of a single wage earner. 166 CASE STUDY Table 12.1. Residential Consumer Survey Results Observation Net income earning rate Outage cost number (Cr$ per hour)a (Cr$ per hour) 1 7.4 6 2 7.4 7 3 7.4 13 4 10.5 12 5 11.1 15 6 14.2 10 7 15.4 20 8 18.5 25 9 18.5 35 10 19.7 20 11 21.5 15 12 21.5 25 13 24.6 15 14 24.6 40 15 27.7 20 16 30.8 35 17 40.3 30 18 40.3 30 19 45.5 50 20 48.0 60 21 55.1 45 22 64.6 55 23 64.6 60 24 73.9 85 25 99.1 60 26 116.3 133 27 166.2 150 a US$1 = Cr$12.35 (end 1976). indicated by the hypothesis to be tested are shown by the broken and solid lines, respectively. The numerical results of the regression are pre- sented in table 12.2. The basic unrestricted fitted equation is: (12.1) OCR = 1 + 02 Y + U where OCR = (n X 1) vector of outage costs per hour; 01, #2 = coeffi- cients to be estimated; Y = (n X 1) vector of net income earning OUTAGE COST MEASUREMENT 167 Figure 12.1. Relation between Outage Cost and Net Income Earning Rate for Residential Customers 160 - OA 120 -Theory (constrained) 0- 0. 0/ / Fitted (unconstrained) 80 - 8 0 0 0 to 0 0 40 -O o 0 0 0 0 00 0 o I I I 1I 0 40 80 120 160 Net income earning rate (cruzeiros per hour) rates per hour; U = (n X 1) vector of disturbances; and n = 27 = number of observations. The usual assumptions regarding the OLSQ model are considered valid.3 Since the null hypothesis to be tested is that j3 = 0 and 02 = 1, this yields the restricted model: (12.2) OCR = Y + U. A Chow test for homogeneous linear restrictions on the coefficients, was performed to ascertain whether the unrestricted equation (12.1) fitted the observed values significantly better in terms of the sum of 3. See J. Johnston, Econometric Methods (New York: McGraw-Hill, 1972), chap. 5, pp 121-75. 168 CASE STUDY Table 12.2. Analysis of Regression Results Sum of Estimated Cor- squares Degrees coefficientsa rected of re- of Equation 1 /2 R2 siduals freedom E. 1 (unrestricted) 3.355 0.896 0.901 3,228.2 25 (15.12) E. 2 (restricted) 0 1 - 3,650.2 27 a. t-statistics are given in parentheses under the coefficient value. squares of the residuals, than the restricted equation (12.2) derived from the theoretical model.4 From the results of table 12.2, F = 1.634. Therefore, since F252 (0.20) = 1.72, the null hypothesis, Ho:#, = 0 and 02 = 1, is accepted at the 20 percent level: that is, the restricted equation is accepted as the correct one.5 The slope (p2) of the fitted equation (12.1) is less than unity. A pos- sible explanation for this result is that the ratio of nonwage to wage income tends to rise as the income level increases. This nonwage in- come (for example, property or investment income) may not enter into the consumer's labor-leisure decision. Therefore, since net total income (irrespective of source) is plotted along the x-axis of figure 12.1 rather than net wage income, this would tend to reduce the slope of the fitted line, especially for the higher income levels. Unfortunately, it was very difficult to obtain further information about the breakdown of income by source from the respondents. Saturation effects could also occur at high income levels, which would tend to impose a ceiling on the willingness to pay. Similarly, at the low end of the income scale, there could be a minimum level of outage costs (greater than zero), although 4. See Gregory C. Chow, "Tests of Equality Between Subsets of Coefficients in Two Linear Regressions," Econometrica, vol. 28 (July 1960), pp. 591-605; and Franklin M Fisher, "Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note," Econometrica, vol. 38 (March 1970), pp. 361-66. 5. This statistic is distributed as F with 2 and 25 degrees of freedom: F _ (3650.2 - 3228.2) 3228.2 - 1.634. 2 / 25 Acceptance at the 20 percent level implies acceptance at all lower levels: that is, 10 percent, 5 percent, 1 percent, and so on, for a right tail test. OUTAGE COST MEASUREMENT 169 it is doubtful whether such poor households would have electricity serv- ice. Both of the above effects would tend to reduce the slope 42. The effect of the other neglected terms in the equation from chapter 5 would be to increase slightly the slope of the solid line. The results of the Cascavel residential electricity consumer survey confirm that the chief outage cost imposed on this category of users is the loss of leisure during the evening hours. This occurs approximately during a one-and-a-half-hour period when electricity is considered essen- tial. Furthermore, it may be concluded that during this critical period, the mean income earning rate for a household is an acceptable measure of the monetary value of marginal leisure lost resulting from outages. The willingness of residential consumers to pay the equivalent of their net income earning rate to avoid evening-time outages is not surprising, given the absolute amounts of money involved. For example, on this basis, in 1976 a typical electricity-using household in Cascavel with an annual income of Cr$60,000 (US$4,860) (Cr$28.5 a working hour) would have to pay only Cr$85.5 (US$6.92) more to halve the incidence of outages from six to three hours a year. This represents approximately 9 percent of their annual electricity bill of Cr$920. The total residential outage costs were estimated from survey results. The number of residential consumers, by income category, in each geo- graphic cell is known from the load forecast data discussed in chapter 10, whereas the frequency and duration of outages suffered by them during different periods was computed in chapter 11. The aggregate outage costs imposed on such a group over a given time interval is equal to the number of households, times the mean income earning rate for each, times the product of the frequency and the duration of outages expected to occur during the critical evening hours when electricity is considered essential. If income distributional goals are to be considered, these residential outage costs may be multiplied by appropriate social weights, as described in chapters 9 and 13. Industrial Consumers A survey of twenty-two industrial firms in Cascavel was conducted in 1976 to determine the effect of outages on these firms and to collect other data to estimate the resulting outage costs. (See questionnaire, appendix F.) Some time was spent explaining to the officials the basic purpose of the research and why their particular firm had been chosen. 170 CASE STUDY Questions focused on the market value of the firm's yearly output, its yearly value added, its normal hours of operation, and overtime pay rates as a multiple of normal pay rates. Also, an attempt was made to learn about the company's expansion plans and potential for growth over the next twenty years. Finally, the officials were questioned con- cerning the effects of outages. Would outages disrupt production? Would they result in spoiled products or factors? Could production restart im- mediately after the supply of electricity was restored? In addition, they were asked if any actions had been taken to reduce outage costs, such as purchasing alternative sources of energy or adopting production tech- niques that would make them less susceptible to outage-induced work disruptions. On the basis of the survey information, outage cost functions were estimated for nine types of industries, each one consisting of a group of related but separate firms. These functions relate outage costs as defined in chapter 4, Estimation of Outage Costs, to outage duration.6 More specifically, an outage cost function (OCF) was estimated for each industry type: OCF = a + b-d where OCF = outage cost measured as a fraction of annual value add- ed; d = outage duration in hours; and a and b = coefficients to be estimated. For some industrial groups, step functions were estimated, that is, if d < d*, then OCF, = a, + b,d, and if d t d*, then OCF, = a, + b2d. This was usually the case when large spoilage costs were incurred, be- cause of an outage of duration d* or longer. For some industry types, the outage cost function varied during different periods. For example, only a few of the firms in the group operated normally at night, and thus, the OCF during the night would be different than that estimated for daytime periods. Consider a soy oil producer belonging to the vegetable oils industry group, who could not produce during outages. The restart time for the plant varied between twenty minutes-following an outage that lasted only five minutes-and five hours, after an outage of five or more hours. In addition, this firm incurred spoiled product costs, equal to approxi- 6. Although attempts were made to estimate both direct and indirect outage costs, the latter were found to be negligible. OUTAGE COST MEASUREMENT 171 mately Cr$30,000, if the outage exceeded one-half hour. Therefore, during the outage and restart periods, spoiled product costs as well as idle factor costs were incurred for outages of sufficiently long duration. Next, a-set of observations was determined to relate outage durations and costs. The oil-producing firm planned to operate twenty-four hours a day, or 8,760 hours a year. Thus, one hour of average production ac- counted for about 0.00011 of annual value added. Consider an outage of one hour that involves a restart time of one hour. Idle factor and restart costs for such an outage amounted to 0.00022 of annual value added. However, spoiled product costs must be considered also. Since spoiled costs equaled Cr$30,000 and the firm's annual value added was approximately Cr$112,200 X 103, these costs amounted to about 0.00027 of annual value added. Therefore, total outage costs for an outage of one hour duration was estimated as 0.00049 of annual value added. Following the same procedure for outages of different durations, a set of observations relating outage cost to duration were determined for the soy oil industry. The outage costs were weighted by the share of soy oil in the value added for the vegetable oils industry group. Next, all the other industries belonging to the same group, such as soy storage firms, were treated the same way. Finally, the outage costs of all the industries in the group corresponding to a given outage duration were added together to obtain a set of observations relating outage cost to duration for the whole vegetable oils group. The OCF was fitted to these data points. Outage cost functions were estimated for various periods: that is, day, evening, or twenty-four hours, and for nine industrial groups. The results are summarized in table 12.3. Six of these functions are linear and therefore indicate that for these sectors outage costs increase with outage duration in a fairly smooth, continuous manner. For four of these industry types-mechanical and metallurgy, nonmetallic minerals, wood, and water treatment-outage costs were incurred only during the day period: 0801 to 1800 hours. For the telephone group, the same outage costs were incurred at any time of the day or night. For the food and beverages group, outage costs were linearly related to outage dura- tion only during the evening period from 1801 to 2400 hours. Outage cost functions were piecewise-linear at all times for the vegetable oils group and only during the day for the food and beverage group. These functions reflected the fact that large spoilage costs occurred when the length of the outage exceeded a certain critical duration. 172 CASE STUDY Table 12.3. Industrial Outage Cost Functions OC Estimated coefficientsa Num- function ber Industry typeb (x 10-4)a (X 10-4)b Remarkso A.1, Mechanical linear 0.0013 3.9 D B.3 and met- allurgy A.2 Nonmetallic linear 0.077 3.5 D minerals A.3 Wood linear 0.94 3.9 D A.4 Vegetable piece- 0.037 2.1 d < 0.5 hours, A oils wise- linear 3.6 1.9 d t 0.5 hours, A A.5 Food and piece- 1.22 2.30 d < 0.5 hours, D beverages wise- linear 7.07 2.02 d t 0.5 hours, D linear 0.66 0.72 N A.6 Other log 7.2 2.9 d 0.01 hours, D B.2 Telephone linear 0.002 1.1 A B.3 Water linear -0.27 1.1 d 2hours,D treatment a R > 0 95 for all estimations. b. Linear and log refer to functions of the type C/Q = (a + b - d) and C/Q = (A + b - log,ad), respectively, where C = outage cost, Q = annual value added, and d = outage duration (hours). c. D = daytime operation; N = night-time operation; A = 24-hour operation. The outage cost function estimate for an industrial group was used with estimates of expected outage frequencies and durations to determine estimates of total costs resulting from outages affecting that sector during a given period of the day in a specific year. This was done by following a four-step procedure. First, the expected duration of outages, in hours, was substituted into the outage cost function. The result was an estimate of the average cost of an outage, as a percentage of annual value added during this period.7 Second, this estimate was multiplied by the annual 7. As discussed at the end of chapter 2, Introduction to Reliability, some errors are caused by neglecting the effect of the probable spread of outage durations around their mean values on the nonlinear outage cost functions. These inaccuracies would be small, however, compared with the errors arising from uncertainty in the estimates of the outage cost functions themselves, the mean values of outage frequency and duration, and so on. OUTAGE COST MEASUREMENT 173 value added for the industry type to determine the average cost of an outage for the group. Third, this group cost was multiplied by the ex- pected average frequency of outages for that year to estimate the total annual cost of outages for the group. Fourth, this estimate was adjusted to allow for the fact that some of the firms in the group may not have operated every day of the week during the given period: that is, the estimate of total pecuniary costs of outages was multiplied by a factor equal to the fraction of total hours in this period over the year during which the various firms in the industry type normally operated. Working through another example will help to clarify the procedure. Consider the metals sector. The outage cost function for this sector is: OCF = 0.00000013 + 0.00039 D. In 1976 the average duration of outages for the low-reliability system from 0800 to 1800 hours was 0.2 hours. Thus, the average cost of an outage that affected the metals group during this period in 1976, meas- ured as a fraction of annual sectoral value added in that group of in- dustries, is given by: 0.00007813 = 0.00000013 + 0.00039 X (0.2). Value added in the metals group in 1976 was Cr$4.5 X 106, and there- fore, the average cost of an outage was: Cr$351.6 = Crs(4.5 X 106) X 0.00007813. Multiplying this average cost times the average frequency of outages during this period, 33.8, provided an estimate of the total outage costs for the metals group between 0801 and 1800 hours during 1976: Cr$11,884 = Cr$351.6 X 33.8. The estimates of outage costs determined in this way, however, had to be adjusted to allow for the fact that most firms did not operate every day of the week between 0801 and 1800 hours. Typically, firms worked only half a day on Saturday and none on Sundays; also, holidays re- duced annual working hours. To account for this, the outage cost esti- mates were adjusted by multiplying by a factor equaling the fraction of hours in this period during the year when this particular industry type normally planned to operate. In the case of the metals group, this factor approximately equaled 0.62. Thus, total outage costs in 1976 were: 174 CASE STUDY Cr$7,300 = Cr$11,884 X 0.62. After summing these costs over the three periods and all the different industry groups, estimates were obtained for the costs of outages affect- ing total industrial production in a given year. Other Consumers The discussion in this section is presented in the context of the gen- eral considerations described in chapter 7, Other Outage Costs. The outage costs of commercial consumers, including government offices, were generally found to be minimal, because, almost universally, work could continue by daylight. These customers were not very dependent on electricity-using equipment, such as copying machines, electric type- writers, calculators and cash registers, air conditioners, elevators, and so on. Furthermore there appeared to be a considerable degree of sub- stitutability between electricity-using and nonelectricity-using commer- cial activities during outages. There was also sufficient slack during normal working hours so that jobs delayed by outages could be made up without overtime. Supermarkets, hotels, and restaurants reported minor amounts of food spoilage, but these were unlikely to be significant, except in extremely rare outages lasting up to five hours. It was more convenient to analyze the outage costs of public services, such as telephone and water and sewage treatment, within the framework used for industrial consumers. For public illumination, a minimum esti- mate of outage costs was determined as the net supply cost that the community would have incurred for public illumination during the out- age period. On this basis, the dominant component of the net hourly outage cost in a given geographic cell and year was equal to the value of the stock of capital equipment (estimated in Cr$ to be about 3.5 times the annual kilowatt-hours actually required for public illumina- tion), annuitized over a thirty-year lifetime at the appropriate discount rate, and divided by the annual number of hours of operation. That would be, for example, twelve hours a day for 365 days, for a total of 4,380 hours. Payments for electricity were not included in this calcula- tion, since they would not be incurred during outages, whereas routine maintenance expenditures on public illumination were found to be negligible. Two hospitals of 80 and 200 beds were surveyed to estimate the opportunity costs of productive factors that would be made idle, such OUTAGE COST MEASUREMENT 175 as electricity-using equipment and intermediate products, including blood and medicines, that might spoil because of outages. The principal outage costs occurred during the night, from 1900 to 0600 hours ap- proximately, from idle labor and capital, and the average cost was esti- mated at Cr$0.67 or about US05.5 a hospital bed for every hour of outage. There was sufficient slack time during the day, for labor and for machines such as X-ray units, so that delayed activities could be made up during normal working hours. The hospitals did not have private back-up electricity-generating units, because the existing level of supply relia- bility was considered adequate. Vital facilities such as the operating rooms and intensive care units had relatively inexpensive standby bat- teries, however, minimizing the possibility of loss of human life. The outage costs associated with the remaining consumer types were found to be negligible, because they constituted a minor fraction of the total load or because they were relatively insensitive to the effects of outages. For example, the kilowatt-hour consumption of rural con- sumers in the vicinity of Cascavel was about 1 percent of the total in 1976, and their share of demand would be unlikely to exceed 3 percent of the total even by 1996. Day-school activities were hardly affected by outages. Chapter 13 Distribution System Optimization and Conclusions This chapter focuses on the analysis and comparison of distribution sys- tem costs and customer outage costs, and the optimization of the system expansion plan. Six alternative distribution system plans are analyzed. Basic plans 1 to 3-including two variants of the medium-reliability system, Plans 2A and 2B-correspond to the low-, medium-, and high- reliability systems discussed in chapter 11. Plans 4 to 6 are hybrids, derived from the basic plans. Modified Framework for Cost-Benefit Analysis The Cascavel urban area has experienced dynamic economic and demographic growth over the past two decades, averaging an annual population increase of more than 20 percent during this period. This growth is likely to be sustained at a reduced rate in the future, because of the rich agricultural potential of the land surrounding Cascavel and because of the development close to the city of the major Itaipu hydro- electric site, with a planned capacity of 12,000 megawatts during the next ten years. Furthermore, the state government plans to make the city a regional growth pole. Current conditions, such as a buoyant economy and low unemployment rates, are also likely to continue. 176 DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 177 All costs and benefits were evaluated in efficiency (shadow) prices: that is, ignoring income distributional considerations. Use of shadow prices could be kept to a minimum, however, because economic dis- tortions would not be as severe as in most other developing countries, given the buoyant local economy. The 1976 domestic-priced cruzeiro (Cr$)1 was adopted as the numeraire or unit of account, because, in monetary terms, more than 99 percent of the items to be considered were domestically produced goods and services. Therefore, the shadow pricing was done in a relatively straightforward way. All the domestically produced equipment and materials were valued directly in terms of their domestic market prices, but net of local taxes where applicable.2 An opportunity cost of capital (OCC) of 12 percent was selected as the discount rate, based on the most recent information on Brazil. The shadow wage rate (SWR) applied to labor costs was the same as the market wage rate, given the low unemployment rates in the Cascavel area, and the skilled nature of much of the work involved. This simplified procedure eliminated the need for time-consuming esti- mation of conversion factors for many domestic inputs to convert the values of these items to border prices. (See chapter 9, Shadow Pricing, for details.) Even if the estimates had been made, such an exercise would have had a negligible effect on the final results. Incremental kilowatt losses in the distribution system which contrib- uted to the peak load were considered as additional costs Hydroelectric generating capacity costs were assumed to be US$400 to US$450 a kilo- watt, annuitized over a thirty to thirty-five-year lifetime, at a discount rate corresponding to the occ. Incremental kilowatt-hour system losses were considered costless, because the Parana state system serving Cas- cavel was basically 100 percent hydroelectric and is likely to remain so into the future. Finally, to illustrate the use of social weights, the optimization pro- cedure was repeated using social (shadow) prices. The base case, which used efficiency prices without social weighting, is presented in the next two sections, followed by the results when social weights were applied. The latter had negligible effects on the base case results. 1. US$1 = Cr$ 12 35 (end 1976). 2 The prices of the few imported items, less than 1 percent of the total costs, were known in cruzeiros converted at the official exchange rate. These nominal prices were multiplied by a factor of 1 25, representing the ratio of the shadow exchange rate (SER) to the official exchange rate (OER). Table 13.1. Global Characteristics of the Four Basic Alternative Distribution System Plans Outage costs! kilowatt-hour Outage Outage Supply Total costs, lost, OCK Reliability rate, OR costs, OC costs, SC OC + SC (Cr$/kilowatt- System plan index ((R) (percentage)a (106 Cr$)b (106 Cr$) (10 Cr$) hour) 0 1 (Low-reliability) 0.9935 0.650 150.1 57.5 207.6 14.0 2A (Medium-reliability) 0.9969 0.314 77.2 58.6 135.8 14.9 2B (Medium-reliability) 0.9981 0.191 49.5 57.8 107.3 15.7 3 (High-reliability) 0.9988 0.116 28.4 76.9 105.3 14.8 Note. Present discounted values of quantities from 1976 to 2006 as defined in the text; discount rate = 12 percent. a. OR = 100 - (1-R) = 100 - OE/TE. b. US$1 = Cr$12.35 (end 1976). DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 179 General Characteristics of Outage and Supply Costs In this section, the relations between the global or city-wide relia- bility levels, outage costs, and system costs are discussed. These aggre- gate values are derived by summing the underlying disaggregate results based on the frequencies and durations of outages at the geographic cell level. (See chapters 11, 12, and appendix D.) The chief global char- acteristics of the basic alternative system plans are summarized in table 13.1.3 As the overall reliability level (R) increased, outage costs (OC) declined steadily; supply costs (SC) remained fairly stable until there was a sharp rise in SC between the medium type B and the high-reliability plans: that is, between Plans 2B and 3. Outage costs for each kilowatt- hour lost (OCK) or not consumed because of outages, which is a measure of consumer sensitivity to power supply interruptions, were highest for system Plan 2B. The scalar global reliability index 61 was always greater than 0.99, and therefore its variations were not readily apparent. Therefore it was more convenient to use a new measure of reliability, the outage rate, OR, which decreases as the reliability level in- creases and may be defined as: OR = 100 * (1 - 61) = 100 * (OE/TE). As discussed in the previous chapter, the four types of electricity use for which outage costs were significant include residential, industrial, public lighting, and hospitals. Table 13.2 indicates that the first two categories were the dominant ones in relation to total energy (TE) use and outage costs. For the range of reliability levels considered in this study, the main industrial category appeared to be the one most affected by outages, in relation to OCK, followed by residential, service industrial, hospitals, and public illumination. Outage costs for each kilowatt-hour lost for the main industrial category tended to increase as reliability increased and as the average outage duration decreased, but OCK did not vary much with system reliability for the other categories of users. A more detailed breakdown of outage costs for the two dominant categories, residential and main industrial, is presented in table 13.3. As expected, OC increased as the outage rate (OR) increased for all consumer types. For any given class of residential consumer, the outage 3. Unless otherwise stated, all quantities discussed in this chapter are given in 1976 present value terms, discounted at 12 percent, over the thirty-year horizon, 1976 to 2006 Details of the outage and supply cost calculations and typical com- puter printouts of outage cost results, by cell, by year, and by consumer type may be found in appendix D Table 13.2. Energy Use and Outage Costs, by Major Consumer Category Total energy, TE Outage costs/kilowatt-hour lost, OCK Consumer (gigawatt- Outage costs, OC (106 Cr$)a (Cr$/ kilowatt-hour) category hours) Plan I Plan 2A Plan 2B Plan 3 Plan 1 Plan 2A Plan 2B Plan 3 00 o Residential 484.1 68.2 34.8 20.5 9.9 17.9 18.2 18.6 17.5 Main industrial 371.8 77.4 40.6 27.8 17.8 31.4 33.5 30.0 26.5 Service industrial 224.7 4.1 1.6 1.0 0.6 3.4 3.2 3.8 3.6 Public lighting 60.4 0.2 0.1 - - 0.4 0.4 0.4 0.4 Hospitals 11.7 0.3 0.1 - - 5.9 5.9 5.9 5.9 Note. Present discounted values of quantities from 1976 to 2006 as defined in the text; discount rate = 12 percent. a. US$1 = Cr$12 35 (end 1976). Table 13.3. Disaggregate Energy Use and Outage Costs of Residential and Main Industrial Consumers Total energy, TE 'Outage costs, OC Outage costs/kilowatt-hour Outage rate, OR (giga- (106 Cr$)a lost, OCK (Cr$/kilowatt-hour) (percentage) Consumer watt- Plan Plan Plan category hours) 1 2A 2B 3 1 2A 2B 3 1 2A 2B 3 ResidentiaP Lower 19.9 2.85 1.36 0.83 0.38 16.5 16.8 17.2 16.2 0.870 0.406 0.243 0.117 Lower-middle 152.3 20.11 10.02 5.98 2.87 16.6 16.8 17 3 16.2 0.798 0.391 0.228 0.117 Upper-middle 198.9 27.47 14.00 8.27 4.01 17.6 17.9 18.3 17.2 0.783 0.394 0.227 0.117 Upper 113.1 17.72 9.43 5.46 2.65 20.6 20.8 21.4 200 0.760 0.401 0.226 0.117 Main industrialb A.1 9.7 0.61 0.26 0.14 0.10 24.9 24.9 24.9 25.0 0.269 0.106 0056 0.041 A.2 30.5 1.11 0.48 0.27 0.19 13.6 12.8 11.9 11.8 0.251 0.124 0.074 0.054 A.3 63.9 9.45 5.29 3.92 2.84 36.7 48.0 73.1 75.5 0.403 0.173 0.084 0.059 A.4 146.2 44.13 22.18 15.54 8.73 31.8 35.2 31.9 25.2 0.948 0.431 0.334 0.237 A.5 88.1 19.40 10.07 5.92 4.40 35.0 32.0 21.9 22 1 0.630 0.357 0.306 0.226 A.6 33.4 26.70 2.28 2.03 1.52 16.6 21.2 22.8 22.8 0.482 0.322 0.267 0.200 Note: Present discounted values of quantities from 1976 to 2006 as defined in the text; discount rate = 12 percent. a. U S.$1 = Cr$12 35 (end 1976). b. Residential and main industnal subcategories as described in chapter 10. 182 CASE STUDY cost for each kilowatt-hour lost was relatively unaffected by the relia- bility level but, for any given system plan, residential OCK rose a little with income level. These results were predictable, given that OCK = OC/OE, and both outage costs and outage energy are linearly propor- tional to outage duration for a given income class. For a given relia- bility level, however, OC is linearly proportional to net income, but OE increases less rapidly.4 The values of industrial OCK reflected the nature of the respective outage cost functions given in table 12.3. For industry types A.1 and A.2, the intercept term was small so that the linear outage function (OCF) practically passed through the origin. Therefore, since both OC and OE are linearly proportional to outage duration, their ratio OCK was constant and unaffected by the reliability level. Furthermore, these values of OCK were also quite similar to the corresponding figures for value added per kilowatt-hour. (See table 10.2 in chapter 10.) For industry types A.3 and A.6, the respective OC functions had large intercepts and a logarithmic form, leading to increasing values of OCK as OR and the mean outage duration decreased. The discontinuities in the OC functions for A.4 and A.5, resulting from the large spoilage costs, for outages of duration d > 0.5 hours, tended to dictate the behavior of OCK. In summary, residential consumers suffer outage costs of about Cr$16 to 21 (U.S.$1.30 to 1.70) for each kilowatt-hour lost, over the range of reliability levels considered. Industrial group A.3 (wood) was the most sensitive (approximate range Cr$35 to 75 [U.S $2.80 to 6.10] for each kilowatt-hour lost), especially to outages of shorter duration, whereas OCK was lower for the other groups (Cr$12 to 35 [US$1 to 2.80] for each kilowatt-hour lost). The above industrial outage cost results are consistent with the results of previous studies, given the wide variation in methodologies, countries of application, and timing of the different studies. The residential outage costs presented here, however, are significantly higher because, except in one case (Sweden, 1969), 4. Household OC are the costs incurred because of outages during the critical leisure period, since outages at other times are assumed to have negligible costs. OE, however, is the quantity of kilowatt-hours lost due to outages throughout the twenty-four hours of the day. Therefore their ratio, OCK, is smaller, say, by a factor g, than the outage cost for each kilowatt-hour lost during the critical leisure hours alone. Assuming that 38 to 40 percent of the daily household electricity consumption occurs during the one-and-a-half-hour leisure period, and using the existing distribution of outages at different times of the day, g is approximately 2.3. DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 183 previous studies ignored the cost of foregone leisure (See appendix E for details.) Within the four income classes of the residential consumer category and for a given system plan, OR was quite stable. There were significant differences among values of OR for the different industrial sectors, how- ever, because of different working hours and wide variations in restart times. Hybrid Systems and Optimum Reliability Levels The results of the distribution system optimization procedure described in chapter 3 are summarized in table 13.4 and figure 13.1 on a city-wide basis. Focusing attention on the efficiency priced results in progressing from Plan 1 to Plan 3, there was a steady improvement in overall re- liability, a corresponding decrease in global outage costs (OC), and a sharp increase in the distribution system supply costs (SC) between Plans 2B and 3.5 As a first approximation, the minimum value of the total economic cost to society, that is, the combined outage and distribu- tion supply costs (OC + SC), would most probably occur close to Plans 2B and 3. In the next stage of optimization, the procedure was refined by exam- ining outage and supply costs for specific areas of the city and by using this information as feedback to revise and improve the system design. Typical computer printouts of total outage costs and outage cost for each kilowatt-hour lost and for each geographic cell are shown in fig- ures 13.2 and 13.3. This information and the outage cost results dis- aggregated by consumer category (tables 13.2 and 13.3) indicated that the areas of high population density in the city center and the main industrial area (ZI) suffered the highest outage costs. Therefore several hybrid distribution system designs were considered by varying the levels of reliability for different neighborhoods. 5. Plan 2B is more reliable as well as slightly cheaper than Plan 2A This is because the strengthened feeder configuration of Plan 2B reduces losses more than enough to compensate for the increase in investment costs relative to Plan 2A. The results for both plans are retained, however, to show that over this range of reliability, SC is essentially constant. Table 13.4. Data for Optimization of the Distribution System Efficiency prices Social prices Outage Supply Outage Total Outage Total rate, OR costs, SC costs, OC costs, TC costs, OC costs, TC System plan (percentage)a (106 Cr$)b (106 Cr$) (106 Cr$) (106 Cr$) (106 Cr$) 1 (Low-reliability) 0.650 57.5 150.1 207.6 145.3 202.8 2A (Medium-reliability) 0.314 58.6 77.2 135.8 74.2 132.7 2B (Medium-reliability) 0.191 57.8 49.5 107.3 47.9 105.7 3 (High-reliability) 0.116 76.9 28.4 105.3 27.6 104.5 4 (Hybrid A) 0.184 59.9 44.5 104.4 42.9 102.8 5 (Hybrid B) 0.166 65.2 44.3 109.5 44.1 109.3 6 (Hybrid C) 0.159 67.4 39.3 106.7 39.1 106.5 Note: Present discounted values of quantities from 1976 to 2006 as defined in the text; discount rate = 12 percent. a. OR = 100 . (1-(R) = 100 - OE/TE. b. US$1 = Cr$12.35 (end 1976). DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 185 Figure 13.1. Optimization of the Outage System: Costs Versus Outage Rate 200- 8 150- 5; OC -100- 50- O 0.2 04 0.6 Outage rate (percentage) Note: SC = distribution system supply costs; OC global outage costs; and TC = total costs. The plotted data points and solid lines refer to efficiency priced costs; the broken lines indicate the costs in terms of social pnces. In hybrid Plan 4, the reliability of service to the main industrial zone (ZI of figure 10.1) was maintained at the same level as in the high- reliability Plan 3. The distribution system for all other areas was de- signed according to the medium-reliability Plan 2B. Plans 1 and 2A were ruled out as viable alternatives for any specific area, because the potential saving in reducing SC by changing from a higher reliability design to either of these two plans was generally much smaller than the corresponding increase in OC. In Plan 5 the city center areas, ZC, ZCR, and ZR1 were provided with a high-reliability distribution system; the rest of the city received medium-reliability type B service. Finally, in 186 CASE STUDY Figure 13.2. Medium-Reliability Plan B: Present Discounted Value of Outage Costs, by Cell (thousands of Cr $) 0 N 6 5 29 11 22 M 70 60 48 9 L 4 64 72 72 71 45 52 74 K 7 72 131 120 140 210 61 82 42 92 159 183 171 231 124 101 21 65 138 488 545 424 316 581 H 31 57 57 136 391 603 846 457 314 G 7 45 64 71 142 124 278 346 456 926 F 1 21 5 14 50 166 157 132 158 293 593 E 11 22 22 31 106 81 117 350 106 261 205 D 16 22 32 0 105 73 314 109 247 332 240 c 19 56 53 438 74 72 81 96 136 30 49 45 46 60 623 273 A . J5 6 13 50 41 853 124 163 1,000 1 2 3 4 5 6 7 8 9 10 11 Note: Discount rate = 12 percent. DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 187 87 0 11 8 1 00ý4335 25 14 145 76 67 ( 128 154 198 109 7 12 25 31 16 5 152 125 190 99 241 57 10 30 16 2 915 687 306 245 455 85 48 21 2 3 542 342 296 52 76 108 95 8 22 1 390 39 13 6 25 47 220 77'\\ 7 58 29 74 80 120 348 0 337 1 15 30 2 ý O 4 477 57 52 47 000 22 58 1,384 1,178 987 101 81 1,372 1,402 977 997 1,060 1,001 77 56 32 19 35 33 2 12 13 14 15 16 17 18 19 20 21 22 188 CASE STUDY Figure 13.3. Medium-Reliability Plan B: Outage Cost per Kilowatt-hour Lost, by Cell 0 N /i 14.5 9 3.96 13.89 1397 m 15.80 13.56 158 13.54 /36 12.92 1329 11.91 12 83 15 11 12 81 1276 13.03 13.09 K 13.13 12.83 8.98 11.56 13.33 17.64 11.01 9.95 10.97 13 69 10.10 14.39 12.38 13.03 9.96 6.42 12.11 12.07 10 17 15.88 17.20 15.64 14.45 14.96 H 13.23 12.95 11.51 9.33 6.53 10.33 12.50 8.74 6.57 G 10.43 12.19 11.61 11.94 10.09 9.82 15.09 15.63 14.61 18.59 F 11.63 10.76 9.57 902 868 10.73 14.92 1409 14 52 14.81 16.06 E 11.20 10.69 10.01 8 58 8.14 10.16 10.55 18 09 8.70 12 84 9.07 D 11.23 10.76 7.42 09 14.54 1276 20.27 14.71 19 38 14.18 8.90 C 10.73 5 30 6.28 12.79 12.68 10.06 12.50 15_ 6.51 B 5. 4 35 4.33 4.39. . 6.08 5.2 .4 19322 11.06 A (.37 , : 33 4.42 4.38 4.32 540 25.12 15.46 1342 25.15 1 2 3 4 5 6 7 8 9 10 11 DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 189 31.29 3.56 10.59 11.30 11.06 9.83 12.80 12.8 .53 9. -144,- - 9.98 10.82 17.77 14.13 11. 7.18 10 60 11.13 11.21 11.24 13.15 6.76 10.05 14.01 21.3 1.12 7.60 11.09 11.28 11.24 18.70 13.06 8.76 13.33 19.22 13.0311.19 10.55 11.33 12.19 8.92 7.42 13.93 13.79 9.70 7.96 8.90 1 6.12 10 59 12.3 11.59 9.06 8.99 9.08 9.87 7.78 9.93 10.10 10.27 13 81 8.82 9.54 11.77 9.21 .91 71 23.59 11.79 7.85 9.79 29.32 18.92 7.77 7.49 1199 6 13.18 612 30.99 31.15 31.93 12 70 12.59 29 71 30.21 29.28 29.28 29.87 29 87 30.41 12.64 9.30 3 "07 -;70 43 10.92 9.75 10.53 9 18 9.84 10.57 12 13 14 15 16 17 18 19 20 21 22 190 CASE STUDY Plan 6 both the city center and the main industrial zone were supplied at high-reliability, whereas all other areas obtained medium-reliability type B service. The results for the hybrid plans, also presented in table 13.4 and figure 13.1, indicated that Plan 4 had the lowest total costs.6 Clearly, further fine-tuning of the optimization procedure is possible by exam- ining different parts of the city in greater detail and by varying the design of the distribution system in these areas. For the purposes of this study, demonstrating the application of the new methodology, how- ever, it was considered sufficient to identify an approximate range of reliability levels 0.125 < OR < 0.16 (see arrows in figure 13.1) within which the optimum distribution system plan should lie. Since the greatest potential savings in OC would be realized by the main industrial con- sumers, the possibilities for improving reliability in the ZI area even beyond the high level of Plan 3 could have been examined by further fine-tuning, as discussed in chapter 2, Long-Range Distribution System Planning. This could be done, for example, by using reclosers, remote controlled switches, more line inspections, underground systems, and so on. The optimum system design corresponding to the minimum of the TC curve probably would have provided very high-reliability service for the ZI consumers, a slightly lower level of reliability (between Plans 2B and 3) for the city center, and reliability of service corresponding to Plan 2B elsewhere in the city. It was interesting to examine the variation of Gt over the twenty-year plan period, as shown in figure 13.4. For a given system plan there was a steady improvement in reliability with time. As loads increased, more substations and feeders had to be provided, reducing the average length of a feeder. Therefore the probability of outages and the annual outage frequency, both of which are proportional to feeder length, also de- creased, leading to increased overall reliability. The new optimum reliability levels could affect the demand forecast and outage costs through the price and reliability expectation feedback loops shown in figure 1.1 of chapter 1. These feedback effects were not investigated, however, because of lack of information on how the orig- inal prices and expected reliability levels should be revised. The results were relatively insensitive to an arbitrary 10 percent change in the demand forecast; Plan 4 remained the best one tested. A range of dis- 6. The plotted data points for hybrid Plans 5 and 6 are off the trend line of Tc for optimally designed systems. DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 191 Figure 13.4. Evolution of Outage Rate over Time 1.2 - -------------- ----1 O0.4 0 --------- ------- 2A ---- - --------2 0 I I I I I 1976 1980 1984 1988 1992 1996 Note: Broken lines indicate the discounted aggregate value of outage rate. count rates from 10 to 14 percent were tried, but these changes also did not have much effect on the results, with the exception of different values of PDV. Finally, the results were hardly affected by variations of (a) the shadow of wage rate, in the range 0.8 to 1.0 times the market wage rate, and (b) the ratio of overtime to normal wage rates, in the range of 1.5 i v/w8 A 1. (See appendix D for details.) Effects of Social Weighting In the earlier discussion, the optimization analysis was concerned exclusively with efficiency prices. This section considers the effect of social pricing on the earlier results. The question is particularly relevant for residential consumers, whose outage costs for each hour of outage differed widely, because of differences in hourly income earning rates ranging from Cr$8.7 to 108 in 1976. The outage costs for each energy unit lost were more stable across the different income classes, varying from about Cr$16 to 21 for each kilowatt-hour lost. 192 CASE STUDY These results on hourly costs of outages, which followed directly from the theoretical model presented in chapter 5, Residential Outage Costs, seem to argue in favor of high-reliability service for high-income neigh- borhoods and low-reliability service in low-income neighborhoods. As a first impression, such an interpretation could be considered inequitable on income distributional grounds. As discussed in the Summary and Conclusions, however, better reliability levels should also imply higher electricity prices. Also, outage costs may be interpreted in the economic sense as a reduction in earnings. Therefore the outage costs of low- income groups could be assigned a higher social weight than the outage costs of high-income groups, based on the economic principle of dimin- ishing marginal utility of income consumption. This type of weighting procedure would help to reduce the effects of income disparities on out- age costs and on the resultant optimal reliability levels in different geo- graphic areas. The outage costs of residential consumers were adjusted directly by dividing the mean level of net earnings in each income class by the average net income of the total urban population. This yields the weight- ing factors 3.679, 1.419, 0.694, and 0.296 for the lower, lower-middle, upper-middle, and upper income groups, respectively. (See appendix B for details.) The effect of this social pricing procedure was to stand- ardize the outage costs during each hour of outage for all income groups at the average net income earning rate-about Cr$32 for every working hour in 1976. In this new situation, however, the outage costs for each unit of energy lost exhibited large differences, varying from Cr$6 to 60 for every kilowatt-hour lost for the high- and low-income groups, re- spectively. These results may be contrasted with the earlier results using efficiency pricing alone, when the outage costs for every hour of outage varied widely according to the income level, whereas the outage costs for each kilowatt-hour lost were practically constant.' It is not clear how outage costs incurred by nonresidential consumers would affect the incomes of various groups in the economy. For exam- ple, owners of industries may absorb losses in reduced profits or may pass them on to the consumer through increased product prices. Allo- cating outage costs that affect public illumination and hospitals by in- come group would be equally difficult. Therefore these types of outage costs were assigned a weight of unity in the subsequent analysis, which 7. See also, Mohan Munasinghe, "Costs Incurred by Residential Electricity Consumers Due to Power Failures," Journal of Consumer Research (March 1980) DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 193 was equivalent to making the neutral assumption that, on the average, the income distributional effect of all such costs would be borne by those whose income is close to the societal average. The same argument applied to the treatment of system supply costs. The results of the social pricing exercise are summarized in table 13.4 and figure 13.1. The major effect was a small overall reduction in residential outage costs and, consequently, total costs. Consumers with above average income had social weights less than unity and suf- fered greater (unweighted) outage costs than those at lower income levels, where the weights were larger than unity. Neither the ranking of the alternative expansion plans by total costs, nor the general con- clusions regarding the optimal range of global reliability levels, however, were altered. Yet, if the model had been fine-tuned at a more detailed level, social weighting would have had an effect on distribution net- work optimization by small areas, especially if specific neighborhoods tended to be dominated by particular income groups. This could be quite helpful in analyzing outage costs in low-income or slum areas, provided the social weights were estimated and applied sensibly. Summary and Conclusions Since it was to be used for distribution network planning, the demand forecast developed in the case study is highly disaggregated: (a) by twenty-four categories of consumers; (b) by 247 geographic cells, each 0.25 square kilometers; and (c) by year, over a twenty-year period. Other variables and parameters of the problem were also estimated at the same level of detail and then were aggregated in various ways: that is, over the different customer types, geographic areas, or time. In par- ticular, estimating the frequency and duration of outages during three different periods of the day-0001 to 0800, 0801 to 1800, and 1801 to 2400 hours-and distinguishing between working and nonworking days emphasized the degree of detail required to determine outage costs accurately. The results of the residential outage cost survey and analysis showed that (a) the chief effect of unexpected outages on electricity-using house- holds was the loss of a critical ninety-minute period of leisure during the evening hours when electricity was considered essential by consumers, whereas domestic activities interrupted during the day could be re- scheduled with relatively little inconvenience; and (b) over this one- 194 CASE STUDY and-a-half-hour period, the monetary value of lost leisure could be measured by the net wage or income earning rate of affected households, as confirmed by their willingness to pay to avoid outages in the short term. Industrial outage costs were estimated on the basis of a detailed study of spoilage, factors of production made idle, and recovery of lost pro- duction during both normal working hours and overtime. The results of the analysis indicated that there were wide variations in the effects of outages on industrial consumers, depending on the type of industry, the duration of the outage, and the time of day during which it oc- curred. This approach would be helpful to rank industries by their sensitivity to outages, for example, for emergency load shedding. The outage costs of other types of electricity users were also esti- mated but found to be relatively small, since their activities were not greatly affected by outages, or their consumption of electricity was a negligibly small fraction of the total load. The distribution network was designed and supply costs were deter- mined by using a computerized simulation approach. Using feedback information from the cost-benefit module on disaggregate outage costs and system costs to improve the design of the distribution grid was the most noteworthy feature of the optimization procedure. The initial alternative system expansion paths each were designed on the basis of a different target reliability criterion that could be applied uniformly over the whole city. The cost-benefit comparison of the re- sulting outage costs and system costs indicated that as global reliability improved, outage costs decreased fairly steadily. Supply costs, however, were practically constant until a critical level of reliability was reached, after which these costs increased sharply. Next, several mixed or hybrid network expansion plans were designed, based on the principle of pro- viding the highest reliability service to areas with the highest outage costs, and so on. This feedback procedure yielded the optimum system expansion plan in which the city center with high population densities and the main industrial zone received high-reliability service, whereas other areas of the city were served at a lower reliability level. The optimum system expansion plan and reliability levels were rela- tively unaffected over a range of variations in the demand forecast, discount rate, and shadow prices considered in the study. In particular, the application of social shadow prices or social weights to reflect in- come distributional consideration did not have much effect on the final results. DISTRIBUTION SYSTEM OPTIMIZATION AND CONCLUSIONS 195 The principal conclusion of the case study is that the long-range ex- pansion plan of a typical urban distribution system may be optimized, with respect to reliability, by using a new economic criterion for system planning, in which the sum of both outage and system costs is minimized. In particular, fine-tuning the procedure permitted the level of distribu- tion reliability to be varied by small areas to yield a more optimal net- work design. The same basic methodology could be used to optimize a total system plan-for example, at the generation and transmission level-provided appropriate reliability indexes were used. If the optimum expansion plan-corresponding to the minimum point of the total costs curve in figure 13.1 and involving about Cr$97.5 mil- lion-had been adopted, it would have resulted in a net saving to Cascavel of about Cr$8 million (US$0.65 million) in present discounted value terms during the next thirty years. This assumes that the conven- tional choice would have been the alternative Plan 3. Of this net sav- ing, the reduction in system costs would have amounted to Cr$15 million, whereas the corresponding outage costs would have increased by Cr$7 million. As noted earlier, however, since only the distribution network was optimized, it is possible that an equivalent reduction in total costs may have been achieved at lower supply cost, by varying the reliability level of the generation and transmission system. If the lower supply costs implied by the optimum expansion plan were distributed uniformly among all consumers, the average electricity price would have decreased by less than Cr$0.01 a kilowatt-hour, which is negligible compared with the 1976 average residential tariff of Cr$0.82 a kilowatt-hour. The approach used here, however, indicates that the optimum reliability level would tend to be higher for areas in which outage costs are greater and, therefore, on the basis of the pricing ob- jectives of economic efficiency and fairness, electricity tariffs should also be higher in such neighborhoods. Allocation of the decreased supply costs only to those consumers receiving lower reliability service outside the ZI area would have resulted in an average price decrease of only Cr$0.011 a kilowatt-hour, which is still very small. The cost allocation would be somewhat different with a marginal cost-based tariff, but in this case, also, the increase in the price level is not likely to be very significant. Because of the wide variation in electricty consumption patterns, power system characteristics, and so on in different countries, the results of the case study cannot be easily extrapolated to a world-wide scale. As a rough estimate, however, the net saving from system opti- 196 CASE STUDY mization, discussed earlier, may be used. This is about 5 percent of the estimated total distribution system investment costs, or approximately 0.05 percent of the total value added in the Cascavel urban area during the study period. If even half these percentage values were taken on a conservative basis, the net potential savings on total electric power sec- tor investments in the capital-scarce developing countries alone would amount to about (constant 1977) US$400 to 500 million a year, during the next decade. Additional work must be done in refining the conceptual framework for measuring outage costs and improving the methods of estimation. In particular, the relation between outage expectation and adaptation of consumer behavior must be investigated in the context of indirect versus direct outage costs and long- versus short-run effects. The effect of various pricing policies on optimum reliability levels, through the de- mand forecast, should also be examined. To test and strengthen the new methodology further, more case studies are required that would cover various aspects of system planning. For example, generation and trans- mission could be studied in several countries where a different mix of consumers, as well as varied socioeconomic and geographical condi- tions would be considered. In this context two specific practical difficul- ties are likely to arise. First, on the supply side, appropriate generation and transmission system reliability indexes, which are meaningful at the consumer level, would have to be computed. (See chapter 2, In- troduction to Reliability.) Second, on the demand side, shortcut meth- ods would have to be used to estimate outage costs for the large geographic areas affected by changes in reliability at the generation and transmission level. (See chapter 4, Estimation of Outage Costs.) This would reduce the data-gathering problem to manageable proportions. Appendixes  Appendix A Basic Mathematical Concepts for Reliability Modeling The ideas developed in this appendix are intended as an aid to under- standing the basic mathematical concepts involved in reliability model- ing. Therefore, fairly simple cases are considered here in a conceptual way. More detailed treatment of these topics can be found in the refer- ences cited below and in chapter 2. Laws of Probability' The fundamental laws of probability used in reliability modeling may be illustrated by analyzing the two-event case. Let P(A) and P(B) de- note the probabilities (each lying between zero and unity) of the occur- rence of events A and B, respectively. Furthermore, let P(A + B) rep- resent the probability of either A or B or both taking place: that is, the union of A and B. Also, let the probability of the occurrence of A and B P(A + B) = P(A) + P(B) - P(A X B). 1. For details, see: Athanasios Papoulis, Piobability, Random Variables, and Stochastic Processes (New York: McGraw-Hill, 1965), chap. 2; or Vijay K. Rohatgi, An Intioduction to Probability Theory and Mathematical Statistics (New York. John Wiley, 1976), chap. 2. 199 200 APPENDIXES simultaneously be given by P(A X B): that is, the intersection of A and B. Then, the following relation holds true: P(A + B) = P(A) + P(B) - P(A X B). If the events A and B are mutually exclusive, P(A X B) = 0, and therefore the simple additive law of probability is obtained as: (A.1) P(A + B) = P(A) + P(B). Next, let P(A/B) denote the probability of event A taking place, given the fact that B has already occurred. Then the following expression may be written: P(A/B) = P(A X B)/P(B). If the events A and B are mutually independent: P(A/B) = P(A), and therefore, the simple multiplicative law of probability is derived as: (A.2) P(A X B) = P(A).P(B). The probability of the event A not taking place is given by the com- plementarity rule: (A.3) P(A) = 1 - P(A). The above laws may be generalized to obtain the corresponding re- sults for the N event case. Thus, for a set of N mutually exclusive events, equation (A.1) gives rise to: P(A +B -----+N)= P(A)+P(B)±-----+P(N). Similarly, if the events are mutually independent, equation (A.2) can be rewritten: P(A X B X ----- X N) = P(A).P(B) ------P(N) Finally, in the long-run context, the expected value of a random variable Aj, which can take on different values for i = 1 ------ n, with corresponding probabilities P(A), is given by: BASIC CONCEPTS FOR RELIABILITY MODELING 201 E(A,) = ' A,P(A,). Discrete State Continuous Transition Markov Process Modern reliability studies attempt to represent random equipment failures or outages by means of stochastic models. Therefore the class of discrete state, continuous transition Markov processes is often used for this purpose.2 A simple generation capacity model is treated below to illustrate the use of this approach. Consider a single generating unit that at any given moment must be in one of two possible discrete states, depicted in figure A.1: (a) the U or up state, in which the unit is ready and available for use; and (b) the D or down state, in which the unit is off-line and unavailable for use. The rules governing transitions between the states may be deduced from the following important properties of these states: (a) The states are mutually exclusive and collectively exhaustive; (b) The probability of a given transition between states occurring during any small instant of time, At, is proportional to At, but is independent of the elapsed time, t (this implies that the tran- sition time may be represented by exponential probability den- sity functions of time); and (c) The probability of transition from a given state depends only on the current state and is independent of the past history of the machine. At any given time, t, suppose the probability of finding the generator in state, i, is given by P(t). From property (a), it follows that: (A.4) PU (t) + PD (t) = 1. Let the rate of departure or transition rate out of state i be denoted by A. From property (b), the probability of transferring from state i to the other state during any small duration of time at is given by: [X,*P, (t)*At]. 2. See for example- Chanan Singh and Roy Billinton, "Frequency and Dura- tion Concepts in System Reliability Evaluation," IEEE Transactions on Reliability, vol. R-24 (April 1975), pp. 31-36. 202 APPENDIXES Figure A.1. Basic Markov State-Space Representation of a Single Generator Available U xU XD (Failure rate) (Repair rate) D Unavailable Note: U = upstate, D = down state; and X. = transition rate out of state i. If transitions into and out of state U are considered, it follows that: Pu(t + At) = Pu(t) - XUPu(t)*At + XD'PD(t)*A1. Rearranging terms, yields: XD'PD(t) - Xu*Pu(t) = [P(t + At) - Pu(t)]/At = APU(t)/At. Assuming steady-state conditions, in the long-run, APu(t) = 0; and therefore: BASIC CONCEPTS FOR RELIABILITY MODELING 203 (A.5) XD'PD - XU*PU = 0 where P, is the steady state value of P, (t). Equation (A.5) summarizes the fact that for such a Markov process with no trap states, the sum of the rates of transition into a given state, weighted by the availabilities of the originating states, must be equal to the sum of the corresponding weighted rates of departure from that state. This general result also holds true for more than two connected states, and may be represented in the simplified Chapman-Kolmogoroff form: Z X, to .P, = P,* E X o k for any given state i. A Iyp,s Al kXs The steady-state form of equation (A.4) may be written: (A.6) PU + PD =L Solving equations (A.5) and (A.6) yields: PD =XU/(XU + XD) and PU = XD/(Xu + ND). Now this rather abstract mathematical model may be interpreted in terms of quantities commonly encountered in power engineering practice. Suppose that over a long observation period, data have been gathered on (a) the average time it takes a generator to fail-the time spent in the up state (Tu); and (b) the average time required for repairs fol- lowing such a failure-time spent in the down state (TD). Then it fol- lows that: (A.7) Availability of the machine = Pu = Tu/ (TU + TD), (A.8) Forced outage rate = PD = TD/(Tu + TD) = I - availability, (A.9) Failure rate = Xu = 1/Tu, and (A.10) Repair rate = XD = 1/TD. 204 APPENDIXES Table A. 1. Characteristics of Two Generators in Parallel Aver- Aver- age age time time Fail- Capac- to to ure Repair Forced ity, C fail- repair, rate, A rate, AD A vail- outage (mega- ure, TU TD (per (per ability, rate, watts) (days) (days) day) day) PU PD 40 100 2 0.01 0.5 0.9804 0.0196 60 100 2 0.01 05 0.9804 0.0196 Next consider the the operation of two generators in parallel. In this example, to clarify the presentation, numbers are assigned to the two generators as given in the first three columns of table A.1. The state- space diagram for the system consisting of four states is shown in figure A.2. The diagram indicates a limitation of the model. During any small interval of time At, only one unit is allowed to change state. For exam- ple, when one unit fails or is repaired, the other unit cannot simultane- ously fail or be repaired, thus forbidding direct transitions between the 0- and 100-megawatt states, as well as between the 40- and 60-megawatt states. On the basis of equatidns (A.7) to (A.10), the numbers in columns 4 to 7 of table A. 1 may be computed. Next it is possible to deduce the characteristics of the four system states. For example, the availability or probability of the 0-megawatt state is equal to the probability of both generators being unavailable. Assuming the independence of the failure of the two units and using equation (A.2) yields the availability of the zero capacity state:3 Po = P(40 megawatt down) X P(60 megawatt down) = 0.0196 X 0.0196 = 0.00038. 3. If the failure of one generation affects the other, then the analysis becomes more complicated, typically involving conditional probabilities. A further com- plication can arise if common mode failures occur, that is, the simultaneous failure of two or more components which are not consequences of one another, but BASIC CONCEPTS FOR RELIABILITY MODELING 205 Figure A.2. State-Space Diagram of Two Generators in Parallel 100 megawatts, both up 0 01 0.01 0.5 0 5 60 megawatts: 40 megawatts: 40 megawatts down. 40 megawatts up, 60 megawatts up 60 megawatts down 001 0.01 0 5 0.5 0 megawatts: both down Note- Transition rates are shown as numbers of failures or repairs per day As depicted in figure A.2, the total departuri o te out of the zero capacity state is equal to the rate of dearture to the 40-megawatt state plus the rate of departure to the 60-megawatt state, where equation (A. 1) has been used, since these two transitions are mutually exclusive. This result may be written: which result from a common cause. See, for example, R. N. Allan, E. N. Dialynas, and I. R. Homer, "Modelling Common Mode Failures in the Reliability Evalua- tion of Power System Networks," Proceedings of the IEEE Power Engineering Society Witer Meeting, New York, 1979, paper no. A79040-7. 206 APPENDIXES Xo = 0.5 + 0.5 = 1.0 per day. Therefore, the mean duration,, or holding time, in the 0 megawatt state is given by To = 1/X0 = 1.0 days. The frequency of occurrence of the zero capacity state is equal to the weighted sum of the transition rates into this state, which is also equal to the weighted sum of the transition rates out of the 0 megawatt state. (See equation (A.5) and subsequent discussion.) Therefore, the frequency of the zero capacity is given by: Fo = Po - x, = 0.00038 X 1.0 = 0.00038 per day. The complete sets of results for all the four Markov states are sum- marized in table A.2. Now that the capacity model has been defined, a load model is re- quired to estimate the well-known loss-of-load-probability (LOLP) in- dex. Suppose the daily peak megawatt demand over one year may be represented by a normal distribution with a mean, , = 6 megawatts, and standard deviation, r = 10 megawatts. By definition, LOLP equals the expected number of days within a given period of time that demand D exceeds availability capacity C. Therefore, during a one-year period: LOLP = 365 X P(D > C) that is, (A.11) LOLP = 365 X [P(D> 0)*Po+P(D> 40MW).Po40 + P(D > 60 MW)-P,o + P(D > 100 MW)*Plool Table A.2. Characteristics of the Capacity States Capacity Avail- Duration, Tj Frequency, Fj state, C, ability, P, (days) (per day) (megawatt) 0 0.0004 1.0 0.0004 40 0.0192 1.96 0.0098 60 0.0192 1.96 0.0098 100 0.9612 50.0 0.0192 BASIC CONCEPTS FOR RELIABILITY MODELING 207 For a normal distribution: P(D > L) = I - (1//27r)- [exp (-1P/2)]*dl. These values may be read off a standard statistical table.4 The four critical values of (L - ,u)/a, occurring at L = 0, 40, 60, and 100, are: -6, -2, 0, and 4. Evaluation of equation (A. 11) yields: LOLP = 365 X [(1.0 X 0.0004) + (0.9772 X 0.0192) + (0.5 X 0.0192) + (0 X 0.9612)] = 365 X 0.0288 = 10.5 days per year. Therefore, the LOLP is equivalent to 10.5 days per year, which may be interpreted to mean that over a long period, the load is likely to exceed available capacity 10.5 days per year, on the average. This section concludes with a brief summary of the generalized case. If there are n generators, then there will be a total of 2n possible com- bined Markov states. At a more sophisticated level, it is possible to consider multilevel deratings of generators as well, instead of only the simplified up and down states. At any given moment, it is important to know which of the 2n states have sufficient capacity to meet a given stochastic load, and which do not. The frequency of encountering a capacity deficit state, the duration of such a state, and the magnitude of the deficit are also quantities to be estimated.5 The complete Markov process can be described in terms of the fol- 4. Richard S Burington, Handbook of Mathematical Tables and Formulas, fifth edition (New York: McGraw-Hill, 1973), chapter 22 and table 18 5. Because of the complexity of the calculation, certain simplifying assumptions are usually made. See for example, J D. Hall, R J Ringlee, and A J. Wood, "Frequency and Duration Methods for Power System Reliability Calculations: Part I-Generation System Model," IEEE T,ansactions on Powet Apparatus and Systems, vol. PAS-87 (Sept 1968), pp. 1787-96; and R J. Ringlee and A J. Wood, "Frequency and Duration Methods for Power System Reliability Calculations: Part II-Demand Model and Capacity Reserve Model," IEEE Transactions on Power Apparatus and Systems, vol. PAS-88 (April 1969), pp. 375-88. A recent and more rapid Fourier method for calculating the probability density function of capacity shortages, which leads to the estimation of LOLP, is presented in N. S. Rau and Karl F. Schenk, "Application of Fourier Methods for the Evaluation of Capacity Outage Probabilities," Proceedings of the IEEE Power Engineering So- ciety Winter Meeting, New Yo,k, 1979, paper no. A79103-3. 208 APPENDIXES lowing set of first-order linear differential equations,6 which are analo- gous to the one from which equation (A.5) was derived: dP(t)/dt = M-P(t) where P(t) is a vector of the instantaneous state probabilities, and M ru is the state transition matrix, which gives the transition rates between all possible pairs of states. Monte Carlo Simulation In the Monte Carlo method, a gaming model of the power system is set up and simulated to determine system performance.' The range of application of these models has been discussed in chapter 2, Introduc- tion to Reliability. A simplified version of one type of Monte Carlo simulation of a model of a generation system is described below, to illus- trate the use of the Monte Carlo technique in long-run reliability evaluation. A capacity model may be basically set up along the lines of the se- quential simulation approach, with the up and down states of indi- vidual represented by randomly drawn numbers, for example, using a random number generating computer subroutine. As an example, con- sider the 40-megawatt generator described in the previous section on Markov processes, which has average times to failure and repair of 100 and 2 days, respectively. Given that the machine is up, or available on a particular day, its subsequent state is determined by selecting a random number from the discrete set of integers: U = {1, 2,-------,99, 100). The incidence of failure is associated with one of these integers, say 50. Therefore, if the number 50 is drawn, the generator is deemed to be down on the following day. If any other integer is selected, the machine would be still available. 6. See Harvey M. Wagner, Principles of Operations Research, second edition (Englewood Cliffs, New Jersey: Prentice-Hall, 1975), chap. 18. 7. See P. L. Noferi, L. Paris, and L. Salvaderi, "Monte Carlo Methods for Power System Reliability Evaluation in Transmission and Generation Planning," Proceedings of the Annual Reliability and Maintainability Symposiums, Washing- ton, D.C., January 1975, pp. 460-69. BASIC CONCEPTS FOR RELIABILITY MODELING 209 Similarly, given that the generating unit has failed and is already in the down condition, its state on the next day is determined by the in- teger set: D= 1, 2}. If a random selection from the set D yields the number 1, repairs are assumed to be complete, and the machine would be up; if the integer 2 is selected, the generator would continue in the down state for another day. It is intuitively clear in the above model that if the machine is avail- able on a given day, the probability of its failing on the next day is 0.01. If the unit is already down, however, the probability of its being up on the following day is 0.5. It can be shown rigorously that this process of random number selection will converge in the long run to yield the desired average times to failure and repair: that is, 100 and 2 days, respectively. The larger the number of such simulations, the more accurately the model represents the state of the machine. The state of the complete system may be built up by simulating the condition of many interconnected components, including generators, transmission lines, and so on. This procedure gives rise to many pos- sible system states, however, each of which requires several simulations for greater accuracy of the long-run results. Therefore the Monte Carlo approach tends to be relatively time consuming. The random number representation of component behavior could be modified to include the effects of the state of one component on the condition of another dis- tinct but related item of equipment: that is, the states of different com- ponents do not necessarily have to be mutually independent. A typical load may be represented during a given period by a simple probabilistic model of the type also described in the previous section; peak megawatt demand on a particular day of the year might be speci- fied by a normal distribution having a given mean and standard deviation. The relevant properties of the various capacity states, such as the availability, frequency, and duration (described in the previous section on Markov processes), may be determined through simulation. Relia- bility indexes can be estimated by comparing these characteristics with the results obtained from the load model. Thus, for example, the LOLP of the system may be calculated on the basis of the number of days in which the available supply, as determined by the random model of capacity, is insufficient to meet the demand, which is established by randomly drawing a value from the normally distributed load. Appendix B Shadow Pricing Concepts Conversion Factors The conversion factor for a given commodity is the ratio of its border price, in units of the chosen foreign exchange numeraire, to its domestic price. The general case of an electric power sector input is considered below. The input from this sector is also consumed by nonpower sector users and supplied through imports as well as through domestic pro- duction. In figure B.1, WS and DS are the world and domestic supply curves, while TS = WS + DS constitutes the total supply curve. DD is the domestic demand curve of nonpower sector users, and TD is the total domestic demand when the requirements of the power sector PD are included. The effect of the increased demand PD is to drive up the domestic market price of the input from P to P + AP; the corresponding world market c.i.f. (import) prices are smaller by a factor 1/(1 + tm,), where tm, is the rate of import duty on the input. Without the power sector demand, the level of consumption (from nonpower sector users only) would be Q = D, of which M would be supplied through imports and Note: The framework presented in Lyn Squire and Herman G. van der Tak, is used (For citation, see footnote 2, this appendix.) 210 Figure B. 1. Conversion Factor for an Importable Commodity World price Domestic price Domestic price TD DD+PD TS = WS + DS WSDS 'P +AP ) (P + AP)/( + t.) P 'p -- - -- --- -tI P/(l + r ) -- -.- -- II I I II I I I M M + AM Quantity S S +AS Quantity D - AD Q = D Q + AQ Quantity WORLD SUPPLY DOMESTIC SUPPLY DOMESTIC MARKET Note: WS = world supply; DS = domestic supply, TS = total supply, DD = domestic demand of nonpower sector users; TD = total domestic demand when the requirements of the power sector PD are included, and tm = rate of import duty on input. 212 APPENDIXES S from domestic production. With PD included, the total domestic con- sumption is Q + AQ, which is composed of nonpower sector demand D - AD and power sector demand (AQ + AD). In this situation, the respective quantities M + AM and S + AS are imported and domes- tically supplied.' Next, the marginal social cost (msc) of meeting the power sector demand is considered. First, there is the increased expenditure of foreign exchange, in border prices, for extra imports: AFX = M.AP. (1 + e,)/(1 + ti) where e. = PA- M/M.AP is the price elasticity of world supply. Second, consider the increased resource cost of additional domestic supply: ARC = f* (S-AP*ed) where ed = P. AS/S. AP is the price elasticity of domestic supply, and f is the factor that converts the cost of supply from domestic to border price. Third, the decrease in the benefit of consumption of nonpower sector consumers should be considered as a cost: ABD = w,. (D*AP*nd) where n = P-AD/D-AP is the relevant price elasticity of demand (absolute value), and w, is the social weight attached to domestic consumption at the relevant consumption level. Fourth, there is the effect resulting from the increase in the income of nonpower sector consumers: Al, = (b, - iv).[D-AP- (nj - 1)] where b, is the border priced resource cost of increasing domestic con- sumption (of other goods and services) by one unit, and once again w, is the corresponding benefit. Finally, the effect of increased income accruing to domestic producers is evaluated: AI, = (bp - w,)- (S- AP) where b, and w, represent the border-priced resource cost and marginal 1. For convenience, the formula is developed in the increments AP, AQ, and so on. SHADOW PRICING CONCEPTS 213 social benefit (MsB), respectively, of a one-unit increase in the income of the producers. The total cost of the input to the power sector, in border prices is: ABP = AFX + ARC + ABD + Alc + AI. The corresponding cost of the input in domestic prices is: ADP = P. (AD + AQ) = AP. (D*nd + S*ed + M*e,). Therefore, the expression for the conversion factor may be written: ABP CF, = - ADP M[(1 + e.)/(l + t-)] + S(f-ed + b, - w,) + D(b,*nd + w, - b,) M.e,, + S*ed + D*nd Often, this expression may be considerably simplified for specific situa- tions. Tradable Case I. Small country assumption: that is, e. -* 00. Therefore: CF 1 tm Nontradable Case Ha. No imports and perfectly elastic supply: that is, M = 0 (thus S = D) and ed -co, or Case lIb. No imports, perfectly inelastic demand, and no income effects: that is M = 0, nd = 0, w, = b,, and we = b,. Therefore: CF, = f Case Ila. No imports and perfectly elastic demand: that is, M = 0, nd -+ c, or Case Ib. No imports, perfectly inelastic supply, and no income effects: that is, M = 0, ed = 0, w, = b,, and w. = b,. Therefore, 214 APPENDIXES CF3 = b,. The conversion factor for an electric power sector input that is domes- tically produced for export as well as for nonpower sector domestic con- sumption may be derived analogously: X[(n.- 1 )/(1 - t.)] + S(f.ed + b, - w,) + D(b,nd + w - b,) X*n, + S*ed + D*nd where X represents exports, t, is the tax rate on exports, n. is the price elasticity of world demand, and the other symbols are as defined earlier. Income Effects If the income of a particular group of consumers is increased by one unit (in domestic prices), the social value of this change in units of the numeraire is (w - b). The interpretation of b and w is discussed below. The Msc to the economy is represented by b, resulting from the use of the increased income. For example, if all the new income is consumed, then b is the revelant consumption conversion factor or resource cost (in units of the numeraire) of making available to con- sumers one unit worth (in domestic prices) of the marginal basket of goods they would purchase. In this case, b = Egi - CF,, where g, is the proportion of the ith good in the marginal basket, and CF, is the appro- priate conversion factor. The corresponding MSB of increased consumption may be broken down further: w = d/v; where 1/v is the value (in units of the nu- meraire) of a one-unit increase in domestic-priced consumption accruing to someone at the average level of consumption c. Therefore, v may be roughly thought of as the premium attached to public savings, compared with "average" private consumption. Under certain simplifying assump- tions, b = 1/v.2 If MU(c) denotes the marginal utility of consumption at some level c, then d = MU(c)/MU(c). Assuming that the marginal 2. If the marginal product of capital equals the consumption rate of interest (See Lyn Squire and Herman van der Tak, Economic Analysis of Ptojects [Balti- more. Johns Hopkins University Press for the World Bank, 1975], p. 68.) SHADOW PRICING CONCEPTS 215 utility of consumption is diminishing, d would be greater than unity for "poor" consumers with c < E, and would be less than unity for "rich" consumers with c > E. Two specific values of w are particularly impor- tant. First, the level of consumption for which w = 1 is called the critical consumption level (CCL). At the CCL the marginal value of domestic priced private consumption is equal to the value of the numeraire. Sec- ond, when w = b, the income effects cancel out, and social prices be- come equal to efficiency prices. As an example, consider the case of the outage costs of residential consumers in the Cascavel case study, which could be treated like fore- gone income-consumption. In the shadow-pricing analysis conducted in chapter 14, the numeraire was chosen for convenience to be the do- mestic priced cruzeiro (Cr$). Therefore, it was possible to make the simplifying assumptions that b = 1 and I/v = 1. Suppose that OC was the outage cost (in domestic prices) incurred by a household at the consumption level c, which resulted in an equivalent loss of welfare in units of the domestic-priced numeraire. The effect of the income distributional considerations was to introduce an additional correcting factor OC - (w - b), so that the outage cost or negative bene- fit, measured in social prices, may be written: 0C. = OC-b + OC(iv - b) = OC.d. The simplest form of marginal utility function that could be as- sumed was: MU(c) = c-n. Therefore: d = MU(c)/MU( ) = (E/c),. The additional assumption that the distribution parameter n = I gave: d = E/c = I/i where i/i is the ratio of net incomes that was used as a proxy for the consumption ratio. The appropriate weights were obtained by substitut- ing for 1, the average net income of all households in Cascavel (Cr$67.7 Income group Lower Lower-middle Upper-middle Upper d 3.679 1.419 0.694 0.296 216 APPENDIXES X 103 per year, in 1976), and the corresponding values of i for the various income groups from table 11.1 of chapter 11. Because all incomes were assumed to increase uniformly at 4 percent every year, while the income structure of the population remained the same, the social weights d were constant over time. Therefore, in the social pricing exercise, all domestically priced outage costs were weighted by the factors d, relevant to the income groups under consideration. Appendix C Load Forecasting and Distribution Primary Models Land Use and Distribution of Population The load forecast modeling process began by examining maps showing future land use plans and detailed zoning regulations for Cascavel, Brazil. (See figures 10.1 and 10.2 in chapter 10.) The first part of the Cascavel zoning regulations set out the permitted uses of land for each zoning classification. For example, the ZR1 zone is predominately residential but may also be used for clinics, restaurants, schools, and so on. The second segment of the zoning regulations de- fines the ratios of buildings to land, the ratios of floor area to land area, and the minimum lot sizes. The next stage in the development of the model was the division of the area into 0.25-square-kilometer geographic cells as illustrated in figure 10.2 of chapter 10. The fractional area of each cell allocated to the various types of zones was measured and entered into a first-stage data base. Then it was necessary to determine the allocation of con- sumers, saturation factors, energy usage, load factors, and the time when currently unoccupied outer geographic cells would come into service, as described below. 217 218 APPENDIXES Allocation of Residential Consumers For each of the study years, the previously estimated population by income class (see chapter 10, Demand Forecast) was allocated among the various residential areas in the following manner. First, each class of land was divided into a reasonable mixture of single family, multiple family, commercial, and industrial areas within the restrictions of the zoning regulations, as summarized in table C.l. Second, the available land for residential use in the above table was then divided among the income levels as shown in table C.2. Third, reasonable ratios of floor area to land area were determined for multiple family dwellings. These ratios reflected the amount of land occupied by the building and the height of the building or number of floors. For example, the ZR2 zoning regulations permitted two-thirds of the land to be occupied, and the maximum ratio of floor area to land area was 2. By 1996 it was estimated that two-thirds of ZR2 land would be occupied by single-story buildings and one-third by two-story build- ings. Therefore the overall ratio of floor to land area would be: Ratio = (2/3 X 2/3) + (1/3 X 4/3) = 0.9. Table C.1. Land Use, by Zone Percentage of available land allocated to Residential use Type Sin- Multi- Commercial use Industrial use of gle ple Me- zbne family family Light dium Heavy Service Main ZR1 65 20 15 - - - - ZR2 70 15 15 - - - - ZR3 90 - 10 - - - - ZCR - 80 - - 20 - - SCR - 80 - 20 - - - ZC - - - - 100 - - SC - 40 - 60 - - - SL - 40 - 60 - - - ZI - - - - - - 100 SI 30 - - - - 70 - LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 219 The ratios for other zones were determined in a similar manner, as shown in table C.3. Fourth, the city was divided into the three saturation regions shown in figure 10.2 of chapter 10. For each region, a saturation factor, defined as the ratio of actual to the maximum population allowed by the zoning regulations was determined (see table C.4) to account for the total forecast population, by income class and in any given year (see table 10.1 of chapter 10). Fifth, data were obtained from COPEL regarding recent trends in lot sizes and apartment floor areas, as summarized in table C.5. Finally, the number of dwelling units (DU) per cell was determined by income class on the basis of the following expression. DU = (LA X FAL X FIC X LM X SF)/DA Table C.2. Allocation of Residential Land, by Income Class Income class (percentage) Lower- Upper- Dwelling type Zone Lower middle middle Upper Single family ZR1 - 20 50 30 ZR2 10 50 35 5 ZR3 70 20 10 - SI 70 20 10 - Multiple family ZRI - 20 50 30 ZR2 10 50 35 5 SCR - 60 30 10 SC 10 40 40 10 SL 10 40 40 10 ZCR - 35 40 25 Table C.3. Ratio of Floor Area to Land Area Zone Ratio Zone Ratio ZR2 0.9 SC 2.0 ZR1 1.0 SL 2.0 SCR 2.0 ZRC 3.0 220 APPENDIXES Table C.4. 1996 Saturation Factors, by Saturation Region (percentage) Saturation factor Region Region Region Consumer category 1 2 3 Residential Lower 73.6 67.2 50.4 Lower-middle 86.1 77.7 58.3 Upper-middle 90.7 82.8 62.1 Upper 92.0 84.0 63.0 Commercial and public illumination 85.6 77.9 58.5 Table C.5. Average Residential Lot Size and Apartment Floor Area, by Income Class Average area (square meters) Income class Single family lot Apartmenta Lower 400 100 Lower-middle 500 150 Upper-middle 750 225 Upper 1,000 300 a. Includes allowances for common entry ways, stairs, elevators, and halls. where: LA = residential land area; FAL = fraction of land allocated to single or multiple families (see table C.1); FIC = fraction of land allocated to a given income class (see table B.2); LM = ratio of floor area to land area (see table C.3); SF = saturation factor by region and income class (see table C.4); and DA = average area of dwelling unit by income class (see table C.5). For example, the number of apartments for upper middle-income families in a given cell in the first saturation region, which contained 100,000 square meters of ZCR land, would be determined as follows: LA = 85 percent of 100,000 = 85,000 square meters where 15 percent of land has been set aside for streets, sidewalks, and so on; FAL = 80 percent; FIC = 40 percent; LM = 3.0; SF = 90.7 percent; DA = 225 square meters; therefore: LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 221 DU = (85000 X 0.8 X 0.4 X 3.0 X 0.907)/225 = 74011/225 = 329 apartments The total energy and power requirements by income class, by cell, and by year were calculated as the product of the numbers of households by income class, by cell, and by year as determined above, and the cor- responding energy and power consumption for each household. (See chapter 10, Demand Forecast.) The commercial and street lighting load forecasts are described in detail in the following sections, because they were linked closely to the pattern of land use. The other categories of consumption have already been dealt with at length in chapter 10, Demand Forecast. Commercial Requirements The commercial sector was divided into three basic types. Light com- mercial (LC) was confined to residential areas and consisted of such enterprises as shops and professional offices. Medium commercial (SC and SL zones), also referred to as strip commercial, was found along the main streets. Typical strip businesses included supermarkets, motels, restaurants, clinics, offices, and hardware-dry goods stores. Heavy com- mercial (ZC zone) was concentrated in the center of the city and con- sisted of high-rise offices, department stores, hotels, and government offices. The electrical requirements for the three commercial zones were based on the following factors. (a) The zoned land was divided to reflect multiple usage, as table C.1 indicates. (b) Saturation factors were determined as the average of the four residential saturation factors in each region (see table C.4), based on the premise that the volume of commercial activity would be directly proportional to population levels. (c) A reasonable ratio was determined between building area and land area for each type of zone, based on zoning regulations, availability of land, current building trends, and the relation 222 APPENDIXES between population and commercial requirements; the selected values are shown in table C.6. (d) A survey, made to determine the relation between building areas and energy requirements, indicated that large businesses used about 45 kilowatt-hours/square meter/year, small businesses used about 15 kilowatt-hours/square meter/year, and the aver- age was 38.6 kilowatt-hours/square meter/year (table C.7). These figures were used to develop energy requirements for dif- ferent types of business users, as shown in table C.6. (e) Load factors for various types of businesses obtained from COPEL billing data. These factors varied from 25 percent for small busi- nesses to 35 percent for large ones, as shown in table C.6. Street Lighting Requirements Street lighting electrical requirements were based on the types of streets in Cascavel, COPEL's street lighting standards, and the mixture of streets used in the various zones. The five types of streets in Cascavel were the following: (a) Express: for heavy commercial areas (b) Important: arteries for multifamily residential, medium-commer- cial, and industrial areas (c) Main: connector streets for residential, medium-commercial, and industrial areas (d) Normal: for urban residential areas (e) Secondary: for fringe urban residential areas Table C.6. Commercial Load Forecast Parameters Energy consumption density Ratio of (kilowatt-hours! Annual Commercial building year! load factor class to land square meter) (percentage) LC 0.60 15.0 25.0 SL 2.00 15.0 30.0 Sc 1.00 35.0 32.5 zc 2.00 35.0 35.0 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 223 For each type of street, COPEL supplies a standard grouping of sodium or mercury vapor lamps as shown in table C.8. The mixture of streets required to serve the transport needs of the occupants of each zone and the resultant electrical requirements, in kilowatt-hours/square meter/year, are shown in table C.9. The total street lighting energy requirements for a particular type of land use was computed from the following equation: Energy (kilowatt-hours/year) = (0.15 LND) X SAT X EN where LND = land area in square meters devoted to the given type of land use, of which 15 percent is assumed to be allocated to streets; SAT = saturation factor same as for commercial load (see table C.8); Table C.7. Summary of the Survey of Commercial Consumers Energy Annual consumption energy density Floor area consumption (kilowatt- (square (kilowatt- hours/year! Type of business meters) hours) square meter) Large Appliances and furniture 1 1,870 83,116 44.1 Appliances and furniture 2 600 24,623 41.0 Appliances and furniture 3 1,885 79,630 42.2 Variety and dry goods 850 42,330 49.8 Supermarket 1,560 141,880 90.9 Dry goods and fabrics 1,200 27,860 23.2 Medium and small Furniture 600 10,075 16.8 Shoe store 200 5,035 25.2 Dry goods 350 5,360 15.3 Hardware 500 6,660 13.3 Small appliances 115 2,690 23.4 Groceries 500 26,910 53.8 Other Bank 1,800 16,930 9.4 Hotel 1,000 28,715 28.7 Newspaper 700 29,125 41.6 Total 13,720 529,938 38.6 224 APPENDIXES Table C.8. Standard Street Types and Lighting Characteristics Kilo- watt- Kilo- Kilo- hours! Street Lamps! watts! watts! square Type of width Lighting kilo- kilo- square meter! street (meters) standards" meterb meterc meterd yeare Express 30 Two 400 watt 133 53.2 0.00177 6.46 sv/15m Impor- 25 One 700 watt 50 35.0 0.00145 5.29 tant Mv/20m Main 20 One 400 watt 40 16.0 0.00080 2.92 Mv/25m Normal 17.5 One 250 watt 40 10.0 0.00057 2.08 Mv/25m Second- 15 One 125 watt 40 5.0 0.00033 1.22 ary Mv/25m a. Two 400 watt sv/15 m = two 400-watt sodium vapor lamps every 15 meters; Mv = mercury vapor lamps, and so on. b. Lamps/kilometer = (number of lamps/n meters) X (1,000/n). c. Kilowatts/kilometer = (lamps/kilometer) x (kilowatts/lamp). d. Kilowatts/square meter = (kilowatts/kilometer) X (street width in kilo- meters). e Kilowatt-hours/year/square meter = (kilowatts/square meter) x (3,650 hours), assuming that the lamp will be switched on ten hours a night. and EN = street lighting energy requirements in kilowatt-hours/square meter/year, for the given type of land use (see table C.9). Street lighting power demands are derived from the equation: Demand (kilowatts) = Energy (kilowatt-hours/year)/3,650 (hours of use a year) For example, street lighting requirements for 100,000 square meters of ZCR in saturation region 1 would be given by: Energy = (.15 X 100,000) X .856 X 3.62 = 46480 kilowatt-hours/year Demand = 46480/3650 = 12.7 kilowatts Land Use and Load Forecast By 1996, Cascavel will encompass many geographic cells which pres- ently consist of vacant land. The time schedule shown in figure C.1 was LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 225 Table C.9. Allocation of Streets and Street Lighting Energy Requirements Kilo- watt- hours/ Allocation (percentage) year! Type of Ex- Impor- Nor- Sec- square land use Zone press tant Main mal ondary meter Single ZR1 - - - 100 - 2.08 Family ZR2 - - - 100 - 2.08 Residen- tial ZR3 - - - - 100 1.22 SI - 100 - - - 5.29 Multiple ZR2 - - - 100 - 2.08 Family ZR1 - - - 100 - 2.08 Residen- tial SCR - 30 40 30 - 3.38 SC - 30 40 30 - 3.38 SL - 40 60 - - 3.87 ZCR - 40 30 30 - 3.62 Commer- cial LC - - - 100 - 2.08 SC - 30 40 30 - 3.38 SL - 40 60 - - 3.87 ZC 60 20 20 - - 5.52 Industrial SI - 100 - - - 5.29 ZI - 40 30 30 - 3.62 developed for serving the cells currently without power, based on dis- cussions with the city authorities and COPEL regarding the expansion of municipal services (roads, water, sewerage, and so on) and the avail- ability of power supply. Currently served geographic cells are shown with a 1976 date, whereas the dates that electricity services will begin are indicated for the other cells. Finally, land use and electrical loads were forecast, by consumer category and by cell, for the years 1980, 1984, 1988, 1992, and 1996, using a computerized model that implemented the methodology de- scribed above. The residential forecast is summarized in table C.10, and the com- mercial industrial, public lighting, and special institutions forecasts are summarized in table C. 11. 226 APPENDIXES Figure C. 1. Cell Initializing Schedule for Load Forecast, by Cell 0 N/ N < 1988 1l8 988 1988 1988 1984 1984 1984 1984 1984 1980 L 1984 1980 1980 1980 1980 1980 1980 1980 K 'T1984 1980 1976 1976 1976 1976 1976 1980 1984 1980 1976 1976 1976 1976 1976 1976 1976 1976 1976 1976 1976 1976 1976 1976 H 1984 1980 1976 1976 1976 1976 1976 1976 1976 G 1984 1980 1976 1976 1976 1976 1976 1976 1976 1976 F 1992 1984 1980 1976 1976 1976 1976 1976 1976 1976 1976 E 1988 1984 1980 1976 1976 1976 1976 1976 1976 1976 1976 D 1988 1984 1980 1 76 1980 1980 1976 1976 1976 1976 1976 C 1984 1980 1980 1980 1976 1976 19 976 B 198 1980 1980 1980) 198 <6 976 A / 80 l84 1984 1980 8 1980 1976 1976 1980 1976 1 2 3 4 5 6 7 8 9 10 11 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 227 - 1976 1984 1988 1988 1988 1976 1976 1976 ~ 0 19ddL__J)RR 1976 1976 1976 1976 197 1980 1984 1988 1988 1988 1976 1976 1976 1976 1976 980 1984 1988 1988 1988 1976 1976 1976 1976 1976 1976 1984 1984 1988 1992 1976 1976 1976 1976 1980 1976 1976 1984 1984 1992 1976 1976 1976 1976 1980 1980 1976 1976 1980 1976 1980 1980 1980 1980 1980 1980 1980 16 6 1980 1980 1984 1984 1984 18 OP 1980 1- 1976 1980 1980 1980 1984 1980 1980 1980 1980 1976 1980 1984 1984 1984 1984 1984 1984 1984 1980 1980 -19 -J9 1 1976 1980 1984 1976 1980 1984 12 13 14 1,5 16 17 1ig 19 20 21 22 228 APPENDIXES The 1976 Cascavel service area, the 1976 kilowatt demand by cell, and the 1976 load densities are shown in figures C.2, C.3, and C.4, re- spectively. For comparison, the corresponding set of diagrams for 1996 are shown in figures C.5, C.6, and C.7. Table C.10. Summary of the Residential Forecast Income class Upper- Lower- Items Total Upper middle middle Lower Land use (X 10- square meters) 1976 14,840 1980 23,134 1984 27,471 1988 29,321 1992 29,330 1996 29,336 Dwelling units 1976 10,236 1,333 3,591 4,478 834 1980 19,989 2,267 6,516 8,936 2,270 1984 32,597 3,327 10,108 14,994 4,168 1988 45,888 4,465 14,290 21,319 5,813 1992 61,426 5,492 18,524 27,804 9,605 1996 72,944 6,371 21,561 32,316 12,697 Energy require- ments (mega- watt-hours) 1976 14,045 4,377 5,858 3,556 256 1980 28,917 7,978 11,990 8,132 817 1984 51,018 12,508 20,824 15,893 1,792 1988 79,752 18,040 33,010 25,796 2,907 1992 115,897 24,167 47,792 38,370 5,571 1996 152,052 30,732 61,837 50,801 8,685 Demand (kilowatts) 1976 4,281 1,249 1,783 1,160 90 1980 8,866 2,277 3,650 2,652 287 1984 15,722 3,570 6,339 5,184 629 1988 24,632 5,148 10,049 8,413 1,021 1992 35,917 6,897 14,548 12,515 1,957 1996 47,214 8,771 18,824 16,569 3,051 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 229 Distribution Primary Model The distribution primary model (DPM) that was used in the plan- ning, design, and operation of the Cascavel distribution system consisted of a data base and a group of modular programs for data entry, data editing, and system analysis (see figure C.8). The modeling process began with the division of the primary feeders (or circuits) into nodes and sections. Nodes are points on a circuit such as branches, changes in conductor size or number of phases, location of major loads, and so on. Sections are the lines between the nodes. Numbers were then assigned to the nodes and sections. Figure C.9 Table C. 11. Summary of the Forecast: Commercial, Industrial, Public Lighting, Special Institutions, and No Load Forecast Com- Public Special mer- Indus- light- institu- No Items cial trial ing tion load Land use (X 10 square meters) 1976 5,282 1,404 3,799 84 3,092 1980 6,669 5,325 6,199 138 6,533 1984 7,312 5,596 7,126 213 10,031 1988 7,561 5,625 7,501 288 12,202 1992 7,565 5,622 7,512 363 12,807 1996 7,557 5,621 7,502 438 12,795 Energy require- ments (mega- watt-hours) 1976 13,500 22,428 3,001 588 0 1980 28,300 34,946 4,897 976 0 1984 51,399 53,901 7,197 1,446 0 1988 82,799 85,001 9,399 1,918 0 1992 122,500 135,098 11,500 2,361 0 1996 164,472 216,962 13,534 2,750 0 Demand (kilowatts) 1976 4,855 9,715 820 139 0 1980 10,176 15,675 1,339 233 0 1984 18,481 24,320 1,973 348 0 1988 29,773 38,353 4,241 710 0 1992 44,050 60,958 5,189 871 0 1996 59,149 97,895 3,708 676 0 230 APPENDIXES Figure C.2. Service Area in 1976 0 N M L H G F E B A Note. -commercial area; = urban area; and = suburban area. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 231 1 13 4 11 18 1 2 2 2 12 13 14 15 16 17 18 19 20 21 22 232 APPENDIXES Figure C.3. Kilowatt Demand in 1976, by Cell 0 N M K 8 62 50 41 2 42 119 56 148 48 51 23 45 49 194 144 195 246 208 H 32 32 269 317 427 986 751 G 5 18 16 67 109 232 394 385 F 4 70 31 64 130 154 213 149 E 1 21 12 42 61 78 124 127 D 133 31 51 122 120 c 22 67 166 B A 8 33 7 1 2 3 4 5 6 7 8 9 10 11 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 233 2 16 --- -- 435 43 53 87 11 56 98 127 178 40 719 252 204 73 65 12 449 345 175 9 6 2 157 19 44 4 2 4 30 15 3 56 67 86 24 12 13 14 15 16 17 18 19 20 21 22 234 APPENDIXES Figure C.4. Load Density in 1976 0 N L1 K H G F E D C B 1 2 3 4 5 6 7 8 9 10 11 E](0 to 1,000 kilowatts) LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 235 12 13 14 15 16 17 18 19 20 21 22 236 APPENDIXES Figure C.5. Service Area in 1996 N M L K -- ------M-- l H G F E D c 1 2 3 4 5 6 7 = 9 1011 Note: 18=corfimercial area,1= urban area; and 11= suburban area.- LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 237 1 13 1 15 1 1 18 1 20 2 2 12' 13 14 15 16 1 7 18 19 20 21 22 238 APPENDIXES Figure C.6. Kilowatt Demand in 1996, by Cell 0 N N 301 7 g 153 59 114 4 M 238 243 29\ 197 243 32 17 302 243 235 231 147 168 239 K 32 243 706 454 407 261 292 432 228 301 815 491 622 719 845 1,501 80 243 820 1,215 1,133 1,003 1,183 2,380 H 177 243 239 964 3,980 3,592 3,642 3,395 3,668 G 61 171 222 243 913 964 1,014 1,133 1,492 2,096 F 16 132 27 68 280 907 448 499 448 944 1,482 E 89 135 94 147 657 300 515 572 734 1,101 1,469 D 123 136 274 11201 306 239 318 257 324 1,063 1,431 C 120 1, 239 243 213 525 324 2,061 B 680 1,598 1,598 1,584 11N\ 1,164 1,20 0 1,643 2,053 A 58 --"1 879 3201 671 ,598 853 675 247 135 135 1 2 3 4 5 6 7 8 9 10 11 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 239 1 3 63 60 11 67 453 243 350 242- - 67 669 1,274 391 324 34 198 135 371 132 45 539 1,111 1,201 318 324ý,7 207 369 136 19 1,459 2,930 2,591 977 829 318 405 129 22 41 3,533 3,181 1,043 193 541 968 857 230 136 15 1,968 319 76 35 136 375 1,209 404 42 301 0 0 0 186 441 357 829 1 6 389 0 11 275 420 243 4 3,9 4 1,090 736 719 452 243 1,133 5935,903 ,889 324 25ý6 4,890 5,903 5,784 5,903 5,312 5,017 413 1 437 104 -3-M944J) 182 135 107 135 13 12 12 13 14 15 16 17 18 19 20 21 22 240 APPENDIXES Figure C.7. Load Densities in 1996 (kilowatts) 0 N L K H G F E D 1 2 3 4 5 6 7 8 9 16 11 Note: = 0-1,000; E= 1,001-2,000, = 2,001-3,000; Q= 3,001- 4,000; 2= 4,001-5,000; and D= over 5,000 kilowatts. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 241 12 13 14 15 16 17 18 19 20 21 22 242 APPENDIXES Figure C.8. Distribution System Model: Data Bank and Program Modules DATA BANK Node file Section file Conductor file Order file MODULAR PROGRAMS MODULAR PROGRAMS Voltage regulation - Conductor loading Line losses Optimized switching Short circuits Regulator setting Capacitor placement Capacitor control setting depicts a typical circuit that has been divided into nodes and sections with appropriate numbers assigned. The data base consisted of conductor, section, node, and order set files. The conductor file contained major conductor characteristics such as ampacity, positive sequence resistance and reactance, and zero se- quence resistance and reactance. The section file contained the physical and electrical characteristics of the line sections such as the length, con- ductor code, number of phases, resistance, reactance, and spacing. The node file was basically concerned with loading, customers, and regulation. Loading information included connected kilovolt-amps of distribution transformers, kilowatt demands, kilovarl demands, and kilowatt-hour usage by phases. Customer information included number for each phase, special loads for each phase, and growth rates. Regula- 1. Kilovar = reactive kilovolt-ampere. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 243 Figure C.9. Cascavel Distribution System: Circuit Number 4 O N Substation L2 K H 120 G FZk 13 14 15 16 17 * 18 19 20 21 Note: Node numbers are indicated by an arrow; other numbers identify the sections. 244 APPENDIXES tion involved the use of line regulators or boosters to provide voltage control on the system. The order set file contained digital maps of each circuit. A program called "load allocate" used an iterative process to assign kilowatt and kilovar demands to each node in proportion to either con- nected kilovolt-amps or peak monthly kilowatt-hours. A voltage/load/ loss analysis program used an iterative algorithm to compute the voltage profile, conductor loading, and line losses on selected circuits. A fault current program used symmetrical components to compute line-to- ground, line-to-line, and three-phase fault currents. Table C.12 Lengths of Feeders for the Low-Reliability System (kilometers) Circuits 1976 1980 1984 1988 1992 1996 North 1 17.1 10.7 13.7 11.0 13.0 10.8 North 2 22.2 9.8 12.0 7 9 5.0 7.3 North 3 21.4 13.7 10.6 6.7 4.0 2.4 North 4 12.9 16.0 9.2 10.9 11.0 11.4 East 1 0.0 0.0 0.0 12.1 8.1 8.1 East 2 0.0 0 0 0.0 4.0 6.1 10.5 East 3 0.0 0.0 0.0 0.0 2.9 2.9 East 4 0.0 0.0 0.0 0.0 2.9 2.9 Southeast 1 0.0 0.0 8.3 2.8 2.8 2.3 Southeast 2 0.0 0.0 6.1 6.6 0.6 1.2 Southeast 3 0.0 0 0 0 0 0.0 6.2 1.6 Southeast 4 0.0 0.0 0.0 0.0 0.0 4.4 South 1 0.0 21.7 11.7 14.6 14.9 10.2 South 2 0.0 22.8 15.2 11.6 12.2 10.9 Southwest 1 0.0 0.0 11.4 8.9 6.5 8.7 Southwest 2 0.0 0.0 9.1 8.7 3.8 5.3 Southwest 3 0.0 0.0 0.0 0.0 13.4 7.6 Southwest 4 0.0 0 0 0.0 0.0 0.0 10.2 Northwest 1 0.0 0.0 0.0 10.2 7.0 2.3 Northwest 2 0.0 0.0 0.0 10.7 12.7 15.3 Central 1 0.0 0.0 0.0 0.0 5.3 3.1 Central 2 0.0 0.0 0.0 0.0 5.8 6.1 Central 3 0.0 0.0 0.0 0.0 0.0 5.6 Central 4 0.0 0.0 0.0 0.0 0.0 7.3 Averages 18.4 15.8 10.7 9.1 7.2 6.6 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 245 Table C.13. Lengths of Feeders for the High-Reliability System (kilometers) Circuits 1976 1980 1984 1988 1992 1996 North 1 17.1 10.9 16.8 11.2 12.0 8.9 North 2 22.2 6.2 6.2 4.6 5.0 3.9 North 3 21.4 5.1 5.1 5.1 4.0 3.1 North 4 12.9 10.4 10.4 8.1 8.0 8.0 North 5 0.0 0.0 0.0 0.0 0.0 5.9 East 1 0.0 0.0 0.0 12.4 8.2 8.2 East 2 0.0 0.0 0.0 2.6 7.2 1.7 East 3 0.0 0.0 0.0 2.4 1.6 10.9 East 4 0.0 0.0 0.0 0.0 1.4 1.2 East 5 0.0 0.0 0.0 0.0 0.0 .9 East 6 0.0 0.0 0.0 0.0 0.0 .9 Southeast 1 0.0 0.0 5.9 2.8 2.8 1.1 Southeast 2 0.0 0.0 2.6 1.1 1.1 1.3 Southeast 3 0.0 0.0 0.0 6.3 6.9 2.8 Southeast 4 0.0 0.0 0.0 0.0 4.6 2.1 Southeast 5 0.0 0.0 0.0 0.0 0.0 7.7 Southeast 6 0.0 0.0 0.0 0.0 0.0 .6 Southeast 7 0.0 0.0 0.0 0.0 0.0 2.3 South 1 0.0 8.8 8.8 11.6 9.8 8.2 South 2 0.0 11.6 11.6 7.4 8.6 6.1 South 3 0.0 8.0 8.3 8.3 6.8 5.3 South 4 0.0 15.1 13.2 70 8.8 4.7 South 5 0.0 0.0 0.0 0.0 0.0 7.4 Southwest 1 0.0 13.3 10.1 10.6 13.6 8.8 Southwest 2 0.0 7.8 6.5 4.7 4.7 3.8 Southwest 3 0.0 0.0 8.8 3.6 7.3 3.8 Southwest 4 0.0 0.0 0.0 5.4 5.9 5.9 Southwest 5 0.0 0.0 0.0 0.0 0.0 5.9 Southwest 6 0.0 0.0 0.0 0.0 0.0 3.4 Northwest 1 0.0 0.0 0.0 5.4 4.8 3.9 Northwest 2 0.0 0.0 0.0 9.1 7.4 4.7 Northwest 3 0.0 0.0 0.0 7.3 5.5 4.4 Northwest 4 0.0 0.0 0.0 0.0 0.0 3.0 Central 1 0.0 0.0 0.0 0.0 3.2 4.7 Central 2 0.0 0.0 0.0 0.0 5.5 3.3 Central 3 0.0 0.0 0.0 0.0 0.0 5.5 Central 4 0.0 0.0 0.0 0.0 0.0 3.3 Averages 18.4 9.7 8.8 6.5 6.2 4.8 246 APPENDIXES Alternative System Configurations The data bases of the load forecast and primary system models were correlated through a group of interface programs. As described in chapter 11, Long-Range Distribution System Planning, the 1996 loads were imposed on the existing distribution system, and an analysis was made to pinpoint voltage, loading, and loss problems. The primary net- work was then expanded by adding substations and feeders until the analysis indicated that reliability and voltage criteria had been met. This process is repeated for the low-, medium-, and high-reliability systems during each of the study years. Tables C.12 and C.13 show the length of feeder for the low- and high- reliability systems. In both cases the average length of the feeders de- creased over time, which was caused by an ever-increasing load density. The decreasing exposure reduced outages and thus increased the average level of future reliability for both plans. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 247 Figure C.10 shows the areas served by the four 1976 circuits. Figures C. 11 and C.12 depict the cells served by the circuits of the low-reliability system for 1988 and 1996, and figures C.13 and C.14 show the areas served by the circuits of the high-reliability system for the same two years. Comparison of figures C.11 with C.13, and C.12 with C.14, shows that, on the average, the high-reliability system serves smaller areas for each circuit, and therefore it has less exposure per feeder and less outages per consumer. Details of the method of calculating outages for the different systems were given in chapter 11. These outage results are summarized in tables C.14 and C.15. 248 APPENDIXES Figure C. 10. Areas Served by Four Existing Circuits in 1976 N I H G F E D C B 1 2 3 4 S 6 7 8 9 10 1 Note: The substation is indicated by the solid black square. Each pattern iden- tifies a separate circuit LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 249 12 13 14 15 16 17 18 19 20 21 22 250 APPENDIXES Figure C. 11. A reas Served by Low- and Medium-Reliability Circuits in 1988 0 N m L KX. H G F E D c .2 B A 1 2 3 4 5 6 7 8 9 10 1 Note: Substations are indicated by solid black squares. Each pattern identifies a separate circuit. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 251 . 1 4 1 6 1 . 19 #ell1 li L lEM ii 12 13 .1 15 16 i 18 19.. 21 2 252 APPENDIXES Figure C. 12. Areas Served by Low- and Medium-Reliability Circuits in 1996 0 N M L K I -.*-f- --- - -- ------ I H G E - D C B A 1 2 3 4 5 6 7 8 9 10 1 Note: Substations are indicated by solid black squares. Each pattern identifies a separate circuit. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 253 ...MB... ---- -- . .. . . . . . ... . .. . . . .l.... .. 12 13 14 15 16 17 18 19 20 21 22 254 APPENDIXES Figure C.13. Areas Served by High-Reliability Circuits in 1988 0 N M * L K JS I H G F E D C B A 1 2 3 4 5 6 7 8 9 10 1 Note: Substations are indicated by solid black squares. Each pattern identifies a separate circuit. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 255 12 13 14 15 16 17 18 19 20 21 22 256 APPENDIXES Figure C.14. Areas Served by High-Reliability Circuits in 1996 0 N M L K H G F E D c B 1 2 3 4 5 6 7 8 9 10 1 Note Substations are indicated by solid black squares. Each pattern identifies a separate circuit. LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 257 12 13 14 15 16 17 18 19 20 21 22 258 APPENDIXES Table C.14. Annual Outages, by Feeder, for the Low- and Medium-Reliability Systems Daily Period, 0001-0800 Daily period, Feeders 1976 1980 1984 1988 1992 1996 1976 1980 North 1 12 8 10 8 9 8 31 20 North 2 16 7 9 6 4 5 41 18 North 3 9 11 8 5 3 2 39 25 North 4 - - 7 8 8 8 24 29 East 1 - - - 9 6 6 - - East 2 - - - 3 4 8 - - East 3 - - - - 2 2 - - East 4 - - - - 2 2 - - Southeast 1 - - 6 2 2 2 - - Southeast 2 - - 4 5 1 1 - - Southeast 3 - - - - 4 1 - - Southeast 4 - - - - 0 3 - - South 1 - 16 8 10 11 7 - 40 South 2 - 16 11 8 9 8 - 42 Southwest 1 - - 7 6 5 6 - - Southwest 2 - - - 6 3 4 - - Southwest 3 - - - - 10 5 - - Southwest 4 - - - - - 7 - - Northwest 1 - - - 7 5 2 - - Northwest 2 - - - 8 9 11 - - Central 1 - - - - 4 2 - - Central 2 - - - - 4 4 - - Central 3 - - - - - 4 - - Central 4 - - - - - 5 - - Averages 13 11 8 7 5 5 34 29 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 259 0801-1800 Daily period, 1801-2400 1984 1988 1992 1996 1976 1980 1984 1988 1992 1996 25 20 24 20 17 11 13 11 13 11 22 15 9 13 22 10 12 8 5 7 20 12 7 4 21 13 10 7 4 2 17 20 20 21 13 16 9 11 11 11 - 22 15 15 - - - 12 8 8 - 7 11 19 - - - 4 6 10 - - 5 5 - - - - 3 3 - - 5 5 - - - - 3 3 15 5 5 4 - - 8 3 3 2 11 12 1 2 - - 6 6 1 1 - - 11 3 - - - - 6 2 - - - 8 - - - - - 4 22 27 27 19 - 21 12 14 15 10 28 21 22 20 - 22 15 11 12 11 21 16 12 16 - - 11 9 6 9 17 16 7 10 - - 9 9 4 5 - - 25 14 - - - - 13 7 - - - 19 - - - - - 10 - 19 13 4 - - - 10 7 2 - 20 23 28 - - - 11 12 15 - - 10 6 - - - 5 3 - - 11 11 - - - 6 6 - - - 10 - - - - - 6 - - 13 - - - - - 7 20 17 13 12 18 16 11 9 7 6 260 APPENDIXES Table C. 15. Annual Outages, by Feeder, for the High-Reliability System Daily period, 0001-0800 Daily period, Feeders 1976 1980 1984 1988 1992 1996 1976 1980 North 1 12 8 12 8 9 6 31 20 North 2 16 4 4 3 4 3 41 11 North 3 15 4 4 4 3 2 29 9 North 4 9 7 7 6 6 6 24 19 North 5 - - - - - 4 - - East 1 - - - 9 6 6 - - East 2 - - - 2 5 1 - - East 3 - - - 2 1 8 - - East 4 - - - - 1- East 5 - - - - - I - - East 6 - - 4 - - I - - Southeast 1 - - 2 2 2 1 - - Southeast 2 - - - 1 1 1 - - Southeast 3 - - - 5 5 2 - - Southeast 4 - - - - 3 2 - - Southeast 5 - - - - - 6 - - Southeast 6 - - - - - 0 - - Southeast 7 - - - - - 2 - - South 1 - 6 6 8 7 6 - 16 South 2 - 8 8 5 6 4 - 21 South 3 - 6 6 6 5 4 - - South 4 - 11 9 5 6 3 - 28 South 5 - - - - - 5 - - Southwest 1 - 10 7 8 10 6 - 24 Southwest 2 - 6 5 3 3 3 - 14 Southwest 3 - - 6 3 5 3 - - Southwest 4 - - - 4 4 4 - - Southwest 5 - - - - - 4 - - Southwest 6 - - - - - 2 - - Northwest 1 - - - 4 3 3 - - Northwest 2 - - - 7 5 3 - - Northwest 3 - - - 5 4 3 - - Northwest 4 - - - - - 2 - - Central I - - - - 2 3 - 15 Central 2 - - - - 4 2 - - Central 3 - - - - - 4 - - Central 4 - - - - - 2 - - Averages 13 7 6 5 4 3 34 18 LOAD FORECASTING AND DISTRIBUTION PRIMARY MODELS 261 0801-1800 Daily period, 1801-2400 1984 1988 1992 1996 1976 1980 1984 1988 1992 1996 31 21 22 26 17 11 17 11 12 9 11 8 9 7 22 6 6 5 5 4 9 9 7 6 21 5 5 5 4 3 19 15 15 15 13 10 10 8 8 8 - - 11 - - - - - 6 - 23 15 15 - - - 12 8 8 - 5 13 3 - - - 3 7 2 - 4 3 20 - - - 2 2 11 - - 3 2 - - - - 1 1 -- - 2 - - - - - 1 - - - 2 - - - - - 1 11 5 5 2 - - 6 3 3 1 5 2 2 2 - - 3 1 1 1 - 12 13 5 - - - 6 7 3 - - 8 4 - - - - 5 2 - - - 14 - - - - - 8 - - - 1 - - - - - 1 - - - 4 - - - - - 2 16 21 18 15 - 9 9 11 10 8 21 14 16 11 - 11 11 7 8 6 15 15 13 10 - 8 8 8 7 5 24 13 16 9 - 15 13 7 9 5 - - - 14 - - 0 0 - 7 19 20 25 16 - 13 10 10 13 9 12 9 9 7 - 8 6 5 5 4 16 7 13 7 - - 9 4 7 4 - 10 11 11 - - - 5 6 6 - - - 11 - - - - - 6 - - - 6 - - - - - 3 - 10 9 7 - - - 5 5 4 - 17 14 9 - - - 9 7 5 - 13 10 8 - - - 7 5 4 - - - 6 - - - - - 3 - - 6 9 - - - - 3 5 - - 10 6 - - - - 5 3 - - - 10 - - - - - 5 - - - 6 - - - - - 3 16 12 11 9 18 10 9 6 6 5 Appendix D Outage and Supply Cost Computations Outage Costs and Energy The expected annual frequency and duration' of outages correspond- ing to each system plan were available for the three daily periods- 0001 to 0800, 0801 to 1800, and 1801 to 2400 hours-by geographic cell over the twenty-year period, 1976 to 1996. These values were used to estimate disaggregate outage costs and outage energy for the nineteen types of consumers in each of the 247 geographic cells at the four-year intervals: 1976, 1980, 1984, 1988, 1992, and 1996. Corresponding results for intermediate years were determined by linear interpolation.2 The detailed outage costs could then be aggregated in various ways for further analysis. The following formulas were used in the computerized model that generated outage costs and energy loss caused by outages. 1. A more refined analysis would use a spread of values for outage duration based on some probability density function. In this study, however, the mean outage duration is used, because the quality of available data does not warrant a more sophisticated measure of outage duration. 2. This procedure involves negligible error, because of the smooth evolution over time of the system planning process and the simulations carried out. 262 OUTAGE AND SUPPLY COST COMPUTATIONS 263 OCR" ,,t* (SR*f,* OC1s, = nj.,,,t*yj.j* ( sfo, dnt 3 OC,r , t= q,.2,e * OF [S, *f, * (d.. m=1 OCI, = g* k,, * E (S * f.,,t *dm.,,) OC", = v * B, (S *f,,,,,, * d,, t -ak2 3 OExI". =*t., e,e*f m d.m,t.) nl~,,.t * (e'l * m, m-=1 OE = q* [eq,,,*St S_f, (,, . + ',(d,..,)}] m-1 OE,,, = E;c.,,,,s (S * fm.,,., dm, t) m-2 OE p= *t E Z (S d,,,,,,, ,,, n,42 = B ,, * E (e" * S" jf, * d,..) m,2 OES, = Es (SS * f2.,,,t ,, where superscripts R = residential; I = industrial; C = .ommercial; P = public illumination; H = hospitals; S = schools; and where subscripts i = 1, . . . , 247 (city geographic cell index); j = 1, . . . , 10 (industrial sector index); k = 1, . . . , 3 (commercial class index); I = 1, . . ., 4 (residential income class index); m = 1 (0001 to 0800 hours), 2 (0801 to 1800 hours), 3 (1801 to 2400 hours) - (daily period index); and t = 1, . . ., 21 (year index). Variables and coefficients which depend on the above indexes are: OC',, and OC',,,, = annual outage costs for consumer category a, subcategory b (Cr$); OE?,1 and OE',, = annual outage energy for consumer category a, subcategory b (kilowatt-hours); 264 APPENDIXES f.',, = annual frequency of outages; d-, = mean duration of outages (hours); n = number of households; yj,j = mean income earning rate (Cr$ per hour); q,,, = annual value added (Cr$ a year); OCF, = industrial outage cost function (see table 12.3); K,, = value of capital stock used for public illumina- tion (Cr$); B, = number of hospital beds; ,= mean kilowatt-hour consumption per hour for each household; E., = mean kilowatt-hour consumption per hour of operation for every unit value added; j = restart time function; Ef EP, and E ,, = total kilowatt-hour consumption for each hour; H eH = mean kilowatt-hour consumption per hour per hospital bed; sa or s"M = scale factor, if normal hours of activity by customer category a does not correspond to hours falling within time period m; g = annuitizing factor for public illumination (Cr$ per hour of usage per Cr$ of capital stock); v = outage cost per hour for each hospital bed (Cr$ per hour per bed). Typical computer printouts of disaggregate results are presented in table D.1. Tables D.2 to D.10 and figures D.1 to D.3 show these results aggregated in different ways (for example, by cell, by consumer type, discounted over time, and so on). Supply Costs and Sensitivity Testing The stream of distribution system costs corresponding to the four basic plans are shown in tables D. 11 to D. 14, which include the effects of shadow wage rates, applied to the labor component of costs as described in chapter 14. Some sensitivity testing was also carried out. The param- eter that had the greatest effect on the computations was the discount rate. Figure D.4 summarizes the effect of using three different discount OUTAGE AND SUPPLY COST COMPUTATIONS 265 rates-8, 10, and 12 percent-to represent the opportunity cost of capi- tal. Although the actual present discounted values changed, the major results and conclusions regarding the optimum range of reliability levels were basically unaltered. Using a shadow wage rate of 0.8 times the market wage rate for the unskilled component of labor in the evaluation of supply costs also had negligible effect on the results. Finally, a varia- tion of the shadow exchange rate in the range 1.0 to 1.25 times the official exchange rate did not affect the results, because there were hardly any imported items. 266 APPENDIXES Table D.1. Medium-Reliability Plan B: Disaggregate Data Residental, by income Special instiutions Lower- Upper- Lower middle middle Upper Hospitals Schools Plan 2, year 1, cell 96, square 454, feeder 0. Outage cost 274.36 417.88 1,308.64 1,022 87 000 0.00 Outage energy 8 37 13 00 4007 26 89 0.00 0 00 Total energy 3,067 75 4,762 46 14,681.58 9,850 01 0 00 0.00 Outage rate 0.2730 0 2730 0.2730 0.2730 - - Plan 2, year 1, cell 97, square 455, feeder 0 Outage cost 0 00 0.00 0.00 0.00 0.00 0 00 Outage energy 0 00 0 00 0 00 0 00 0.00 0 00 Total energy 0.00 0.00 0.00 0.00 0.00 0.00 Outage rate - - - - - Plan 2, year 1, cell 98, square 456, feeder 0. Outage cost 254.77 948.52 1,53020 633.20 0.00 0.00 Outage energy 7 77 29.43 46.82 16.63 000 0.00 Total energy 4,601 63 17,46236 27,731 88 9,850.01 000 0.00 Outage rate 0.1688 0 1688 0.1688 0.1688 - - Plan 2, year 1, cell 99, square 457, feeder 0. Outage cost 101 91 948.52 1,440.19 422.14 000 000 Outage energy 3.11 2948 4406 11 09 000 000 Total energy 1,840 65 17,462 36 26,100.60 6,566 67 000 0.00 Outage rate 0.1688 0.1688 0.1688 0 1688 - - Plan 2, year 1, cell 88, square 446, feeder 0. Outage cost 2221 4,679.58 9,769 76 11,316 49 000 0.00 Outage energy 0.68 145 16 298.33 296 62 0.00 0 00 Total energy 30678 65,880.72 135,396.84 134,616.76 000 0.00 Outage rate 0.2203 0.2203 0 2203 0 2203 - Plan 2, year 1, cell 89, square 447, feeder 0. Outage cost 0.00 4,56682 9,76976 11,31649 0.00 000 Outage energy 000 141.66 298.33 29662 0.00 000 Total energy 000 64,293 23 135,396.84 134,61676 0.00 0.00 Outage rate - 0.2203 0.2203 0 2203 - - Plan 2, year 1, cell 90, square 448, feeder 0. Outage cost 0.00 3,946.63 8,828.10 10,21244 0 00 000 Outage energy 0.00 122 43 269.58 267 68 0 00 0 00 Total energy 613.55 61,118.26 127,240.40 121,483.42 92,667.00 0.00 Outage rate - 0.2203 0.2203 0.2203 - - Plan 2, year 1, cell 91, square 449, feeder 0. Outage cost 44.42 4,341.30 9,181.22 10,21244 78555 0.00 Outage energy 1.35 134.67 280.36 267.68 133.64 0.00 Total energy 613.55 61,118.26 127,240.40 121,483 42 92,667.00 0.00 Outage rate 0 2203 0.2203 0.2203 0.2203 0.1442 - OUTAGE AND SUPPLY COST COMPUTATIONS 267 Main industry, by kind Metallurgy Non- Public and metallic Vegetable Food and illununa- mechanical minerals Wood oils beverage Other tion 0.94 1 88 48.63 9834 51 61 1825 2968 004 0.16 064 400 2 31 0.80 6830 21.68 68 55 36967 461 86 278.40 10564 19,552.00 0 1742 02326 0 1742 08658 0.8288 07580 03493 000 000 0.00 000 000 0.00 0 00 0.00 0.00 0 00 0.00 0 00 0 00 0 .00 000 000 000 000 000 000 0 00 0 62 1 24 32.15 63 91 33 99 1206 2296 002 0 11 0.43 2.62 1 52 053 52 84 2329 73 65 397.15 496 19 299.09 113.49 24,885.00 0.1072 0.1431 01072 05287 05071 0.4664 02123 0.00 000 0 00 0.00 0 00 0 00 24.60 000 0.00 000 000 000 0.00 5661 10.00 0 00 0.00 0 00 0.00 0.00 26,662 00 - - - - - 02123 37 73 75.24 1,94694 3,964.12 2,07644 73045 36 15 1 51 638 2579 161.21 9300 3206 83 19 1,091.73 3,45275 18,618 54 23,261 66 14,021 45 5,32052 29,625.00 0.1385 0.1849 0 1385 06930 06632 0.6024 0.2808 81.20 161.92 4,19002 8,531 20 4,46873 1,57201 36 15 3 25 3.75 55.50 346.94 200 14 68.99 83.19 2,349 51 7,430.68 40,069.07 50,061.57 30,175 65 11,450.33 29,625.00 0 1385 0 1849 0.1385 0.6930 06632 06025 0.2808 9.91 19.75 511.16 1,04075 545.16 191.77 36.15 040 1.68 677 42.33 2442 842 83 19 28663 90650 4,888.18 6,10720 3,681 24 1,396.87 29,62500 0.1385 0.1849 0 1385 06930 06632 06025 02808 768 15 33 39675 80782 423 14 148.85 35 71 031 1 30 525 3285 1895 6 53 82 19 222.48 703 61 3,794.14 4,740.34 2,857 34 1,084.23 29,26900 0.1385 0.1849 0.1385 06930 06632 06025 0.2808 268 APPENDIXES Table D.1 (continued) Service industry, by kind Water and Metallurgy Commercial, by kind Tele- sewer- and phone age mechanical Other Light Medium He Plan 2, year 1, cell 96, square 454, feeder 0 Outage cost 0 00 0 00 0 00 0.00 0.00 0.00 Outage energy 0.00 0.00 0.00 0 00 38.25 0.00 Total energy 0.00 0 00 0 00 0.00 17,990 00 0 00 Outage rate - - - - 0.2126 - Plan 2, year 1, cell 97, square 455, feeder 0. Outage cost 0.00 0 00 0.00 0.00 0 00 0.00 Outage energy 0.00 0.00 0.00 0.00 0.00 0 00 Total energy 0.00 0 00 0.00 0.00 0 00 0 00 Outage rate - - - - - - Plan 2, year 1, cell 98, square 456, feeder 0. Outage cost 0.00 0.00 0.00 0.00 0.00 0 00 Outage energy 000 000 0.00 000 8 25 18563 Total energy 0.00 000 000 000 6,286.00 141,512.00 Outage rate - - - - 0.1312 0.1312 Plan 2, year 1, cell 99, square 457, feeder 0. Outage cost 303 73 000 0.00 98.35 0.00 0 00 Outage energy 12.30 43.28 54.10 3 94 22 18 87.75 Total enregy 6,774 50 40,363.49 50,449 30 3,675.85 16,906.00 66,897.00 Outage rate 0.1815 0.1072 0 1072 0.1072 0.1312 0.1312 Plan 2, year 1, cell 88, square 446, feeder 0 Outage cost 0 00 0.00 0.00 0.00 0.00 0.00 Outage energy 000 000 0.00 0.00 36 55 17 53 11( Totalenergy 0 00 0 00 0.00 000 21,458 00 10,292 00 64,941 Outage rate - - - - 0.1703 0 1703 0 1 Plan 2, year 1, cell 89, square 447, feeder 0 Outage cost 0 00 0.00 0.00 0 00 0 00 0 00 Outage energy 000 000 000 000 3876 000 11( Total energy 0 00 0.00 0 00 0.00 22,759 00 0.00 64,941 Outage rate - - - - 0 1703 - 01 Plan 2, year 1, cell 90, square 448, feeder 0. Outage cost 0.00 0 00 0.00 0.00 0 00 0.00 Outage energy 0.00 000 0.00 0.00 41.81 0.00 9( Total energy 0 00 0.00 0.00 0.00 24,547.00 0.00 53,041 Outage rate - - - - 0.1703 - 0 1 Plan 2, year 1, cell 91, square 449, feeder 0. Outage cost 0 00 0.00 0.00 0.00 0 00 0 00 ( Outage energy 0 00 0.00 0.00 000 36.11 49.11 94 Total energy 0.00 0.00 0.00 0.00 21,201.00 28,832.00 55,613 Outage rate - - - - 0.1703 0.1703 0.1 OUTAGE AND SUPPLY COST COMPUTATIONS 269 Table D.2. Medium-Reliability Plan B: Residential, Public Illumination, and Hospital Outage Costs, by Year (thousands of Cr$) Residential, by income group Public Lower- Upper- illumi- Hospi- Year Lower middle middle Upper Total nation tals 1976 10.78 144.58 241.38 212.13 608.87 4.13 5.72 1977 21.75 230.63 362.47 296.23 911.09 5.13 6.11 1978 32.73 316.69 483.57 380.32 1,213.31 6.12 6.50 1979 43.71 402.74 604.66 464.42 1,515.52 7.12 6.88 1980 54.68 488.80 725.75 548.51 1,817.74 8.11 7.27 1981 59.06 534.64 778.92 575.72 1,948.33 7.98 8.59 1982 63.44 580.48 832.08 602.92 2,078.92 7.86 9.90 1983 67.82 626.32 885.25 630.12 2,209.51 7.73 11.21 1984 72.20 672.16 938.41 657.32 2,340.10 7.61 12.53 1985 85.06 762.93 1,049 02 706.91 2,603.92 8.02 12.10 1986 97.91 853.70 1,159 64 756.51 2,867.74 8.44 11.67 1987 110.76 944.46 1,270.25 806.09 3,131.56 8.85 11.24 1988 123.61 1,035.23 1,380.86 855.68 3,395.38 9.27 10.82 1989 147.16 1,079.75 1,418.40 851.10 3,496.41 9.51 11.27 1990 170.71 1,124.27 1,455.95 846.51 3,597.44 9.76 11.73 1991 194.27 1,168.79 1,493.49 841.93 3,698.47 10.00 12.19 1992 217.82 1,213.31 1,531.04 837.35 3,799.50 10.24 12.65 1993 241.88 1,310.96 1,677.96 923.69 4,154.48 10.22 13.46 1994 265.94 1,408.61 1,824.88 1,010.04 4,509.46 10.20 14.27 1995 290.00 1,506.26 1,971.80 1,096.38 4,864.44 10.18 15.08 1996 314.07 1,603.91 2,118.72 1,182.73 5,219.42 10.16 15.89 270 APPENDIXES Table D.3. Medium-Reliability Plan B: Industrial Outage Costs, by Year and Kind of Industry (thousands of Cr$) Main industry, by kind Metal- lurgy and Nonme- Food me- tallic Vege- and chani- min- table bev- Year cal erals Wood oils erages Other Total 1976 9.02 17.98 465.37 938.12 493 66 174.60 2,098.75 1977 11.38 2262 513.67 1,265.19 589.58 206.45 2,608.90 1978 13.75 27.26 561.98 1,592.27 685.50 238.30 3,119.05 1979 16.11 31.90 610.28 1,919.34 781.42 270.15 3,629.21 1980 18.48 36.54 658.59 2,246.41 877.34 302.01 4,139.36 1981 17.00 33 58 574.42 2,052.71 790.94 272.52 3,741.17 1982 15.52 30.63 490.25 1,859.01 704.55 243.03 3,342.98 1983 14.04 27.68 406.07 1,665.30 618.15 213.55 2,944.79 1984 12.56 24.73 321.90 1,471.60 531.75 184.06 2,546.60 1985 13.35 26.31 314.40 1,605.41 555.41 190.03 2,704.92 1986 14.15 27.91 306 89 1,739.22 579 07 196.00 2,863.24 1987 14.95 29 50 299.39 1,873.03 602.72 201.97 3,021.56 1988 15.74 31.09 291.88 2,006.84 626.38 207.95 3,179.88 1989 15.78 31.14 272.00 1,874.30 609.05 203.08 3,005.36 1990 15.81 31.20 252.13 1,741.76 591.73 198.22 2,830.84 1991 15.85 31.25 232.25 1,609.22 574.40 193.36 2,656.32 1992 15.88 31.31 212.37 1,476.67 557.08 188.49 2,481.81 1993 17.71 34.91 215.20 1,717.66 602.95 203.33 2,791.76 1994 19.54 38.51 218.03 1,958.64 648.83 218.16 3,101.71 1995 21.37 42.11 220.85 2,199.62 694.70 233.00 3,411.65 1996 23.20 45.72 223.68 2,440.60 740.58 247.83 3,721.60 OUTAGE AND SUPPLY COST COMPUTATIONS 271 Service industry, by kind Water and Metallurgy Tele- sewerage and Industry phone treatment mechanical Other Total total 32.57 0.00 0.00 10.45 43.02 2,141.77 41.92 000 0.00 1327 55.19 2,664.10 51.28 0.00 0.00 16.09 67.37 3,186.42 60.63 0.00 0.00 18.92 79.54 3,700.75 69.98 0.00 0.00 21.74 91.72 4,231.08 67.46 0.00 0.00 21.24 88.70 3,829.87 64.94 0.00 0 00 20.73 85.67 3,428.65 62.42 0.00 0.00 20 23 82.65 3,027.44 59.90 0.00 0.00 19.73 79.63 2,626.23 67.56 0.00 0.00 22.82 90.38 2,795.30 75.22 0.00 0.00 25.90 101.12 2,964.36 82.89 0.00 0.00 28.99 111.87 3,133.43 90.55 0.00 0.00 32.08 122.62 3,302.50 111.83 0.00 0.00 40.22 152.05 3,157.41 133.11 0.00 0.00 48.37 181.49 3,012.33 15440 0.00 0.00 56.52 210.92 2,887 24 175.68 0.00 0.00 64.67 240.35 2,722.16 182.92 0.00 0.00 69.40 252.32 3,04407 190.15 0.00 0.00 74.14 264.29 3,365.99 197.38 000 0.00 78.88 276.26 3,687.91 204.61 0.00 0.00 83.61 288.23 4,009.83 272 APPENDIXES Table D.4. Medium-Reliability Plan B: Present Discounted Values of Outage Costs (thousands of Cr$) Residential, by income group Dis- Public count Lower- Upper- illumi- rate Lower middle middle Upper Total nation 0.08 1,432.82 9,571.52 13,044.84 8,292.33 32,341.51 97.58 0.10 1,078.92 7,475.60 10,260.74 6,646.71 25,461.98 80.62 0.12 833.10 5,983.41 8,273.23 5,458.70 20,548.45 68.10 0.14 658.72 4,897.01 6,821.65 4,580.56 16,957.93 58.65 Special institutions Commercial, by kind Dis- count Hospi- rate tals Schools Light Medium Heavy Total 0.08 126.39 - - - - - 0.10 102.91 - - - - - 0.12 85.82 - - - - - 0.14 73.07 - - - - - -, Negligible. OUTAGE AND SUPPLY COST COMPUTATIONS 273 Main industry, by kind Metal- lurgy and Nonme- Food me- tallic Vege- and chani- min- table bev- cal erals Wood oils erages Other Total 193.76 382.75 4,900.78 21,915.50 8,056.47 2,755.84 38,205.11 160.34 316.85 4,349.12 18,244.75 6,833.28 2,342.61 32,246.95 135.93 268.69 3,916.67 15,541.24 5,921.10 2,033.95 27,817.59 117.63 232.60 3,569.67 13,498.74 5,223.30 1,797.45 24,439.40 Service industry, by kind Metal- Water lurgy and and Tele- sewerage mechani- Industry phone treatment cal Other Total total 1,178.30 0.00 0.00 427.94 1,606.24 39,811.35 923.09 0.00 0.00 330.14 1,253.23 33,500.17 742.85 0.00 0.00 261.75 1,004.60 28,822.18 612.65 0.00 0.00 212.87 825.53 25,264.92 274 APPENDIXES Table D.5. Medium-Reliability Plan B: Present Discounted Values of Outage Energy (megawatt-hours) Residential, by income group Dis- Public count Lower- Upper- illumi- rate Lower middle middle Upper Total nation 0.08 83.08 552 97 703.70 382.09 1,721.83 224.59 0.10 62.60 432.61 556.84 308.69 1,360.74 185.54 0.12 48.37 346.82 451.59 255.38 1,102.16 156.73 0.14 38.28 284.28 374.40 215.75 912.70 134.97 Special institutions Commercial, by kind Dis- count Hospi- rate tals Schools Light Medium Heavy Total 0.08 21.50 2.02 178.04 378.17 504.32 1,060.53 0.10 17.51 1.53 139.04 298.61 403.80 841.44 0.12 14.60 1.18 111.39 241.64 331.32 684.35 0.14 12.43 0.93 91.34 199.93 277.80 569.08 OUTAGE AND SUPPLY COST COMPUTATIONS 275 Main industry, by kind Metal- lurgy and Nonme- Food me- tallic Vege- and chani- min- table bev- cal erals Wood oils erages Other Total 7.77 32.13 67.17 667.62 367.99 120.91 1,263.59 6.43 26.60 59.55 564.60 311.74 102.78 1,071.70 5.45 22.57 53.58 487.92 269.83 89.24 928.58 4.71 19.54 48.79 429.37 237.80 78.86 819.07 Service industry, by kind Metal- Water lurgy and and sewerage mechani- Industry Telephone treatment cal Other Total total 47.75 119.93 235.60 17.15 420.43 1,684.02 37.40 95.92 181.74 13.23 328.30 1,400.00 30.10 78.77 144.09 10.49 263.45 1,192.03 24.82 66.24 117.17 8.53 216.77 1,035.84 276 APPENDIXES Table D.6. Medium-Reliability Plan B: Present Discounted Values of Total Energy (megawatt-hours) Residential, by income group Dis- Public count Lower- Upper- illumi- rate Lower middle middle Upper Total nation 0.08 35,476.61 256,069.68 328,299.09 180,792.91 800,638.29 92,818.21 0.10 26,233.53 195,030.37 252,343.16 141,217.87 614,824.93 73,938.12 0.12 19,871.61 152,232.23 198,966.69 113,124.86 484,095.38 60,367.79 0.14 15,404.13 121,582.40 160,397.85 92,734.31 390,118.68 50,389.69 Special institutions Commercial, by kind Dis- count Hospi- rate tals Schools Light Medium Heavy Total 0.08 17,865.94 1,739.19 117,423.62 276,962.35 441,747.71 836,133.67 0.10 14,305.84 1,346.20 89,646.58 211,507.06 337,393.01 638,546.65 0.12 11,729.74 1,068.15 70,176.01 165,606.47 264,205.49 499,987.98 0.14 9,822.65 867.08 56,234.03 132,725.64 211,771.25 400,730.91 OUTAGE AND SUPPLY COST COMPUTATIONS 277 Main industry, by kind Metal- lurgy and Nonme- Vege- Food mechani- tallic table and cal minerals Wood oils beverages Other Total 17,042.28 53,703.16 96,375.59 245,557.35 148,025.01 56,112.28 616,815.66 12,676.73 39,951.67 77,452.55 186,949.03 112,693.67 42,719.25 472,442.90 9,677.42 30,503.30 63,863.91 146,184.74 88,119.57 33,404.10 371,753.04 7,574.30 23,877.71 53,875.12 117,216.16 70,656.47 26,784.56 299,984.32 Service industry, by kind Metal- Water lurgy and and Tele- sewerage mechani- Industry phone treatment cal Other Total total 24,267.45 112,075.27 234,380.65 17,061.92 387,785.28 1,004,600.94 18,319.33 86,006.77 174,286.81 12,688.07 291,300.97 763,743.87 14,201.62 67,799.96 133,013.15 9,683.92 224,698.64 596,451.68 11,290.24 54,803 20 104,081.58 7,578.02 177,753.04 477,737.36 278 APPENDIXES Table D.7. Medium-Reliability Plan B: Present Discounted Values of Outage Rates [(outage energy/total energy) x 100] Residential, by income group Dis- Public count Lower- Upper- illumi- rate Lower middle middle Upper Total nation 0.10 0.2342 0.2159 0.2143 0.2113 0.2151 0.2420 0.10 0.2386 0.2218 0.2207 0.2186 0.2213 0.2509 0.12 0.2434 0.2278 0.2271 0.2258 0.2277 0.2596 0.14 0.2485 0.2338 0.2334 0.2327 0.2340 0.2679 Special institutions Dis- Commercial, by kind count Hospi- rate tals Schools Light Medium Heavy Total 0.08 0.1203 0.1160 0.1516 0.1078 0.0750 0.1268 0.10 0.1224 0.1134 0.1986 0.1412 0.0982 0.1318 0.12 0.1245 0.1106 0.2537 0.1803 0.1254 0.1369 0.14 0.1266 0.1076 0.3166 0.2250 0.1564 0.1420 OUTAGE AND SUPPLY COST COMPUTATIONS 279 Main industry, by kind Metal- lurgy and me- Nonme- Vege- Food chani- tallic table and cal minerals Wood oils beverages Other Total 0.0456 0.0598 0.0697 0.2719 0.2486 0.2155 0.2049 0.0507 0.0666 0.0769 0.3020 0.2766 0.2406 0.2268 0.0563 0.0740 0.0839 0.3338 0.3062 0.2671 0.2498 0.0622 0.0818 0.0906 0.3663 0 3366 0.2944 02730 Service industry, by kind Metal- Water lurgy and and sewerage mechani- Industry Telephone treatment cal Other Total total 0.1967 0.1070 0.1005 0.1005 0.1084 0.1676 0.2042 0.1115 0.1043 0.1043 0.1127 0.1833 0.2119 0.1162 0.1083 0.1083 0.1172 0.1999 0.2199 0.1209 0.1126 0.1126 0.1220 0.2168 280 APPENDIXES Table D.8. Medium-Reliability Plan B: Present Discounted Values of Outage Costs (Cr$/kilowatt-hours lost) Residential, by income group Dis- Public count Lower- Upper- illumi- rate Lower middle middle Upper Total nation 0.08 17.25 17.30 18.54 21.70 18.78 0.43 0.10 17.23 17.28 18.43 21.53 18.71 0.43 0.12 17.22 17.25 18.32 21.37 18.64 0.43 0.14 17.21 17.23 18.22 21.23 18.58 0.43 Special institutions Commercial, by kind Dis- count Hospi- rate tals Schools Light Medium Heavy Total 0.08 5.88 - - - - - 0.10 5.88 - - - - - 0.12 5.88 - - - - - 0.14 5.88 - - - - - -, Negligible. OUTAGE AND SUPPLY COST COMPUTATIONS 281 Main industry, by kind Metal- lurgy and Nonme- Vege- Food mechani- tallic table and cal minerals Wood oils beverages Other Total 24.95 11.91 72.96 32.83 21.89 22.79 30.24 24.95 11.91 73.03 32.31 21.92 22.79 30.09 24.95 11.91 73.10 31.85 21.94 22.79 29.96 24.95 11.90 73.17 31.44 21.97 22.79 29.84 Service industry, by kind Metal- Water lurgy and and Indus- sewerage mechani- try Telephone treatment cal Other Total total 24.68 0.00 0.00 24 95 3.82 23.64 24.68 0.00 0.00 24.95 3.82 23.93 24.68 0.00 0.00 24.95 3.81 24.18 24.68 0.00 0.00 24.95 3.81 24.39 282 APPENDIXES Table D.9. Medium-Reliability Plan B: Grand Total, by Year Outage Outage costs Outage Total Outage rate cost (thou- energy energy outage (Cr$/ sands (mega- (mega- energy x 100 kilowatt- of watt- watt- total hours Year Cr$) hours) hours) \energy lost) 1976 2,760.49 161.19 53,490.19 0.3013 17.13 1977 3,586.42 206.28 64,532.89 0.3197 17.39 1978 4,412.35 251.37 75,575.59 0.3326 17.55 1979 5,238.27 296.47 86,618.29 0.3423 17.67 1980 6,064.20 341.56 97,66099 0.3497 17.75 1981 5,794.77 338.73 114,869.91 0.2949 17.11 1982 5,525.34 335.89 132,078.82 0.2543 16.45 1983 5,255.90 333.06 149,287.74 0.2231 15.78 1984 4,986.47 330.23 166,496.65 0.1983 15.10 1985 5,419.34 359.63 189,420.69 0 1899 15.07 1986 5,852.22 389.03 212,344.73 0.1832 15.04 1987 6,285 09 418 43 235,268.78 0.1779 15.02 1988 6,717.97 447.83 258,192.82 0.1734 15.00 1989 6,674.61 459.10 290,316.28 0.1581 14.54 1990 6,631.26 470.36 322,439.74 0.1459 14.00 1991 6,587.91 481.63 354,563.20 0.1358 13.68 1992 6,544.55 492.89 386,686.66 0.1275 13.28 1993 7,222.24 532.15 427,328.90 0.1245 13.57 1994 7,899.93 571.40 467,971.14 0.1221 13.83 1995 8,577.61 610.66 508,613.38 0.1201 14.05 1996 9,255.30 649.91 549,255.61 0.1183 14.24 OUTAGE AND SUPPLY COST COMPUTATIONS 283 Table D.10. Medium-Reliability Plan B: Present Discounted Values of the Grand Totals Outage Outage Outage Total Outage rate cost costs energy energy outage (Cr$/ Dis- (thou- (mega- (mega- energy X 100 kilowatt- count sands watt- watt- total hours rate of Cr$) hours) hours) energy lost) 0.08 72,376.82 4,714.49 2,753,796.25 0.1712 15.35 0.10 59,145.68 3,806.76 2,106,705.61 0.1807 15.54 0.12 49,524.55 3,151.05 1,653,700.71 0.1905 15.72 0.14 42,354.57 2,665.96 1,329,666.36 0.2005 15.89 284 APPENDIXES Figure D. 1. Medium-Reliability Plan B: Present Discounted Value of Outage Energy, by Cell (megawatt-hours) 0 N 0 2 2 0 1 m 4 4 5 N,3 K4 0 L 0 5 5 4 5 3 4 5 K 0 5 14 10 10 11 5 8 3 6 15 12 13 17 12 15 1 5 13 30 31 27 21 38 H 2 4 5 14 59 58 67 52 47 G 0 3 5 6 14 12 18 22 31 49 F 0 2 0 1 5 15 10 9 10 19 36 E 1 2 2 3 13 7 11 19 12 20 22 D 1 2 4 5 7 5 15 7 12 23 27 C 016 5 5 8 7 21 B 5 11 10 10 102 8- 24 A 9 _ ,5 1 2 11 7 33 8 12 39 1 2 3 4 6 7 8 9 10 11 Note. Discount rate = 12 percent. OUTAGE AND SUPPLY COST COMPUTATIONS 285 2 0 1 0 0 ,k4 3 2 0 1 11 5 JL 12 14 11 7 6) 1 2 2 1 0 11 18 18 7 11l 5 1 2 1 0 48 52 34 18 23 6 4 2 0 0 60 46 21 3 7 13 10 1 2 0 33 4 1 10 2 6 22 70 4 3 7 6 13 1 14 0 1 3 2 ýCk 25 7 6 31 9 44 37 30 7 6 00 46 46 33 34 35 33 2 3 1 5 3 2 12 13 14 15 16 17 18 19 20 21 22 286 APPENDIXES Figure D. 2. Medium-Reliability Plan B: Present Discounted Value of Total Energy, by Cell (gigawatt-hours) 0 N 0 N -v0 0 0 0 M 1 0 0 2 2 1 2 1 1 2 K 0 2 7 4 .4 4 3 3 1 2 7 5 5 7 7 12 0 2 7 12 12 10 13 23 H 1 1 2 8 39 37 38 34 37 G 0 l 2 2 8 8 10 12 18 24 F 0 0 0 0 2 8 4 5 4 9 14 E 0 1 0 1 6 4 4 6 6 9 11 D 0 1 2 9 2 2 4 2 3 8 11ý c 0 8 2 2 3 2 "12j B 4 9 9 8 6 6-'212 A--*, N 4_ 1 1 9 5 8 2 4 6 1 2 3 4 5 6 7 8 9 10 11 Note: Discount rate =12 percent. OUTAGE AND SUPPLY COST COMPUTATIONS 287 10 0 0 0 0 20 0 4 2 9E 2 I 6 11 4 3 3 1 1 1 0 0 5 9 10 3 4 2 1 1 0 0 18 29 23 9 10 2 2 0 0 0 35 31 11 1 4 8 6 1 1 0 20 2 0 0 1 3 12 4o 2 1 4 3 6 3 5 0 2 3 119 =9z4 9 4 4 2 1 9 29 29 9 3 0 4 1 1 0 1 1 0 12 13 14 15 16 17 18 19 20 21 22 288 APPENDIXES Figure D. 3. Medium-Reliability Plan B: Outage Rate, by Cell [(outage energy/total energy) X 100] 0 N /0.230 _ý,0 ý.230 0.230 0.230 m 0.234 0 230 0.23 0.230 /20 0.239 L 10.228 0.224 0.237 0.255 0.248 0.247 0.249 0.241 K 0.228 0.237 0.207 0 238 0247 0.268 0.178 0.210 0.214 0.243 0.217 0.247 0.236 0239 0.158 0.132 0.207 0.206 0.187 0.244 0.255 0.254 0.168 0.167 H 0.167 0226 0.193 0.172 0.152 0.157 0.175 0.153 0.129 G 0.165 0.223 0.230 0.229 0.174 0 151 0.177 0.178 0.169 0.208 F 0229 0.207 0.219 0.232 0.203 0.186 0.223 0.181 0.234 0.214 0.249 E 0.214 0.207 0259 0.246 0.201 0.174 0234 0.306 0.184 0.211 0.191 D 0 214 0.2071 0.198 01169 0.242 0.244 0.386 0 301 0.355 0.265 0.232 C 0.207 0 129 0.436 0.244 0.282 0.218 0.287 0.2 0.168 B 0.139 126 0.117 07.118 03; 0.145 0 \ýýý 65 0 .192 A . J.L 0117] 0.094 0.094 0.129 0.154 0.389 0.281 0.286 0.583 1e 2 3 4 5 6 7 8 9 10 11 Note: Discount rate = 12 percent. OUTAGE AND SUPPLY COST COMPUTATIONS 289 0 367ý 0.168 0.241 0.234 0.233 820 204 0.242 0.2f w 0.215 0.232 022 0.208 0.2 _ 0.234 0.211 0.129 0.249 0.244 0.20 0.141 0.242 0.154 0.191 0.192 0225 0.193 0.175 0.216 0.26 0.178 0.130 0.154 0.192 0.192 0268 0.178 0.146 0.200 0.237 0.22 0.172 0.210 0.192 0.169 0170 0.145 0.183 0.201 0.182 0.169 0.162 0.118 0 210 0.17 0 166 0.157 0.183 0.201 0 202 0.176 0.178 0.185 3 0.193 0.175 0.189 10.182 0.195 N0.198 0. 41 11 0.243 0.171 0 091 0.095 0.088 30.4 Ó 0 269 0 157 0.154 0.135 ØØ"0.088 0.102 0.152 0 129 0.330 0 270 0.264 0 .190.158 0.116 0.116 0.135 0 135 0.126 0 271 0 265 0.238\ 0.265 0.266 0 238 12 13 14 19 16 17 18 19 20 21 22 290 APPENDIXES Table D.11. Low-Reliability Distribution System Costs (1976 Cr$ - 103) and Losses Losses Recur- Mega- Investment costs rent Total Kilo- watt- Year Stations Lines costs costs watts hours 1977 0 828 16 844 719 1,851 1978 0 962 34 996 906 2,287 1979 0 1,118 55 1,173 1,124 2,793 1980 0 1,295 79 1,375 1,376 3,379 1981 15,515 576 695 16,787 1,394 3,479 1982 0 655 709 1,365 1,413 3,593 1983 15,515 743 1,333 17,592 1,436 3,723 1984 0 828 1,370 2,198 1,462 3,870 1985 0 781 1,364 2,145 1,416 3,750 1986 15,515 870 1,986 18,372 1,365 3,615 1987 0 977 2,006 2,984 1,308 3,464 1988 15,515 1,089 2,635 19,240 1,244 3,295 1989 0 679 2,647 3,327 1,356 3,591 1990 15,515 743 3,267 19,526 1,480 3,924 1991 5,973 832 3,531 10,336 1,615 4,281 1992 11,946 915 4,039 16,900 1,764 4,680 1993 0 686 4,053 4,739 1,901 5,041 1994 0 750 4,068 4,819 2,051 5,435 1995 5,973 818 4,332 11,124 2,214 5,866 1996 0 894 4,350 5,244 2,393 6,336 1997-2006 0 0 4,350 4,350 2,393 6,336 Note: The annual expenses are associated with new substations and primary mains. Items which are common to the different plans have been excluded, such as the 1976 existing plant, primary laterals, distribution transformers, secondaries, services, and meters OUTAGE AND SUPPLY COST COMPUTATIONS 291 Table D. 12. Medium-Reliability A Distribution System Costs (1976 Cr$ -103) and Losses Losses Recur- Mega- Investment costs rent Total Kilo- watt- Year Stations Lines costs costs watts hours 1977 0 876 16 892 1978 0 1,018 34 1,052 1979 0 1,183 57 1,240 Same losses as 1980 0 1,368 84 1,452 forlow- 1981 15,515 662 703 16,880 reliability 1982 0 753 716 1,469 distribution 1983 15,515 854 1,341 17,710 system 1984 0 977 1,360 2,337 1985 0 1,038 1,380 2,418 1986 15,515 1,157 2,009 18,681 1987 0 1,300 2,033 3,333 1988 15,515 1,449 2,668 19,632 1989 0 875 2,685 3,560 1990 15,515 957 3,309 19,781 1991 5,973 1,071 3,576 10,620 1992 11,946 1,177 4,092 17,215 1993 0 930 4,109 5,039 1994 0 1,013 4,130 5,143 1995 5,973 1,108 4,307 11,478 1996 0 1,210 4,422 5,632 1997-2006 0 0 4,422 4,422 Note See note to table D.1. 292 APPENDIXES Table D. 13. Medium-Reliability B Distribution System Costs (1976 Cr$ -103) and Losses Losses Recur- Mega- Investment costs rent Total Kilo- watt- Year Stations Lines costs costs watts hours 1977 0 877 16 893 582 1,499 1978 0 1,019 34 1,053 734 1,852 1979 0 1,185 58 1,243 910 2,262 1980 0 1,370 84 1,454 1,115 2,737 1981 15,515 809 708 17,032 1,129 2,818 1982 0 916 726 1,642 1,145 2,910 1983 15,515 1,033 1,358 17,906 1,163 3,016 1984 0 1,156 1,383 2,539 1,184 3,135 1985 0 1,045 1,403 2,448 1,147 3,038 1986 15,515 1,165 2,034 18,714 1,106 2,928 1987 0 1,312 2,058 3,370 1,059 2,806 1988 15,515 1,464 2,695 19,674 1,008 2,669 1989 0 932 2,713 3,645 1,098 2,909 1990 15,515 1,019 3,340 19,874 1,199 3,178 1991 5,973 1,142 3,610 10,725 1,308 3,468 1992 11,946 1,253 4,130 17,329 1,429 3,791 1993 0 932 4,147 5,079 1,540 4,083 1994 0 1,020 4,168 5,188 1,661 4,402 1995 5,973 1,117 4,436 11,526 1,793 4,751 1996 0 1,224 4,461 5,685 1,938 5,132 1997-2006 0 0 4,461 4,461 1,938 5,132 Note: See note to table D 1. OUTAGE AND SUPPLY COST COMPUTATIONS 293 Table D.14. High-Reliability Distribution System Costs (1976 Cr$ -103) and Losses Losses Recur- Mega- Investment costs rent Total Kilo- watt- Stations Lines costs costs watts hours 1977 0 1,613 28 1,642 531 1,405 1978 0 1,875 61 1,937 500 1,323 1979 18,887 2,179 727 21,793 464 1,227 1980 0 2,522 774 3,296 422 1,117 1981 0 631 784 1,415 486 1,286 1982 18,887 718 1,426 21,032 559 1,480 1983 0 814 1,441 2,255 642 1,698 1984 0 931 1,457 2,389 736 1,949 1985 18,887 1,204 2,105 22,196 736 1,948 1986 0 1,343 2,127 3,470 735 1,946 1987 18,887 1,509 2,780 23,177 735 1,944 1988 0 1,680 2,810 4,491 733 1,942 1989 18,887 817 3,450 23,155 856 2,267 1990 0 893 3,467 4,360 994 2,632 1991 14,025 999 4,037 19,061 1,142 3,024 1992 9,350 1,100 4,323 14,773 1,307 3,462 1993 14,025 1,223 4,895 20,143 1,393 3,690 1994 4,675 1,335 4,973 10,983 1,488 3,939 1995 4,675 1,458 5,055 11,189 1,590 4,211 1996 0 1,592 5,082 6,674 1,702 4,508 1997-2006 0 0 5,082 5,082 1,702 4,508 Note: See note to table D.1. 294 APPENDIXES Figure D.4. Relation between Costs and Outage Rate TC (8 percent) 250- TC (10 percent) ZOC (8 percent) 200- TC (12 percent) .1-OC (10 percent) U 150- 1OC (12 percent) 0 -- - ----------------------SC (8 percent) -----------------------------SC (10 percent) 50--_-- /---- -----------------------------SC (12 percent) 0 0.2 04 0.6 Outage rate (percentage) Note: Discount rate given in parentheses TC = total cost, OC = outage cost, and SC = supply cost. Appendix E Comparison with Previous Studies Comparing the results of this study with previous studies is difficult because, in the latter, outage costs have been calculated on the basis of many different units: that is, dollars for each kilowatt lost, dollars per kilowatt-hour lost, dollars an hour, total dollar value, and so on. Therefore, wherever possible, all the results have been reduced to outage cost for each kilowatt-hour lost, for standardized outage durations of 0.33 hours (20 minutes) and 1.5 hours, respectively, corresponding to representative values of duration for the high- and low-reliability sys- tems described in the case study. This information is presented in tables E.1 and E.2. All money values have been converted to US$ on the basis of official exchange rates prevailing when the studies were undertaken, and the U.S. deflator of GDP has been used to adjust for the effects of inflation up to 1977.1 Given the lack of uniformity in the methodologies adopted, as well as the differences among the countries and in the timing of the previous studies, the range of outage costs per kilowatt-hour lost (that is, US$0 to 7 for each kilowatt-hour) for the various types of industries examined 1. More refined inflation adjustments, including the use of the actual rates of inflation by industrial sector in the different countries, followed by conversion to US$ at the 1977 exchange rates, would not be worthwhile, given the inaccuracies inherent in the original outage cost estimates. 295 296 APPENDIXES Table E.1. Industrial Outage Costs Costs in US$ for each kilowatt-hour lost for an outage of duration Industry 0.333 1.5 Study type hours hours Comments Swedena All 1.97 0.96 Very aggregate level (1948) Swedenb Mines 0.81 0.54 Based on the results (1969) Smelting 0.05 0.10 of a survey of sev- Iron and steel 0.34 0.41 enty firms repre- Workshop 2.26 3.03 senting 28 percent Ouarrying 0.17 1.31 of total industrial Timber 0.38 0.45 consumption. Pulp and paper 0.41 0.22 Graphic 1.96 6.03 Food 0.63 0.63 Textiles 3.49 1.98 Rubber 2.96 1.00 Chemical 0.53 0.29 All 0.75 0.74 Chilee Paper 0.20 0.17 Based on an input- (1973) Basic metal 0.42 0.35 output approach, Nonmetallic using direct plus minerals 0.52 0.43 indirect average Printing 0.86 0.71 kilowatt-hour Metal products 1.11 0.91 requirements to Textiles 1.17 0.96 produce unit Nonelectrical value of output; machinery 1.33 1.33 therefore outage Chemicals 1.83 1.83 costs are average Lumber 1.86 1.86 rather than mar- Rubber 2.01 2.01 ginal. Leather 2.26 2.26 Miscellaneous 2.28 2.28 Furniture 2.28 2.28 Transport 2.56 2.56 Electrical machinery 2.57 2.57 Foodstuffs 2.84 2.84 Petroleum and coal 3.01 3.01 Shoes and clothing 3.20 3.20 COMPARISON WITH PREVIOUS STUDIES 297 Table E.1 (continued) Costs in US$ for each kilowatt-hour lost for an outage of duration Industry 0.333 1.5 Study type hours hours Comments Beverages 3.90 3.90 Tobacco 8.11 8.11 IEEE, Large plant 4.99 2.43 North Small plant 26.69 15.49 Americad (1973) Taiwane Aluminum 0.03 0.03 Based on direct (1975) Fertilizer 0.05 0.05 average kilowatt- Alkali and acid 0.05 0.05 hour requirements Steel 0.06 0.06 to produce unit Paper 0.16 0.16 value of output; Chemical 0.42 0.42 therefore outage Cement 1.22 1.22 costs are average rather than mar- ginal. Ontario- Large user 5.37 2.67 Hydro, Small manufacturer 8.71 4.55 Canadat Commercial user 0.99 1.03 (1976) Cascavel, Telephone 1.98 1.97 Based on a detailed Brazil Nonmetallic theory and survey (1977) minerals 1.00 1.10 of twenty firms. Mechanical and metallurgy 2.00 2.00 Vegetable oils 1.02 2.77 Food and 2.10 3.89 beverages Wood 4.74 2.76 Other 1.78 1.29 a. Dahlin Lolander, "Memorandum Concerning Estimation of the Costs of the National Economy in the Event of a Loss of Supply" (Vattenfall, 1948). b. Swedish Joint Committee for the Electricity Council, "Cost of Interruptions in Electricity Supply" (Stockholm: September 1969). c. Pablo Jaramillo and Esteban Skoknic, "Costo Social de Las Restricciones Energia El&ctrica," Oficina de Planificaci6n (Chile: August 1973). d. IEEE, Reliability Subcommittee at Industrial and Commercial Power System Committee, "Report on Reliability Survey of Industrial Plants. Part 2-Cost of (Footnotes continue on the following page) 298 APPENDIXES Power Outages, Plant Restart Time, Critical Service Loss Duration Time, and Type of Load Loss vs Time of Power Outages," May 1973. e. Taiwan Power Company, "Evaluation of Generating Capacity Reserve for Taiwan Power Company." f. Ontario-Hydro, "Survey on Power System Reliability: Viewpoint of Large Users," report no. PMA 76-5, Ontario, Canada, 1976; processed. Table E.2. Residential Outage Costs Outage costs (US$ per kilowatt-hour Study lost) Comment Swedena (1948) 0.38 to 0.64 Estimated approximately as a percentage of industrial outage costs. Swedenb (1969) 0.74 to 1.48 Based on estimated costs of interrupted household ac- tivities; not verified em- pirically. Chilec (1973) 0.30 Based on annuitized value of household appliances made idle. California, U.S.d (1977) 0.1 Based on household appli- ances made idle Englandd (1977) 0.5 to 1.5 Related to earning rate Jamaicae (1976) 0.06 Based on annuitized value of household appliances made idle. Cascavel, Brazil (1977) 1.3 to 2.0 Based on an explicit house- hold utility maximizing model and verified em- pirically by the willing- ness-to-pay of consumers. a. Same as a, table E. 1. b. Same as b, table E.il. c. Same as c, table E 1. d Systems Control Inc., "Analysis of Electric Power System Reliability" (pre- pared for the California Energy Resources Conservation and Development Com- mission, Palo Alto, Calif., 1978; processed). e. De Anne S. Julius, "The Economic Cost of Power Outages: Methodology and Application to Jamaica," report no. RES7, The World Bank, Energy, Water and Telecommunications Department (a restricted -circulation document) (Washington, D C., August 1976). COMPARISON WITH PREVIOUS STUDIES 299 is quite comparable with the results of the Cascavel study. The residen- tial outage costs are considerably higher than the corresponding results for the previous studies, however, because they ignored the value of foregone leisure. The 1969 Swedish study that also considered lost leisure explicitly is the only exception. Appendix F Survey Questionnaires Residential Consumers The information from this survey will be used by COPEL' to analyze and improve the quality of electricity services to customers. All responses will be treated as strictly confidential. 1. What was your average monthly electricity consumption during the last three months: .'***'***kilowatt-hours per month .........Cr$ per month 2. Do you feel that: (a) Your electricity supply is good Yes No (b) There are many electricity power outages Yes No 3. (a) On the average, how many minutes of unexpected outages per month have you experienced during the last three months: . . . . . . . . . . minutes per month (b) During what hours is electricity essential for the enjoyment of your leisure:......... (c) Approximately what fraction of outages occurred during these critical hours: . percent 4. If an unexpected outage occurred during these critical hours while you were enjoying your leisure (for example, watching television, 1. The electric power company, Compania Paranaense de Energia El6ctrica. 300 SURVEY QUESTIONNAIRES 301 listening to the radio, reading, having dinner, and so forth), how much extra would you be willing to pay to avoid: (a) A one-minute interruption ............. Cr$ (b) A five-minute interruption ............. Cr$ (c) A thirty-minute interruption ........... Cr$ (d) A sixty-minute interruption ........... .Cr$ (e) A ninety-minute interruption ........... Cr$ (f) A two-hour interruption .............. Cr$ 5. If an unexpected outage occurred at any other time (for example, while housekeeping) how much extra would you be willing to pay to avoid: (a) A one-minute interruption ............. Cr$ (b) A five-minute interruption ............. Cr$ (c) A thirty-minute interruption ........... Cr$ (d) A sixty-minute interruption ........... Cr$ (e) A ninety-minute interruption ........... Cr$ (f) A two-hour interruption .............. Cr$ 6. Do you feel that: (a) Electricity is an important service Yes No (b) The service is too expensive Yes No 7. On average, how do you spend your evening/night-time leisure hours: (a) Watching television ........... hours (b) Listening to the radio .......... hours (c) Reading .......... hours (d) Having dinner .......... hours (e) In conversation .......... hours (f) Going out .......... hours (g) Other .......... hours 8. When do you normally go to sleep: .......... P.M./A.M. 9. If we were to reduce the incidence of unexpected outages to half its present level, how much extra would you be willing to pay on your monthly electricity bill: .......... Cr$ per month 10. How many persons live in this household: .......... persons 11. (a) What are your principal sources of income: (b) What was the average monthly income (gross of taxes) of your household during the last three months: .......... Cr$ per month 302 APPENDIXES 12. If the level of unexpected outages were to double, what reduction in your monthly electricity bill would you consider to be fair: .......... Cr$ per month Industrial Consumers 1. Name of firm and principal outputs produced. 2. Name(s) and title(s) of official(s) interviewed. 3. (a) If there is an unexpected interruption in the supply of electricity, what is the value of materials and products that are spoiled? (b) Does this value vary with the duration of the outage? 4. (a) While the power is out, what percentage of normal output is not produced? (b) Does this vary with the duration of the outage? 5. (a) After the power is restored, how long is it before production can begin again? (b) Does this restart time vary with the duration of the outage? (c) What percentage of normal output is not produced during this restart period? (d) Does this percentage vary with the duration of the outage? 6. Is there any slack productive capacity, and if so, how much more could be produced per hour of work following the outage than is normally produced? 7. (a) What is this firm's yearly value added? (b) What are your normal working hours? (c) What is your overtime pay rate? (d) Do you own alternative energy sources, and, if so, how much did they cost, and how often have they been used? (e) Have you altered your production techniq.ues to reduce outage costs? 8. If your output is reduced because of an outage, will you make it up by working overtime? 9. What are this firm's expansion plans for the next twenty years, and how rapidly will its output increase during this period? Glossary Aggregation: Adding together or combining, for example, the electrical loads of different consumers. Auto-consumption: The consumption, within a household, of self- produced goods and services that do not enter the market. Busbar: A conductor or group of conductors that serves as a common connecting point for two or more electrical circuits, for example, in a substation. Captive generation: The generation of electricity by private individuals using their own plant, instead of drawing power from the main electricity grid (also called auto-generation). Cold reserve: Reserve generating capacity available for service, only after a specified time has elapsed, because the generators are not maintained at operating conditions (see also Hot reserve). Cross section data: Data relating to several different objects at a given point in time (see also Time series data). Demand side: Considerations relating to the demand for electricity. Direct outage costs: Economic costs incurred during outages (see also Outage costs). Disaggregation: Breaking up into smaller components, for example, a load forecast. Elasticity of demand with respect to price (or income): The percentage change in demand divided by the percentage change in price (or in- come). Fault: The malfunction of an electrical circuit in a power system, for example, the short-circuiting of a line. Forced outage: The unexpected failure of a component in a power sys- tem, for example, a generator (see also Planned outage). 303 304 GLOSSARY Growth pole: A geographic center for economic growth and develop- ment. Hot reserve: Reserve thermal generating capacity available for service promptly, because the generators are maintained at operating conditions (see also Cold reserve). Indirect outage costs: Economic costs incurred as a result of actions designed to avoid the effects of anticipated outages (see also Outage costs). Iterate: To run through a modeling procedure repeatedly. Load shedding: Deliberate removal of specific loads from the system to avoid system failure during a power supply shortage. Matrix model (for load forecasting): A mathematical model involving representation and manipulation of probabilistic data in matrix format. Nonspinning reserve: Reserve generating capacity not connected to the busbars, but able to carry the load only after a specified time has elapsed. Numeraire: A common unit of account or yardstick for measuring the economic value of goods and services. Objective function: A mathematical expression used in an analytical model, the value of which is usually maximized or minimized. Operating reserve: Reserve generating capacity, normally consisting of both the spinning and nonspinning reserves. Outage (of a component): The condition of a power system component when it cannot perform its function satisfactorily because of an event associated directly with the component. Outage (at the point of use): Unavailability of electric power to the consumer. Outage costs: The economic costs resulting from a shortage of electricity supply, including frequency and voltage fluctuations, as well as inter- ruptions of supply. These costs consist of both direct and indirect outage costs. Parametrize: To define a curve or mathematical function in terms of one or more parameters. Pareto optimal: An economic condition that occurs when no one can be made better off without making someone else worse off. Peak suppression: The suppression of peaks in the electricity demand curve, for example, by shedding load. Piecewise linear: The property of a graph or mathematical function indi- cating that it is composed of several linear segments. Planned outage: The preplanned unavailability of a component in a GLOSSARY 305 power system, usually for preventive maintenance or construction (also called scheduled outage). Rating period: Time interval during the day or season of the year, within which a specific price (or rate) is charged for electricity consumption. Ring main busbar: A busbar designed in the form of a loop to provide redundancy. Spinning reserve: Reserve generating capacity connected to the busbars and ready to meet the load immediately. Stochastic process: A process that is random in time. Supply side: Considerations relating to the supply of electricity. Time horizon: A future period for which forecasts or plans are made. Time series data: Data relating to a given object, during several succes- sive time periods (see also Cross section data). References The word processed indicates works that are reproduced by mimeograph, Xerox, or any other manner other than conventional typesetting and printing. Allan, R. 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Index Accounting rate of interest (ARI), 114, Captive generation, defined, 303 115 Cascading failure, 16 Aggregation, defined, 303 Cascavel, Brazil, study, 8, 118, 120, 136, Alert state, 17 140, 142, 147, 148, 149, 163-75, American National Standards Institute 176, 177, 195, 196, 215, 217, 222, (ANSI), 138 224,226,297,298,299 Annual peak demand, 146 Case study ARI See Accounting rate of interest methodology of, 118 Auto-consumption, defined, 303 objectives of, 117 CCL. See Critical consumption level Central Electricity Generating Board Behavior, consumer (CEGB),16 model of household, 8 cEs. See Constant elasticity of substi- modification of, 7, 46, 196 tution Blackout. See Outage CF. See Conversion factor Border price (BP), change in, 213 Chilean study, 55, 56, 58, 59, 60, 296, BP See Border price 298 Brazil Cold reserve, defined, 303 pricing policy of, 120 Commercial electricity requirements, voltage criteria in, 138 221-22 Brazilian study. See Cascavel, Brazil, Compania Paranaense de Energia E16c- study trica (COPEL), 124, 125, 131, 138, Brownouts. See Voltage, reduction in 139, 143, 160, 219, 222, 223, 225 Bur,n1uts Constant elasticity of substitution (CES), Busbar, 143 defined, 303 102 ringmain 305Construction conversion factor, 112 ringConsume behavior, 7, 8, 46, 196 Consumet surplus, 51 California study, 298 Consumers, categories of, 58-60 Canaian tudy 297Consumers' labor-leisure choice, 8, 71, Canadian study, 297168 Capacity, 1, 32, 89, 99, 177, 206, 208, Conversion factor (CF), 110, 112, 213 209 in shadow pricing, 210-14 excess, 14 coPEL. See Compania Paranaense de Capacity-limited generating system, 23 Energia E16ctrica Capital, opportunity cost of, 114, 177, Correlation methods of demand fore- 265 casting, 92-93 315 316 INDEX Cost. See also Costing; Price; Pricing excess, 15 commercial outage, 80-81 forecast of. See Demand forecast direct, 55 global, 1, 34 distribution systems, 292-94 industrial, 72 economic, 34 investment considerations, 25 financial vs. economic, 61 load duration analysis role, 148 global outage, 183 loss of, 160 idle factor, 52, 55, 75-76, 170 loss of at peak, 159 idle production, 194 as model input, 28 indirect, 55 in Monte Carlo simulation, 209 industrial outage, 72-79, 296-97 national context, 88 marginal, 31 off-peak, 26 marginal outage, 27 peak,18,26,97,146 marginal social, 33 public illumination, 82, 224 marginal system, 33 reductions in, 15 nonfactor, 76 reliability expectation effects on, 44 operation and maintenance, 160, 161 reliability levels and, 36 opportunity, 2, 52 residential, 62, 71 outage. See Outage cost rural, 175 overtime production, 77-79 in sensitivity testing, 29 public services outage, 82-83 shadow pricing, 210 recovered (RC), 76, 212 shoulder, 26 reliability, 33 stochastic, 50 residential outage, 193 uncertainties of, in model, 33 restart, 170 U.s , I rural outage, 85 Demand forecast, 7,13, 29, 33, 44, 89, shortage, 15, 25, 28 90, 96, 104, 119-33, 190, 193, 194 social, xx, 6, 7, 33 methods of, 91-94 spoilage, 81, 83, 174, 175, 194, 302 Demand side, defined, 303 substation construction, 160 DF. See Diversity factor substation recurrent, 162 Direct outage cost, 46, 55, 72, 83, 303 supply. See Supply cost Disaggregation, defined, 303 system. See System cost Distribution, 10-11, 41, 139, 141, 142. Cost-benefit analysis, 6, 25, 28, 29, 40 See also Distribution system modified framework for, 176-77 long-range planning of, 134-62 Costing, 102-4. See also Cost; Price; losses of, 91 Pricing planning of, 20, 30, 89-91, 95, 101, methods of, 103 102,119,121,134-62 Cost minimizing model, 31 primary model of, 227-44 Critical consumption level (CCL), 215 reliability of, 24 Cross section data, defined, 303 Distribution grid, 11, 118 Distribution line, I11 Distribution system (network), 16, 30, Daily load cycle, 20 43. See also Distribution Daily peak demand, 20 components of, 136 DC-load flow model, 100 construction design for, 142-46 Demand, 1, 36, 52. See also Load cost of, 292-94 analysis of, 24 design criteria, 135-46 annual peak, 146 design of, 152-54 computer model, 244 failure of, 51, 56 consumer surplus loss and, 51 optimization of, 176-96 daily peak, 20 reliability criteria for, 139-42 elasticity of, 303 stages of development, 134-35 empirical estimation of, 52 study of, 117 estimation of, 52 voltage standards for, 137-39 exceeding supply, 13 Diversity factor (DF), 90 INDEX 317 "Dollar value effect," 57 244,245,246 Domestic price (DP), change in, 213 annual outage by, 258-61 Double-worst-fault design, 18 primary, 11, 101, 121, 136 Down state, 10 Financial cost vs economic cost, 61 DP. See Domestic price Fluorescent lights, 14 DU See Dwelling unit Forced outage, 303 Duration of outage. See Outage, dura- Foreign exchange (FX), change in, 212 tion of Free trade exchange rate (FTER), 112 Dwelling unit (DU), 219 Frequency and duration (FAD) Of out- age See Outage, frequency and duration of Economic cost, 34 Frequency fluctuations, 14, 15 vs. financial cost, 61 Frequency reductions, 15, 16 Economic criteria, 24-27 Frequency variations, 45, 137 Economies of scale, xx FTER. See Free trade exchange rate Effective wage ratio, 78 FX. See Foreign exchange Efficiency prices, 108 Efficiency shadow wage rate (ESWR), 113 GDP. See Gross domestic product EHV. See Extra high voltage Generation, 10, 21, 136, 138, 155, 195, Elasticity of demand, 303 196, See also Generation system Electric energy requirements, 1 analytical studies of, 23 Electricity consumption capacity of, 20, 56, 177 by category, 58-60 captive, 303 commercial, 131, 221-22 failure of, 24 hospital, 131 indexes of, 22 industrial, 129-3 1 losses of, 91 residential, 124-29 planning of, 18, 19, 30, 94-95, 99- Electricity-independent leisure, 68 101,117 Electricity price. See Price reliability of, 24 Emergency state, 17 standby, 49, 84 Energy-limited generating systems, 23 Generation system (network), 43. See Energy requirements, also Generation English study, 298 capacity-limited, 23 ESWR. See Efficiency shadow wage rate energy-limited, 23 EUSE. See Expected unserviced energy failure of, 51 Excess capacity, 14 reliability of, Exces caacit, 14Generation-transmission index, 21 Excess demand, 15 Generators, 14 Expected loss of load (XLOL), 20 Global demand, 34 Expected unserviced energy (EUSE), 20. Global outage cost, 183 See also Loss-of-energy expectation Global reliability, 33, 38, 194 Extra high voltage (EHV), 11 Grid, 73, 85, 101, 147 distribution, 11, 18 Gross domestic product (GDP), 57, 295 Factor cost (FC) component of outage Growth pole, 304 cost, 76 FAD. See Outage, frequency and dura- tion of High voltage (iv), 11 Failure. See also Outage Hot reserve, 304 cascading, 16 Household activities, 63-64 mean time to, 22 Household behavior, 8 Fault, defined, 303 Housekeeping activities, 63, 64 FC. See Factor cost HV. See High voltage Feeders, 16, 102, 134, 140, 146, 148, Hybrid network expansion, 194 149, 150, 153, 154, 155, 183, 190, Hybrid systems, 183-91 318 INDEX Idle factor cost (IFC), 52, 55, 75-76, residential activity, 63, 64 170 survey of, 300, 301 Idle production cost, 194 value of, 65-69 Idle resources, 76 work and, 70 IEEE study, 297 LF. See Load factor IFC. See Idle factor cost Lightning, 16 Income Linear outage function, 182 change in, 212 Load, 19, 20, 95. See also Demand distribution of, 108, 177 expected loss of, 20 effects of, on shadow pricing, 214-16 peak, 140, 141 Independent increment simulation, 22, Load centers, 11 23, 24 Load duration analysis, 148 Indirect outage cost, 46, 55, 73, 304 Load duration curve (LDC), 97 Industrial consumption, 129-31, 169- Load factor (U), 90 74, 302 Load forecast, 89-94, 119, 217-26 Industrial outage cost, 169-74, 296-97 Load-point indexes, 26 types of, 72-81 Load shedding, 8, 15, 16, 32, 46, 51, 56, Insecure state, 17 194,304 Institute of Electrical and Electronics Local optima, 30 Engineers (IEEE), 297 LOEE. See Loss-of-energy expectation Integrated system, 16 LOLE. See Loss-of-load expectation Interconnection, 11, 13, 16, 30, 100, LOLP. See Loss-of-load probability 140, 143, 146, 147 Long-run marginal cost (LRMC), 32 Interruption of power. See Outage Loss-of-energy expectation (LOEE), 19, Interruption of supply. See Outage 20, 21, 38. See also Expected un- Investment in power systems, 1, 2, 25, serviced energy 87-89 Loss-of-load expectation (LOLE), 20 lumpiness of, 33, 35 Loss-of-load probability (LOLP), 19, 20, needs for, 2 21, 23, 24, 30, 32, 206, 207, 209 Istanbul study, 55, 58, 60 LRMC. See Long-run marginal cost Itaipu hydroelectric site, 176 Lumpiness of power system invest- Iterate, 304 ments, 33, 35 Jamaica, electricity consumption in, 58 Macroeconomic model, 106 Jamaica Public Service Company study, Marginal cost pricing, xix, 43 57,58,59,L60,298 Marginal outage cost (MOC), 27, 31, 40 Marginal rate of substitution (MRS), Kilowatt not served, 30 67,S69,e70 Marginal social benefit (MSB), 111, 112, 214 Labor-leisure choice, 8, 71, 168 Marginal social cost (msc), 33, 106, Land use, 120-29, 217,L224-26 111, 112, 113, 114,212,214 Laws of probability, 199-208 Marginal supply cost (MSC), 40 LDC. See Load duration curve Marginal system cost, 33 Leisure Marginal value of electricity-indepen- costing example, 69 dent leisure, 68 cost of lost, 183 Market price, 7 daily period of, 165 Matching, 15 electricity-independent, 68 Matrix model, defined, 304 equipment used for, 69 Mean time to failure, 22 habit patterns of, 163 Meters, 11, 161 loss of, 60, 68, 113, 169, 194, 299 MOC. See Marginal outage cost marginal value of, 70, 71 Monte Carlo simulation, 22, 23, 24, 26, outage timing and, 147 208-9 INDEX 319 MRS. See Marginal rate of substitution annual by feeder, 258-61 MsB. See Marginal social benefit causes of, 15 msc. See Marginal social cost of components, 18 MSC. See Marginal supply cost consequences of, 14 cost. See Outage cost defined, 304 NB. See Net benefits duration of, 6, 26, 60, 76, 80, 140, Negative outage cost, 106 152, 153, 164, 170, 194, 295, 300 Net benefits (NB), 32 effect of, on production, 52 change in, 35, 36 effect of, on system, 148 Net economic benefits, 37 energy (OE), 38, 182, 263 Net social welfare, 31, 32 in England, 16 New York City Metropolitan Transpor- expectation, 44 tation Authority, 86 forced, 303 New York City power failure of 1977, frequency and duration of (FAD), 19, xxi, 83, 86 20, 21, 22, 23, 24, 26, 41, 118, New York State, outage cost for, 57 146, 147, 149-52, 159, 172, 178, NFC. See Nonfactor cost 193,262,302 Nonfactor component of outage cost, 76 frequency of, 6, 75, 153, 155, 172, Nonfactor cost (NFC), 76 190,301 Nonspinning reserves, 15, 304 New York City 1977, xxi, 83, 86 Numeraire, 109-10, 304 parameters of, 146-52 Nutrition, 63, 64 planned, 304 probability and expectation of, 18-21, 23 Objective function, defined, 304 probability of, 190 OC. See Outage cost rate (OR), 178, 183, 190 OCC. See Opportunity cost of capital reliability and, 20, 33 OCF. See Outage cost function on secondary system, 143 OCK See Outage cost per kilowatt- simulations of, 37-44 hour lost social cost and, 50 OE. See Outage energy theory, 6, 20 OER. See Official exchange rate timing of, 62 Official exchange rate (OER), 112 waiting time during, 151 Off-peak demand, 26 Outage cost (OC), xx, 39, 42 Off-peak rates, pricing of, 27 aggregate, 37 OLsO. See Ordinary least squares re- averted, 40 gression basic, 76 Ontario study, 297 change in, 36 Operating reserves, 15, 304 characteristics of, 178-83 Operation and maintenance cost, 160, commercial, 80-81 161 computations of, 262-94 Opportunity cost, 2 defined,304 of capital (OCC), 114, 177, 265 direct, 46, 72, 83 defined, 52 duration and, 60 Optimization empirical estimation of, 41, 118, 120 methods of, 96 estimation of, 34, 41, 45-61, 118, scope of, 30 120, 196 Optimum reliability levels, 25, 37-44, function (OCF), 170, 171, 173, 182 106, 183-91 generation failure and, 155 change in, 43 global, 183 OR. See Outage rate hospital, 263 Ordinary least squares regression indirect, 46, 55, 73, 304 (oLsQ), 165 industrial, 72-81, 78, 79, 169-74, 194, Outage 263,296-97 analysis of data from, 146-48 marginal, 27, 31, 40 320 INDEX Outage cost (continued) Power failure See Outage measurement of, 46, 55-58, 163-75, Power interruption See Outage 196 Power shortage. See Shortage methods of estimating, 49-53 Power surges See Surges nature of, 45-49 Power system investments. See System negative, 106 investments New York State, 57 Present discounted value (PDV), 29, 34 outage energy ratio to, 182 Price. See also Cost, Costing; Pricing outage rate and, 190 border (BP), 213 per kilowatt-hour lost (OCK), 30, demand and, 34, 93 178, 182 domestic (DP), 112, 114, 213 previous studies, 295 efficiency, 108 prorating of, 32 growth of, 29 public illumination, 263 load shedding and, 51 public services, 82-83 market, 7, 106 reliability and, 4, 178 net welfare and, 32 reliability expectation effects on, 36, opportunity cost and, 58 44 optimization of, 33 reliability indexes and, 26 shadow. See Shadow price residential, 69-71, 163-69, 193, 215, social, 108 216, 263, 298 stability and, 88 rural, 85 theory, 4, 6, 7 secondary effects of, 85-86 transfer, 31 social, 28-29, 33 uncertainty and, 88 social weighting and, 191, 192, 193 Pricing. See also Cost; Costing; Price; special institutions, 83-84 Tariffs supply cost and, 87 efficiency, 192 survey of, 302 marginal cost, 43 system cost and, 178, 185, 195 neutral, 120 theory, 4-8, 14, 17 objectives of, 195 time of day and, 30 optimal, 50 transmission failure and, 155 peakload,27 Overload, 16, 20 shadow. See Shadow pricing levels of, 15 social, 191, 193 Overtime, 77-79 Pricing policy, 27, 31, 32, 44, 87, 88 Primary feeders, 11, 101, 121, 136 Probabilistic methods, 18, 19 Parametrize, 304 Probability, laws of, 199-208 Parana state system, 177 Production Pareto optimal, 304 agricultural, 85 PDv. See Present discounted value commercial activity, 81 Peak demand, 18, 26, 96, 97 defined,52 annual, 146 effects of outage on, 52 Peak load, 19, 140, 141 foregone, 58, 170 pricing, 27 household, 62 Peak rates, pricing of, 27 idle factor cost, 75 Peak suppression, 304 indirect outage cost, 73 Period of overtime, 78 overtime, 77-79 Perturbation technique, 22 secondary outage effects on, 86 Piecewise linear, 304 Profit, social, 112 Planned outage, 304 Profit-maximizing level of output, 77 Planned power cuts, 14, 142 Purchased power, 15 Population distribution of, 217 forecast of, 125, 128 Quality of service, 10 Power cuts, planned, 14, 142 Quantity of electricity, 51, 111 INDEX 321 Rating period, 305 Savings to society, 7, 8 RC. See Recovered cost SC. See Supply cost Reactive volt-amps (VAR), 159 Scalar global reliability index, 178 Recovered cost (RC), 76 SCF. See Standard conversion factor change in, 212 Secure operations, 17 Redundancy, 10, 14, 16 Secure state, 17 Regression, ordinary least squares Security, 16, 18 (OLSQ), 165, 167 assessment models of, 21 Reliability, 154-62 indexes of, 17, 18 benefits of, 33 Sensitivity testing, 29 concepts of, 9-16 demand in, 29 generation, 8 and supply cost, 264-65 global, 38, 194 Sequencing, 15 indexes of, 17, 18, 19, 20, 21, 22, 23, Sequential simulation, 22, 23 24, 26, 30, 32, 41, 42, 178, 195, SER. See Shadow exchange rate 196, 209 Service inlet, 11, 138, 161 levels of. See Reliability levels Shadow exchange rate (SER), 112, 265 measures of, 16-24 Shadow price, 2, 7, 30, 106, 108 optimization of, 28-71, 33 Shadow pricing, 35, 177, 194 outage and, 20, 33 application of, 110-15 outage cost and, 4 conversion factors in, 210-14 standards for distribution systems, demand in, 210 139-42 general principles of, 105-8 standards of, xv, xvi, 3 income distribution effects on, 108 transmission, 8 income effects on, 214-16 Reliability levels (R), 37 numeraire of, 109-10 actual, 48, 49 Shadow wage rate (SWR), 113, 114, benefits from different, 33 177,264,265 cost for different, 33 Shortage, 4, 6, 7, 17, 26, 32 critical, 49 built-in, 13 demand and, 36 cost of, 15, 25, 28 expected, 46, 47, 48, 49 supply, 45 global, 33, 34, 38, 178 Short-run marginal cost (SRMC), 32 index of, 41, 42 Shoulder demand, 26 optimum, 25, 37-44, 106, 183-91 Shoulder rates, pricing of, 27 supply cost and, 25, 28, 34, 183 Single worst-fault design, 18 Repair time, 22 Social benefits, 28, 32 Reserves Social cost, xx, 6, 7, 33 cold, 303 Social cost-benefits, 4 hot, 304 Social price, 108 margin, 18, 19 Social pricing, effects of, 191 nonspinning, 15, 304 Social profit, 112 operating, 15 Social savings, 7, 8 spinning, 14, 15 Social weighting, effects of, 191-93 Residential consumers, 124-29, 163- Social welfare, 31, 32 69, 300-302 SPC. See Spoiled product cost allocations of, 218-21 Spinning reserves, 14, 305 Residential demand, 62, 71 Spoilage cost, 72, 81, 170, 174, 175, Residential outage cost, 193, 298 194,302 empirical estimation of, 69-71 in hospitals, 83 Restart cost, 170 Spoilage effect, 52, 55 Restorative state, 17 Spoiled product cost (SPC), 74-75, 170 Ring main busbar, 305 SRMC. See Short-run marginal cost Ring system, 16 Stability, 16 Rural demand, 175 Standard conversion factor (SCF), 112, Rural outage cost, 85 114 322 INDEX Standby generation, 84 System investments, 1, 2, 25, 87-89 States of power systems, 10, 17, 201 lumpiness of, 33, 35 Steady-state probabilities, 18 System planning, 94-102 Stochastic demand, 50 costing in, 102-4 Stochastic process, 19, 305 investment decision in, 87-89 Street lighting requirements, 131, 222- load forecast in, 89-94 24 System reliability, xv Studies, review of, 54-61 System security, 16, 18 Substations, 11, 101, 121, 134, 136, 142, System states. See States of power 143, 146, 150, 153, 244 systems capacity of, 154 System supply cost (SC). See Supply construction cost, 160 cost recurrent cost, 162 Subtransmission, 11 Supply and demand, 13, 15, 25, 28, 33, Taiwan study, 55, 58, 60, 297 50, 88, 210 Tariffs, 29, 32, 33, 59, 93, 195 Supply cost, 37, 39, 42, 50, 178, 185 TB. See Total benefit change in, 36 TC. See Total cost characteristics of, 170-83 TE See Total energy computations of, 262-94 Third World, 117 computerized simulation of, 194 Three-phase fault to ground, 16, 100, income effects on, 193 244 optimum reliability levels and, 183 Time-dependent probabilities, 18 outage cost and, 41, 87 Time horizon, 305 partial optimization and, 195 Time series data, 305 public illumination and, 174 Total benefit (TB), 37 reliability levels and, 25, 28, 34 Total cost (TC), 42, 190 sensitivity testing and, 264-65 Total energy (TE), 38, 178 system planning and, 102, 103, 104 Transfer price, 31 theory, 4, 6, 7, 13 Transformers, I1 U.S, 103 Transition rate matrix, 19 Supply costing methods, 103 Transition rates, 19 Supply interruption See Outage Transmission, 10-11, 136, 155, 196. Supply shortage, 45 See also Transmission system Supply side, 305 failure of, 24 Surges, 14, 15, 45 indexes of, 22 Survey, 58, 71, 163, 222, 223of, 91 Survy, 8, 1, 13, 22,223planning of, 20, 30, 94, 100, 101, 117 questionnaires for, 300-302 reliability of, 24 Swedish study, 57, 58, 59, 182, 296, Transmission system (network), 11, 43, 298, 299 89. See also Transmission Switches, 16 failure of, 56 SWR. See Shadow wage rate performance criteria for, 100 Synchronization, 15 reliability of, 8 System components, 10 Trend line method of demand forecast- System cost, 4 ing,91-92 computerized model of, 118 Tripping of lines, 15 global reliability and, 194 national context of, 30 and other cost, 178 Up state, 10 and outage cost, 29 planning and, 95, 142, 154-62, 195 theory, 6, 8, 17, 25 VAR. See Reactive volt-amps uncertainty of, 44 Voltage, 11, 22, 45 System design, 94-102, 152-54 extra-high, 11 System failure. See Outage fluctuations in, 137 INDEX 323 high, 11 Willingness-tO-pay, 49, 50, 51, 62, 71, oscillations in, 16 82, 83, 164, 168, 169, 194, 301 reduction in, 11, 14, 15, 16, 20 World Bank, The, xv, 117 standards of, for distribution systems, Worst case concept, 96 137-39 Worst-fault design, 8 variation in, 64 Welfare maximizer, 31 XLOL See Expected loss of load A~iv~Ja fl Lvai; i kl? ~l a. 合