Optimal Peak Load Pricing of Electricity Under Uncertainty - Some Welfare Implications 9783639263534

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CONTENTS

Acknowledgement

Chapter 1 Prologue

1

Chapter 2 A Survey of the Theory of Public Utility Pricing

15

Chapter 3 The Performance of the Kerala Power System

32

Chapter 4 Reliability Analysis of the Kerala Hydro-Power System

59

Chapter 5 Optimal Peak load Pricing of Electricity under Uncertainty – Some Welfare Implications

86

Chapter 6 The Optimal STD Prices for Kerala Electric Power System

107

Chapter 7 Epilogue

129

Appendices Bibliography

i

CONTENTS IN DETAIL Chapter 1 Prologue

1 – 14

1.1 Energy: General Background

1

1.2 Electric Power

2

1.3 The Electric Power utility

2

1.4 Tariffs

3

1.5 Seasonal Time of Day Pricing

4

1.6 General Framework for Implementing STD Pricing

4

1.7 Problems and drawbacks

6

1.8 STD Pricing in Practice

7

1.9 Objectives of the Study

9

1.10 Methodology

10

1.11 Data Base

10

1.12 Plan of the Study

11

1.13 Limitations of the Study

12

Notes

12

Chapter 2 A Survey of the Theory of Public Utility Pricing

15 – 31

2.1 Introduction

15

2.2 Public Utilities

15

2.3 Marginal Cost Pricing

17

2.4 Second Best Dilemma

19

2.5 Monopoly Pricing

20

2.6 Regulated Monopoly Pricing

21

2.7 Ramsey Pricing

21

2.8 Non-Linear Pricing

22

2.9 Load Factor and Pricing of Electricity

23

2.10 Review of the Theory of Peak Load Pricing

24

2.10.1 Deterministic Models

24

2.10.2 A basic peak Load Model

26

2.10.3 Peak Load Pricing Under Uncertainty

27

2.11 Conclusion

28 ii

Notes

29

Chapter 3 The Performance of the Kerala Power System

32 – 58

3.1 Introduction

32

3.2 The Kerala Power System – An Overview

33

3.2.1 The Growth of the Kerala Power System

34

3.2.2 The Rule of Power Cut

35

3.2.3 The Cost of Low Capacity Utilization

36

3.3 Dissecting the Plight

37

3.3.1 The Inadequate Capacity Additions

37

3.3.2 Unaccountable System Planning

39

3.3.3 The Dismal Financial Front

44

3.3.4 A Legacy of Unaccountability

48

3.4 The Power Sector Reform

50

3.5 Conclusion

52

Notes

53

Chapter 4 Reliability Analysis of the Kerala Hydro-Power System

59 – 85

4.1 Introduction

59

4.2 A Gamble in the Monsoon

59

4.3 The Monsoon Profile

60

4.4 Generation vis-a-vis Precipitation

62

4.5 Shortages and Reliability

64

4.6 System Reliability

65

4.6.1 Availability and Forced Outage Rates

65

4.6.2 Continuous Markov Process

67

4.6.3 Maximum Likelihood Estimation Of Availability

68

4.6.4 Loss of Load Probability (LOLP)

72

4.6.5 Availability and Forced Outage Rates

75

4.6.6 Capacity-Outage Probability and LOLP

78

4.6.7 LOLP

82

4.7 Conclusion

83

Notes

84

iii

Chapter 5 Optimal Peak load Pricing of Electricity under Uncertainty – Some Welfare Implications

86 – 106

5.1 Introduction

86

5.2 Seasonal Cost Structure of A Hydro-Power System

87

5.3 Load Duration Curve

88

5.4 The First-Best Prices

89

5.4.1 All-Hydro System

89

5.4.2 Hydro-Thermal System

93

5.5 The Monopoly Prices

96

5.6 The Ramsey Prices

97

5.7 Constrained Monopoly Prices

98

5.8 Outage Costs

101

5.9 Conclusion

105

Notes

105

Chapter 6 The Optimal STD Prices for Kerala Electric Power System 107 – 128 6.1 Introduction

107

6.2 System Growth and Demand Projection

108

6.3 Structuring the LRMC for the System

111

6.3.1 A Pure Hydro-Power System

111

6.3.2 A Hydro-Thermal System

113

6.3.3 Other Parameters in the Price-Structure

114

6.4. The STD Generation Prices

117

6.5 The Prices Adjusted at Voltage Levels

118

6.6 The Outage Costs

120

6.7 Conclusion

122

Notes

122

Chapter 7 Epilogue

129 – 133

7.1 General

129

7.2 Conclusions

129

7.2.1 Financial Performance

129

7.2.2 Capacity Availability

130 iv

7.2.3 Water Availability

131

7.2.4

STD Prices

131

7.2.4.1 High-Voltage Consumers

132

7.2.4.2 Low-Voltage Consumers

132

7.2.4.3 Transition to the New Tariff

132

7.2.5 Rationing Prices

133

7.3 Qualifications

133

7.4 Extensions

133

Appendix Al A Chance-Constrained Programming Model of STD Pricing of Electricity

135 – 144

A.1.1 Global Approach

135

A.1.2. Simulation Models

135

A.1.3 Mathematical Programming Models

135

A. 1. 4 Chance-Constrained Programming

136

A.1.5 The Method Of Z-Substitutes

138

A.1.6 A Chance-Constrained LP Model Of Electricity Pricing

140

Notes

145

Appendix A2 Electric Power Consumption (KWH Per Capita)

Bibliography

146 – 149

150 – 165

v

ACKNOWLEDGEMENT

This work is based on a revised and to some extent updated version of my Doctoral Thesis on Seasonal Time-of-Day Pricing of Electricity under Uncertainty, carried out at the Department of Econometrics of University of Madras, Madras (now Chennai), India.

Any work, however privately conceived it is, is a concrete outcome of the collective consciousness. And hence I remember now with deep gratitude, love and reverence those kindred spirits who directly helped me through with this project.

The original project was carried out under the supervision of Dr. U. Sankar, then Professor and Head of the Department of Econometrics, Madras University, (now Honourary Professor at the Madras School of Economics); my appreciation bows to him for his enduring encouragement, especially to the heuristic initiative of his students. Though I had started on an ambitious empirical exercise of a chance-constrained linear programming (LP) model of the Kerala power system, inaccessibility to a suitable LP package that time finally drove me to divert my study into a detailed mathematical modeling of a representative power system and its marginalist derivations along with some illustrative empirics.

I am grateful to the University Grants Commission for the financial assistance to this project, awarded through the Junior Research Fellowship (National Eligibility Test) scheme. I was proud to be the first JRF (NET) to join the University of Madras.

I benefitted during the study period from the accessibility to the libraries at Madras University, Madras Institute of Development Studies, Economics Departments of Kerala University and Calicut University, Centre for Development Studies, Trivandrum, Vydhyuthi Bhavanam, Trivandrum, T.N. Agricultural University, Coimbatore, and Indira Gandhi Institute for Development Research, Bombay. Discussions with Ms. T Alagumany, then of the T.N. Agricultural University, on chance- constrained programming helped me a lot. I had also the benefit of discussions on electricity economics with Prof. P.P. Pillai and Dr. (Mrs.) P.P. Pillai of Economics Department, Calicut University. vi

This moment I also take to remember a few of my teachers: the encouraging brotherly affection, (late) Dr. C. Radhakrshnan Nair, then at the Department of Economics, Kerala University showered upon me, is particularly remembered. And my heart is too full for words when I remember now at a loss my college teacher and one-time god-father, Prof. Abdul Razak and his family who choked me with affection and compassion unusual to me.

The study would not have been possible but for the kind and encouraging co-operation of the KSEB. The Board officials and the personnel at the Vydhyuthi Bhavanam, Trivandrum and at the different power stations in Kerala were so co-operative that many of them went out of their way to help me in collecting data and other information for the study ─ with deep gratitude I appreciate their kind service.

A good deal of my grateful appreciation and love is due to my near and dear ones ─ my younger brother Rajan and his friends, especially Srinivasan and family, patiently bore all the problems with my accommodation arrangements in Madras; being hyper-allergic to sound, dirt and indecency, I had to change houses very often. In the absence of any solid recommendation, the University hostel was inaccessible to me for more than three years, but my friend Mohanansundaram, another Ph D fellow in the same Department, brought it within my reach such that I was able to complete formulating the model with all the derivations and writing the original Thesis during the eight months of my hostel stay. Thereafter my friend Soumitra Ganguly (then of Philips Company) was so kind to accommodate me for the remainder of my fellowship period with him after sending his family back home! The compassionate concern with and loving encouragement to the progress of my study by Premkumar and his parents, Unni and Amma, Yoosuf, Mohanan, Sisupalan and the other friends are also gratefully remembered. And then my sisters and brothers, particularly Balannan, who had taken all the household burden upon himself and let me with the studies; and this I dedicate to the burning memory of my parents and my sisters Akkan and Ammini with an unsatiated sense of unfulfilled obligations in the cruel face of untimely exits. And finally my family now – as Rju as usual smiles away my excuses for my absences from her little kingdom and Kala resigns herself to my non-corrigible weekend return to family care, I just seek to balance all, bring all to mind … In balance with this life, this academic pursuit!

vii

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CHAPTER 1

PROLOGUE

“If it weren't for electricity we'd all be watching television by candlelight.” - George Gobal

1.1 ENERGY: GENERAL BACKGROUND

The very life-source on the earth, energy assumes pride of place in both the objective and the subjective realms of knowledge; and coming to down-to-earth experience, it is energy that has lit and kept our civilized life.1 The energy in any form used by man throughout all the time of his earthly existence totals some 900 - 950 thousand twh!2 Moreover, the characteristic feature of energy consumption has been non-uniformity. The pre-historic man used his own brawn and the heat of the first-built fire and consumed about the same amount of energy as his neighbour. But the present age presents tremendous difference in per capita energy usage among the various countries. The difference in electric power consumption is still far substantial (see Appendix A.2). Thus Canada consumed about 16,753 kwh per capita against as little as 146 kwh per capita of Bangladesh and 503 kwh per capita of India in 2006.

The continuously growing world industrial production has extracted energy resources for use at a rapidly increasing rate. In 2008, total worldwide energy consumption was 474 exajoules (474×1018 J) with 80 to 90 percent derived from the combustion of fossil fuels. This is equivalent to an average power consumption rate of 15 terawatts (1.504×1013 W). Compare this with the prediction that by the year 2000, energy usage would reach 160-240 thousand twh.3 The need for more and more power has led to search for new energy sources, along with new modes of converting one form of energy into another. Today the most commonly used forms of energy are solar energy, chemical energy from chemical fuels, hydro power from rivers, seas and oceans, and nuclear energy from fissionable heavy isotopes. There is no gainsaying the fact that the rapid progress in technology and its present level could not have been achieved but for the use of basically new forms of energy, primarily electric power. Electricity can rightly be considered the basis of our civilization.

1

1.2 ELECTRIC POWER

Electricity is the flow of electrons (negatively charged particles) through a conductor. While electricity exists in nature, it is the man-made electric power that makes our life comfortable now. Electricity is generated primarily through the combustion of hydrocarbon fuels (coal, oil, natural gas), nuclear fission, and from renewable resources (hydro, geothermal, wind, biomass, and solar).

Coal retains the largest market share of electricity generation, 34 percent as in 2001, whereas renewable energy, predominantly hydropower, accounted for one-fifth of the world’s energy use for electricity generation in 2001. The nuclear share of energy use for electricity production was 19 percent in 2001 and oil accounted for 7 percent.

Three distinct functions are involved in supplying electricity in its usable form to the customers: generation, transmission and distribution, corresponding to production, transportation to market and retail distribution of many other products, the chief differences being that

i)

electricity moves from the generator to the end-use equipment in a continuous flow at a speed approaching that of light, and

ii)

it cannot be stored in its original form.

Generation, the production of electrical energy from mechanical energy, takes place at central stations normally far away from consumers necessitating the other two processes of transmission and distribution. Transmission is the moving of this electrical energy from generating plants through wire at high voltage to bulk delivery points called substations where it is transformed down to low voltage ready for distribution through low voltage lines to individual meters.

1.3 THE ELECTRIC POWER UTILITY

The electric utility is unique in that its product is one that must be generated at the instant it is to be used. If the utility has excess generating capacity, it can usually meet any anticipated demand; but an over-abundance of excess capacity entails increasing cost for idle hours. At 2

the same time few products have a greater need for quality and reliability — cases of brownouts and black-outs. As a matter of practical economics, electric power systems are so designed as to keep both the black-outs and brown-outs within tolerable limits by means of reserves.

One of the very important components of the electric power system is the customer's load which varies greatly at random according to time of day, day of week and season. A graph showing the variation in the demand for energy along time is called a load curve. From the load curve is derived load duration curve (LDC) defined as showing the amount of time that any given overall load level equals or exceeds a given capacity level. The LDC is one of the most important tools in electric power system planning and analysis.

1.4 TARIFFS

Tariff is the rate of payment or schedule of rates on which charges to be recovered from the consumer of electrical energy are computed. A number of tariff structures has been designed and put in use with various types of consumers.4 Usually cost differences have been the primary justification for rate structure differences. The traditional approach involves division of costs into three categories:

i)

capacity, demand or load costs,

ii)

energy (unit), output or volumetric costs, and

iii)

consumer costs.5

The first of these (‘kw costs’), related to investments in generation, transmission and distribution, vary with the speed and time with which customers use electricity. The second (‘kwh costs’) vary directly with the number of units generated; they are mainly fuel costs and operating and maintenance (o & m) costs. And the last are those costs varying directly with the number of customers served rather than units consumed. They include expenses on connexion, meter reading, billing, collection and consumer services. Then prices are set so as to recover historical (accounting) costs over these three categories with the ‘fair’ contribution from the several customer classes usually grouped in terms of diversity and load factor.

3

This backward-looking embedded (accounting) costs approach, concerned mainly with recovering sunk costs, ignores some very vital issues specially from the angle of efficient resource allocation.6 The prices should be related to the true value of additional resources required for an extra unit of supply and this necessitates a forward-looking estimate, i.e., pricing according to marginal costs (MC), which are calculated on the basis of expansion plans7 and operating schedules of the power system in line with demand variation.

1.5 SEASONAL TIME OF DAY PRICING

The spectre of rising electricity costs can be held in leash to a certain extent through load management of electricity usage, including direct (mechanical) controls on end-use equipments and time-differential tariffs. Load management meets the dual objectives i) of reducing growth in peak load, thus nipping the need for capacity expansion, and ii) of shifting a portion of the load from the peak to the base-load plants, thereby securing some savings in peaking fuels. By moving toward achieving these objectives electric utilities stand to win a cut in operating and capacity costs, share the gain with the consumers and provide a partial solution to the country’s energy dilemma.

Time-differential (peak-load) pricing of electricity is an indirect form of load management that prices electricity according to differences in the cost of supply by time of day and season of year. It reflects the costs in a more accurate manner than do the traditional block rate structures, as it logically stems from the marginal cost pricing theory, yet is compatible with the historical accounting costs. Again, compared to the block rate structures, the seasonal time-of-day (STD) pricing offers more potential for improving system load factors; its cost-based price signal motivates customers to modify their usage patterns, which in turn will move the system toward attaining the above twin goals.

1.6 GENERAL FRAMEWORK FOR IMPLEMENTING STD PRICING The experience of electric utilities that have already implemented STD .pricing serves useful information for formulating a general framework for considering and implementing timedifferential rates. The proposed framework runs through a series of activities.8

The first step is load research, in order to identify customer characteristics and thus to 4

determine the existing load shapes, on the basis of which preliminary steps toward rate design are made — on the part of the electric utility, supply costs and implementation costs are forecast and regulatory and financial requirements assessed; on the part of the customers, elasticity measures are determined; and the new parameters that go into the rate design are input into a cost-benefit analysis of STD rates. Elasticity measures help quantify load-shape modifications introduced by the peak-load tariffs. As such, they help assess the financial benefits of these rates: reduced capacity needs, improvements in s stem reliability levels, and energy conservation. They also signal for allocation of system revenues by customer class.

The cost-benefit analysis yields a new set of cost-effective rates about which an information flow with customers is open and customer reactions received and assessed. Actual application of the rates follows this experimentation.9

Several analytic approaches are available to estimate the own- and cross-price effects of STD tariffs. The principal effects can be determined from an analysis of variance or covariance of independently estimated equations for each rate period. Such estimation techniques impose a minimum of structure but are unable to exploit the implications of utility maximizing behaviour in the neo-classical demand theory in order to evaluate changes in consumer surplus which requires estimated demand curves. Hence the analysis is supplemented by highly structured systems of estimated demand equations. Some researchers, however, have been reluctant to resort to any a priori restrictions on the demand functions. In this case the choice of the functional form which is able to approximate a wide variety of underlying 'true' demand functions, is accomplished through a Taylor expansion in prices around some arbitrary demand function.

Neo-classical consumer theory, on the other hand, imposes restrictions on the electricity demands across different rate periods and frequently between electricity and other goods as well.10 However, a serious problem crops up in specifying empirical models of demand. The infinitely divisible time, in principle, makes the commodity-space infinite-dimensional. Temporal cost variation of electricity supply demands disaggregation of demand by time of day, week, year and so on. This approach in turn entails some assumption of smoothness of preferences lest we be left with a problem of estimating an infinite-dimensional taste parameter. One School (which represents virtually all the existing empirical work in this 5

field) sees preferences to be essentially constant within large blocks of time with abrupt changes in preferences at a few critical instants. The alternative to this discrete, almostalways-constant taste models is continuous-time models in which preference parameters change smoothly with time.11 Discrete-time models yield better approximations to the underlying preference pattern, and are considerably easier to estimate than the alternative one.

Another assumption frequently made in empirical studies related to homotheticity of preference over demand at various times of day, ensuring that quantity ratios and budget shares are invariant to the level of income. But such restrictive assumptions increase the risk of obtaining spurious empirical results.12 Dispensing with the homotheticity assumption involves the problem of admitting some dependence of budget shares on income. An effective approach is to specify preferences within an ‘electricity branch’ of a utility tree and to take total electricity expenditure as an income variable with that branch.13

1.7 PROBLEMS AND DRAWBACKS

Implementation of peak-load pricing involves substantial capital expenditure in changing meters and increasing customer service as well as transition costs of moving from one rate schedule to another. Especially in the case of LV consumers it is doubtful whether the benefits from a peak-load pricing systems are commensurate with the costs of metering and administering such a system.

Countries which have embarked upon STD rate systems have generally designed them for large industrial customers where metering costs constitute a trivial fraction of the total electric bills. To the extent that STD pricing has been applied to residential and small commercial customers in these countries, it has usually been preceded by some experiments and experiences with such rates.

Experiments, however, are not without drawbacks. Decisions on STD pricing will be delayed until the experimental data are evaluated. The experiments, by their very nature, can provide information on only short-run variations in customer behaviour which will typically be underestimates.14 Again, these experimental results, as they are in general, depends on how well the experimental designs were textured. A host of problems, including experimental (‘Hawthorne’) effects, non-random exclusions, participation biases, and incentive payments, 6

may make it very difficult to generalize from experimental results.15

A substantial quantum of information is required for analysis before the actual application of the rates. ceteris paribus parameter such as the own-price elasticity of demand will generate misleading predictions of the impact of STD rates on daily load shapes, unless it is supplemented by data on cross-price elasticities in other periods, income, end-use equipment composition and demographic variables. Moreover, data will be required on `initial conditions' such as the bench-mark shares of period consumption before a set of point-elasticity estimates can be applied to a given utility system. It is in order to note now that a full set of point-elasticity estimates will not yield precise predictions of modified load-shapes except where the underlying consumer preferences are characterized by constant-elasticity demand functions.

1.8 STD PRICING IN PRACTICE

It has long been argued and advocated that the sale of electricity and other services, in which periodic variations in demand are jointly met by a common plant of fixed capacity, should be at time-differential tariffs. SID electricity rates have widely been in use in Europe for several decades to reflect such peak-load cost variations. By contrast, the desirability and feasibility of implementing STD pricing of electricity began to receive serious consideration in the USA only during the 1970s, in response to the problem of rising costs of providing electricity service following the Arab oil embargo.16 The Federal Energy Administration (later the Department of Energy) sponsored a number of 'demonstration projects' designed to gather information on (residential) customer responses to time-differential tariffs.17

The EHV - HV and MV rate structures in European countries, where substantial thermal generation exists, reflect the importance of variations in both STD demand and fuel costs of the least efficient (marginal) plants operated during the various pricing periods. In the Scandinavian countries, blessed with hydro-power potential, seasonal variations in the water availability in terms of extra storage costs in the winter period tend to dictate the rate structure. The EHV - HV and MV rates designed in the developing countries are somewhat simpler owing to the need of a gradual rate structure transition, shortage of appropriate metering, etc. The LV domestic rates in all the relevant countries are also relatively simple as less complex metering is used, for example, demand charge based on peak-load 7

limited by breaker or fuse, or that rolled-in to energy charge using a typical customer's load factor. Off-peak night discounts are offered in some thermal-dominant systems.

Industrial and big commercial customers in Europe have responded to STD prices in many ways by orientating the pattern of production more toward off-peak period, generating own energy from waste heat or combustible residual materials during peak periods, storing heat and energy for peak-period use and so on. The dominant response has been to shift load from the peak to the off-peak period rather than to cut down energy consumption. For example, peak loads of most of the European industries have been reduced by 30 - 90 per cent, while the group load factor of 70 percent of industrial load in the UK has increased from 45 - 75 per cent over 1961-75 period.18

The less complex metering used for the LV customers has somewhat obscured the price signals, and hence for the effective implementation of these tariffs, many European countries have taken a supplementary coordinated package of other domestic load management techniques, including storage (space and water) heating during off-peak hours and central control of specific domestic loads such as ripple control. Peak-shifting has caused some problems especially in France. A combination of methods such as defining a wider peak period, redefining the peak period to include both actual and potential peaks, direct control of certain loads, etc. may be useful to counter this condition.

The European as well as American experiences corroborate that the benefits of implementing STD prices based on LRMC for EHV - HV and MV consumers could be substantial.19 A number of studies into STD pricing experiences have been carried out in several US states.20 Summary analysis of the energy conservation and welfare effects of STD pricing are given by Miedema, Lee and White (1981) and Aigner (1984). Miedema et al. conclude that STD prices reduce peak period consumption relative to control but usually have a negligible effect on off-peak period consumption leading to overall net conservation. Aigner, however, finds that STD pricing is cost-justified only in special cases, for instance, high kwh-use customers with air conditioners. Sexton et al. (1989) demonstrate, based on the STD pricing experiment conducted by the Southern California Edison Company, that the monitoring devices have a significant impact on the distribution of kwh consumption, tending to enhance load- shifting from the peak to the off-peak period. They interpret that these consumption effects represent marginal adjustments by customers to a desired (long-run) 8

equilibrium and hence that the results from STD pricing experiments may have understated customers’ desired response.

Application of STD prices to LV customers in the developing countries should be preceded by more studies to determine whether the substantial metering and service costs involved are sufficiently outweighed by the conservation benefits from improved consumption patterns. It is in order now to note that a British study has indicated that such a cost-benefit analysis would not justify STD prices for residential consumers.21 More generally, load management techniques, such as control of domestic water and space storage, have been found very effective in Europe and promising in the USA.22 The utility of the available load control technologies such as radio and ripple control, power line carrier, time switches, interlocks, load limiters etc. in the developing countries needs to be assessed further in terms of widely varying patterns of energy use, tastes and climate.

In fact, it is the development and availabilit y of hardware and techniques that effectuate the implementation of peak-load pricing.23 Thus progress in solid state technology may concoct cheaper metering which justifies more complex rate structures even for the LV consumers. Moreover improved load management techniques help the utility wield more effectively centralized control of end-use equipments and couple it with more precise and practically instantaneous pricing signals.

1.9 OBJECTIVES OF THE STUDY

In the light of the significance of time-differential tariffs reflecting temporal cost variations in electricity supply, the present study attempts at a marginalist approach to peak-load pricing, supplemented with empirical substantiation, suitable for less developed power systems in the face of inaccessibility to more sophisticated computerized long-range system planning models.

The main objective of this study is to formulate such peak-load pricing rules incorporating reliability considerations under various welfare-related assumptions, which are then used to estimate STD prices for electricity at different voltage levels in normal as well as in power famine situations in Kerala in India. The following tributary objectives make up the preliminary steps to the empirical study:

9

i)

to examine the techno-economic performance of the Kerala hydroelectric power system;

ii)

to analyze the reliability of the system in terms of water availability and outages; and

iii)

to formulate a simple method for estimating outage costs in terms of probability of demand exceeding supply.

1.10 METHODOLOGY

We have formulated a chance-constrained programming model for structuring peak-load prices applicable for the Kerala Power System. But the inaccessibility to a suitably large linear programming computer software has forced us to turn our course and take recourse to marginalist approach. We present an outline of the programming model in Appendix Al.

The present study seeks to structure the LRMC of a less developed power system in terms of the techno-economic parameters of a representative power plant, following, in general, the arguments by Turvey and Anderson (1977, Ch. 15) and Munasinghe and Warford (1982, Ch. 4); however, the model is sufficiently modified to incorporate diverse technology, outage costs and also ‘soft’ deterministic equivalents of chance constraints representing stochastic demand and inflows; and the solution is sought for two power systems, one pure hydro and the other hydro-thermal, under the umbrellas of the first-best, secondbest, monopoly and regulated monopoly assumptions.

For simplicity and convenience of computation in line with the desired adaptability for a less developed power system, we lean less upon sophisticated probabilistic analysis which may be unintelligible and unamenable for practical purposes; and the uncertainty hovering over the power system is captured in terms of chance constraints which can readily be converted into corresponding ‘soft’ deterministic equivalents using availability factors and penalty costs. Though this may detract from the analytical significance of such a study, it accomplishes the offer of an easy-to-use static tool for STD pricing.

1.11 DATA BASE

The relevant data required for the study have been obtained from the office of the 10

Kerala State Electricity Board (KSEB) at Trivandrum. A number of publications by the KSEB, such as Power System Statistics, System Operations, Annual Report, Annual Statement of Accounts, Plan Proposals, etc., and other unpublished reports and records have contributed to the data source. Existing-plant-wise data have been supplemented directly from the reports / log books of the power station considered. Thus, in the calculation of the loss of load probability (LOLP), data on the daily peak-load on each of the 10 power stations have been collected from the log books of the concerned power house for three years from 2001-02. Data on monthly rainfall at each of the dam-site have been supplemented from different volumes of the Yearbook of Surface Water published by the KSEB and also by the Kerala PWD.

For the empirical exercise, data on the techno-economic parameters of the representative plants, Kakkad hydro-electric project and Kayamkulam thermal power project, have been obtained from the Project Reports, Annual Reports, Plan Proposals and different files with the KSEB. Some recent exercises by the Research and Planning Wing of the KSEB have also furnished, though scanty, useful information.

1.12 PLAN OF THE STUDY

In order to develop the theoretical background for the empirical analysis, chapter 2 traces the major traits in the literature on public utility pricing. Chapter 3 looks into the lack-lustre techno-economic performance of the Kerala hydro-electric power system. Next chapter relates the results of the reliability analysis applied to the hydro-power plants in Kerala; water availability is assessed in relation to rainfall and firm power capacity, and LOLP of each plant estimated on the basis of probability of its capacity availability.

Chapters 5 and 6 bear the core of the study: formulation of static time-differential rate rules under the assumptions of welfare as well as profit maximization, both unconstrained and constrained cases, as adapted to a pure hydro and hydro-thermal system, accounting for outage conditions; and the empirical exposition of the rules at different voltage levels for the Kerala power system; a simple formula is derived for outage costs to be incurred in the event of demand exceeding supply and the seasonal penalty costs estimated.

While this first chapter has introduced the concept and indicated the course of the study, the 11

final one condenses and concludes it.

1.13 LIMITATIONS OF THE STUDY

As mentioned earlier, inaccessibility to suitable computer facilities has denuded the study of its dynamic dimension and forced us to focus on a static analysis. As forecast data on transmission and distribution costs are not available, only the generation costs have gone into the computation of STD prices, which therefore remain restricted in its scope of direct application. But it does serve the purpose of empirical exposition of the rules suggested.

NOTES

1. Ancient Greek legend has a Titan, Prometheus, who stole fire from heaven and brought it to people on the earth and who, as punishment, passed many years chained to Mt. Caucasus with an eagle tearing at his liver until freed by Hercules.

2. Venikov and Putyatin (1981, Ch.1).

3. Ibid.

4. For the different tariffs in use, see Edison Electric Institute (1976, Ch. 9), Partab (1970, Ch. 1) and Gupta (1983, Ch. 4); and for criteria for well-designed rates, see Bonbright (1961).

5. See Edison Electric Institute (1976, Ch.9), Turvey and Anderson (1977, Ch. 2) and Crew and Kleindorfer (1986, Ch. 8).

6. For detailed discussion see Turvey and Anderson (1977, Ch.2) and Munasinghe and Warford (1982, Ch.1).

7. There has been controversy about the dichotomy of choice between short-run marginal cost (SRMC) and long-run marginal cost (LRMC) pricing [see Foster (1963, Appendix 1), 12

Walters (1969, pp. 16-22) and Munasinghe and Warlord (1982, pp. 23-24)]. However, a simple reflection upon the temporal nature of these costs can clarify the issue. SRMC relates to the costs of an extra unit of consumption in the short-run with fixed capacity, while LRMC is the cost of meeting an incremental increase in consumption in the long-run with required capacity adjustments. To be more specific, SRMC is nothing but operating costs and LRMC, capacity costs.

8. See, for more details, Malko and Faruqui (1980).

9. Thus, for instance, the British experiment lasted for 5 years, compensated the participants for any adjustments in their stock of appliances taken in response to the tariffs and allowed them to continue on the tariff after the experiment was over.

10. See Aigner and Poirier (1980) for a general review and a critique of demand systems available for STD rate studies.

11. This approach is presented in detail for a continuous-time version of the linear expenditure system in Hendricks and Koenker (1980).

12. Thus, using Monte Carlo techniques Kohler (1980) proves that estimates using an indirect translog utility function with homothetic separability imposed can yield 'significant' price elasticities even when the actual data are devoid of any such characteristic.

13. For a detailed discussion on demand models in the context of SID rate studies, see Hendricks and Koenker (1980).

14. Of course, it is reasonable to assume that they form a lower bound on the potential gains from STD pricing.

15. See Hendricks and Koenker (1980), and Malko and Faruqui (1980); also Aigner and Hausman (1978 a and b).

16. See Mitchell, Manning and Acton (1978) for a review of the European pricing and Joskow (1977) for a history of the US pricing. 13

17. In all, about 15 ‘rate demonstrations’ were undertaken with the encouragement and partial support of the Department of Energy. Their principal features are reviewed in Hill et al. (1979) and Aigner and Poirier (1980).

18. Munasinghe and Warford (1982, p.92).

19. See Mitchell, Manning and Acton (1978) and Reynolds and Creighton (1980).

20. Malko and Faruqui (1980) present a brief survey of large industrial and commercial as well as residential customers' experience in the USA with STD rates. For a survey of the evidence on STD tariffs as applied to residential consumers in the USA, see Hendricks and Koenker (1980) and Caves and Christensen (1980).

21. Domestic Tariffs Experiment, Load and Market Research Report No.121, Electricity Council, London; quoted in Munasinghe and Warford (1982).

22. See deGrasse (1977) and Hastings (1980).

23. Munasinghe and warford (1982, p. 95).

14

CHAPTER 2

A SURVEY OF THE THEORY OF PUBLIC UTILITY PRICING

“Ben Franklin may have discovered electricitybut it is the man who invented the meter who made the money.” - Earl Warren

2.1 INTRODUCTION

The present study focuses on the structure of electric power system generation costs and prices; and this chapter is woven around the theoretical background consonant with the orientation of our empirical pursuit. Thus we start with an attempt at defining public utility in terms of its natural monopoly position and proceed to analyze its welfare implications under the two extreme assumptions of welfare and profit maximization in both unconstrained and constrained domains. We then go into the other terrain of non-uniform prices and explore the role of load factor in determining generation costs, whence we are directly led to our field of study: peak-load pricing.

2.2 PUBLIC UTILITIES

The traditional examples of public utilities are gas, electricity, telephone and water, and the more recent examples, cable television and waste treatment facilities. The technical features defining a public utility are those giving rise to economies of scale in public utilities and their consequent 'natural monopoly' position. Traditional definition of monopoly viewed as a single-product industry runs in terms of everywhere decreasing average cost curve, i.e., C (λx) < λ C(x), 1 0 ;  1 1 ' > 1  ­ ¥
¤

1 1 ' > 1  ­

Dry peak

¤¦

< ? KA › ' © ' } M 1 ' > ¤ ¤ 1 1 ' > 1  ­¤ ›

K? F  

1 1  ¡ ' ? › /}¥¦ ' A › M 1 ' > }¥ }¥¦ 1 1 ' > 1  ­ ¥ K ? F  ? › /}¤¦ ' A F M 1 ' > 1 1 ' > 1  ­ ¤¦

1 1 K? ›  }  } ¡ ' ? F /}¤¦ ' A F M 1 ' > ¤ ¤¦ 1 1 ' > 1  ­ ¤

Here the prices equal marginal costs inflated with weights imposed by the profit level constraint as well as the price-elasticity of period demand. These Ramsey prices warrant that the price-cost margin for each period is proportional to the marginal deficit (MR less MC) incurred in that period.8 The Bailey - White pricing reversal possibility appears here also.

5.7 CONSTRAINED MONOPOLY PRICES

It needs no note that care should be taken to reduce the abuse of monopoly motive to push up the prices beyond certain levels and thus to safeguard the socio-economic development. At the same time the utility should strive to reap a reasonable return on its capital. Hence on the assumption of a fair return, s, larger than the market cost of capital, k, the monopoly behaviour (5.5.1) may be constrained under a rate of return regulation9 of the form:  ∑x ∑G YxG „xG  K∑ †?  @  ' ∑ 1, and the superscript i should be defined in accordance with whether the system is pure hydro or hydro-thermal one.

Maximizing profit subject to the original set of constraints, (5.4.2) – (5.4.5), and (5.7.1), we get the following time-varying prices for our two systems under consideration:

Seasonal

Pure Hydro

Time-of-day Wet off-peak

A›

1 1­

¥¦

Wet peak

A › ' ? › /}¥ K1  1

Dry off-peak

Dry peak

λ

1λ

1 ­¥

A › ' 1 1 ' > 1  ­ ¥

Å

< ?› KA › ' © ' › M 1 ' > ä ¤ 1 1 ' > 1  ­ ¤

?› 1 1 F Å ›  }  } ¡ ' ? F /ä ' A F Æ 1 ' > ä ¤ ¤¦ 1 1 ' > 1  ­ ¤

?F 1 1  } ¡ ' ? › /Û¥ ' A › Æ 1 ' > F  } ¥¦ Ã¥ ¥ 1 1 ' > 1  ­ ¥

iv) Constrained Monopoly Model

Season Wet

Pure Hydro A › ' ? › /Û¥ K1 

λ

1λ 1 1­ ¥

†  1 M

104

A › '