The application of marginal cost pricing principles to a hydro-electric system

Resources and Energy 7 (1985) 353-375. North-Holland

THE APPLICATION OF MARGINAL COST PRICING TO A HYDRO-ELECTRIC SYSTEM

PRINCIPLES

The Case of Hydra-QuCbec* Jean-Thomas BERNARD Universit6

Laval,

Q&bee,

and Josee CHATEL Que., Canada

GlK,

7P4

Received May 1984, final version received April 1985 This paper develops a marginal cost pricing methodology for electricity generated almost entirely from hydro sites. We apply this methodology to the case of Hydro-Quebec, a large hydro-electric utility. Cost minimizing rules for the choice of generating equipment while taking into account the limited availability of water power are derived, and these form the basis for the estimation of the marginal cost of delivering power. Here are the main findings. First, prices based on the marginal cost of delivering power to final users would stand in a ratio of 15: 1 for the peak period versus the off-peak period. Second, prices established under the marginal cost principle would exceed current uniform prices in the peak period for all classes of users and they would decrease in the off-peak period for residential and commercial users. Third, such price changes could generate additional profits to Hydro-Quebec of more than one billion dollars a year even if the change in overall output is rather small. Finally, the welfare gain resulting from the application of marginal cost pricing would range from $270.0 to $530.0 millions a year, without taking into account the added metering expenses required to implement such a pricing scheme. 1.

1. Introduction The energy crisis of the 1970s created a new wave of interest in a seminal topic dealing with electric utilities. This topic is the application of marginal cost pricing principles to the provision of electric power when costs vary over time and consumer classes. Earlier writers had stressed the formulation of appropriate pricing rules while taking into account the most salient economic and technical features of electric power’, while recent contributors have directed their efforts to two related tasks’: (1) the measurement of the variables appearing in the theoretical model, that is, the construction of the appropriate price and cost data, and (2) the evaluation of the effects of *Financial support from FCAC, Minis&e de l’Education, Quebec and from Energy, Mines and Resources, Ottawa, is acknowledged. Special thanks are due to C. Seeto for pointing out an error and for suggesting several improvements. ‘See Dreze (1964). 21nstances of this type of study are Protti and McRae (1980) and Berg (1983). 0165-0572/85/$3.30 0 1985, Elsevier Science Publishers B.V. (North-Holland)

354

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and J. Chatel,

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cost pricing

principles

marginal cost pricing rules in terms of price and quantity changes through the incorporation of users’ responses. The present paper is also part of the more recent vintage, and its main objective is to assess the changes that could result from the application of marginal cost pricing by an electric utility which generates most of its power from hydro sources. This electric utility is Hydro-Quebec which produced 99.9% of its electricity from hydro sources in 1981.3 Furthermore it has access to some hydro sites which could be developed at lower cost than nuclear or thermal alternatives while taking into account distance to customers. Previous studies relied on the assumption that electricity would be generated from nuclear or thermal sources, at least at the margin.4 This paper deals with an almost all hydro electric utility, that is, an electric utility which draws most of its power from hydraulic sources with the exception of some gas turbines. Decision rules for the choice of cost minimizing generating equipment are derived by explicitly incorporating two limiting factors of hydro sites L the hydraulic power that is available at the generating site and the generating capacity that is to be installed - which together determine the power that can be generated. These decision rules form the basis for the computation of marginal costs of delivering electricity to each consumer class (residential, commercial, and industrial) for every loading period of the year (peak, intermediate, and base). The following section presents estimates of the marginal cost of supplying electricity at various voltage levels for each hour of the year while taking into account marginal transmission and distribution losses which vary according to voltage level and intensity of use. Section 3 provides the information with respect to consumer demand and the tariff structure. Particular attention is paid to bridging the link between data on consumption classified under the residential, commercial, and industrial headings, and the tariff structure applied by Hydro-Quebec for the base year, 1980. Section 4 uses the marginal cost estimates and the demand data to assess the impact of the application of marginal cost pricing in terms of changes in price, quantity, revenue, and economic welfare. 2. The costs of supplying electric power from hydro sources

The delivery of electric power to final users requires the operation of several pieces of complementary equipment. Before discussing the costs of major components, a description of the overall electrical network which is the object of this study would be helpful. Fig. 1 provides such a schematic representation. The supply of electrical power can be divided into three 3National Energy Board %ee Protti and McRae exception is Neveu (1978).

(1983). (1980)

for

Canada

and

Lillard

and

Acton

(1981)

for

U.S.

One

Generating stations

GENERATION

Transformers

Transformers

Medium voltage

network.

Transformers

I

DISTRIBUTION

Source: Adapted from Wildi (1978, p. 790) and Neveu (1978, p. 19).

Fig. 1. Schematic representation of Hydro-Qutbec

Transformers

TRANSMISSION

1201240 Volts

Residences Commercial establishments Small lndustrles

I

356

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cost pricing

principles

stages: generation, transmission, and distribution. Transformers are scattered along the network in order to modify the voltage to an appropriate level for either transmission or distribution. Customers can be linked to the electrical network at various voltage levels according to their needs. At one end of the spectrum, there are residential, commercial, and small industrial users receiving power in the range of 120 to 750 volts; at the other end, large industrial users take power up to 230 kV (=230,000 volts). On the demand side, electricity is not a good that is desired for its own sake, rather it is an intermediate good which has to be combined with some complementary equipment to provide the required services in the form of heat, motion, and electrolysis. The demand for these services is subject to a wide range of influences including the level and structure of economic activities, weather conditions, and availability of other sources of energy. As a result, the demand for electrical energy varies over time. In spite of the wide range of influences, the aggregate demand for electricity - made up of demands at different voltages - exhibits regular cyclical patterns over the course of a year. Currently, no economical means of storing electricity on a large scale are available, and thus inventories held by either consumers or producers cannot be used to even out production over time. Suppliers must therefore have access to sufficient generating capacity to meet demand at each point in time. Otherwise the demand of some users would not be satisfied. Marginal costs of supplying electricity to final users depend both on the period when the power is demanded and on the voltage level at which the power is delivered. The latter influences not only the transmission and distribution network but also the associated power losses. In order to illustrate the concept of marginal cost underlying the present study, let us introduce the tool commonly used to represent total demand for electricity as well as its variability over the course of a year, the load duration curve’, which is shown at the top of fig. z3 Let us suppose for the moment that this load duration curve were to remain constant, and that the electric utility were to choose the cost minimizing mix of equipment to satisfy this particular demand. What would be the real cost to be borne by the electric utility in order to permanently supply one additional kWh, if this added kWh were to be demanded by a residential, commercial, or industrial user over any one of the 8760 possible hours in a year? This is the interpretation of marginal cost which is used for estimation purposes. It is based on the cost difference between two plans, that is, the additional cost of changing supply by one kWh over the base plan. 5The load duration curve shows on the according to the capacity (the Y-axis) that number of hours in the course of a year Y-axis. The area under the load duration

X-axis the hours in a year ranked in decreasing order is required over each hour. So the X-axis gives us the when the capacity is at least at the level shown on the curve gives the total annual electricity demand.

J.-T.

Bernard and J. Chatel,

Marginal

cost

pricing principles

357

hours

Total cost of various

generatlng

equipment

ACH Pz 6-h) ACT*

ACHP,

(HJ ACT, I

AC9

I I I

H

9

hours

Hl

Fig. 2. Gas turbine vs hydro turbine with on-site additional hydraulic power.

The use of long-run marginal cost needs further justification. The debate over the choice of short-run versus long-run marginal cost to elicit effkient use of resources by consumers and suppliers of electricity has been settled by Boiteux under some simplifying assumptions.6 However, his solution is not 6Boiteux (1949) has shown that short-run marginal cost pricing together with optimal capacity addition ensure that short-run marginal cost pricing and long-run marginal cost pricing lead to identical price and output for each subperiod. This result is based on the assumption of fixed coefficient technology. The above result no longer holds when this assumption is relaxed. For an analysis of the peak load problem under neoclassical technology, see Panzar (1976).

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and J. Chatel,

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readily applicable to Hydro-Quebec at the moment, since the acknowledged surplus of electric power indicates that Hydro-Quebec is not on an equilibrium course.7 Under such surplus conditions, short-run marginal costs are difficult to assess as they depend on the state of the generating capacity, the availability of water over the year, the transmission capacity as well as the financial criteria under which Hydro-Quebec is operating. The information with respect to these variables is not readily available. In accordance with the long-run view adopted here, a sufficiently long planning horizon has been identilied for data collection, that is, 1970 to 1990. The data refer to projects which fall into three categories: realized, under construction, and on the drawing boards. This is the mix of equipment that was planned by Hydro-Quebec for use in the late eighties under demand growth scenarios adopted in the mid-seventies. An assessment of such long-run marginal costs has to rely on simplifying assumptions. that will be made explicit as the presentation proceeds. Let us stress at the start that no uncertainty of any kind on the demand or supply side is incorporated in the analysis.8 2.1. Generation cost9 The economic analysis of the choice of cost minimizing generating equipment to meet a given demand for electricity as specified by a load duration curve has given rise to numerous theoretical and applied studies.l’ The results depend on the economic and technical characteristics of the available set of generating equipment. In particular, generating equipment differs in terms of initial investment expenses, operating costs, and technical details related to maintenance and reliability. The emphasis thus far has been almost entirely on the choice of thermal generating equipment. For instance, Turvey (1968) and Anderson (1972) both considered the limited availability of hydraulic power, but they failed to develop explicitly the marginal decision rules guiding the choice of hydro equipment. This oversight is not too surprising in the light of the minor role played by hydro power in the overall supply of electricity in most industrialized countries. This is not the case for the particular electric utility which is studied here. The purpose of this section is to derive marginal decision rules for the optimal mix of generating plants in a system which is all hydro, except for See Hydro-Quebec (1982, p. 37). 8Neveu (1978) uses a probabilistic approach. The cost of the peaking unit is spread over all hours according to their probability of being the peak hour. QThis section is based on a previous paper by the authors. See Bernard and Chatel(1984). 1°D. Anderson (1972) provides a comprehensive survey of the main issues, of the methods developed to address them, as well as of the basic decision rules to minimize costs under various circumstances.

J.-T.

Bernard

and J. Chatel,

Marginal

cost pricing

principles

359

the possible presence of gas turbines which are used in the peak period, The framework is similar to the one ‘developed for a thermal system by Turvey (1968), with the difference that the main features of a hydro power system are now explicitly incorporated. Three aspects are underlined: (1) the limited availability of hydraulic power to activate the turbines,l’ (2) the total generating capacity of the turbines which determines the maximum pace at which hydraulic power can be turned into electrical power, and (3) the possibility of developing different hydro sites at rising costs. Once a hydro site becomes operational, its hydraulic capacity is fixed, except for rainfall fluctuations, and the water used at one stage is no longer available at a later stage. For the moment, our purpose is to find the optimal mix of power generating equipment to satisfy demand at the connection with the main transmission network which is designed to serve customers who are scattered over the service area.r2 Costs of site specific transmission lines as well as transmission losses are included in the costs of developing hydro power sites. To satisfy the energy and the capacity requirements embodied in the load duration curve that occur at the connection with the main transmission network, the electric utility is assumed to have access to two types of technology: gas turbines, and hydro power supplied by reservoirs. At this stage two types of cost are associated with each technology: initial investment expenditures and variable operating costs. The first cost is measured by a constant annualized amount per kW which takes into account the economic life of the equipment; the second cost is in terms of per unit of output. Fixed annual operating costs will be discussed in section 2.3. Gas turbines have low capital cost per kW relative to hydro generating plants and to other thermal plants; however they have high variable operating costs which are principally determined by the price of the fossil fuel. They can be turned on quickly and thus accommodate peak demand levels that are fluctuating over time. Since site specific elements of hydro systems are important, the economic characteristics of electricity produced from hydro reservoirs are not amenable to this kind of general formulation. The optimal design and operation of a hydro site for a specific purpose depend upon such factors as geography, distance, weather, and available means of transportation. These factors vary from one water basin to the next. By way of simplification, the following assumptions are made with respect to the set of hydro power sites available for development: first, the marginal cost of increasing hydraulic power required to produce electricity increases at an increasing rate for each site; ‘lHydraulic forces are a function of the height of the fall and of the amount of water that can be dispatched to the turbines. lZThe analysis of the transmission and distribution network for this purpose will be presented in subsection 2.2.

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second, turbines can be added at a power site over the relevant range at a constant cost per kW, but this constant cost differs across power sites, and finally, variable operating costs of hydro sites are assumed to be nil. More formally, the electric utility is assumed to choose the equipment mix that yields the least cost of meeting the demand represented by a given load duration curve. The choice set is made up of gas turbines which can be installed at the annualized cost of AC, per kW and which can be operated at the variable cost of 0, per kWh. The choice set also includes potential hydro power sites where turbines can be installed at a constant annualized cost ACT per kW. The cost of harnessing further hydraulic power for use by additional generating capacity is an increasing function of the number of hours that the additional capacity is in operation. The annualized value of this cost, ACHP,(H), is an increasing function of H. This is the number of hours when the added capacity of one kW is producing. Furthermore, hydro sites can be ranked according to their cost of installing turbines. ACT,
The test to check whether a generating plant mix is optimal with respect to cost minimization is as follows: at the margin, the substitution of one type of equipment for another fulfilling the same function, i.e., operating the same number of hours, should not reduce costs. Let us explore further the implications of this principle: at the margin, cost minimization implies that a kW of gas generating capacity can be substituted by one kW of hydro power including the added cost of developing the required hydraulic power for this added generating capacity. Algebraically: AC,+

H,O,=

ACT,

+ ACHP,(H,),

0) 2

where H, is the number of hours at which the producer is indifferent between installing one additional kW of gas turbine and one additional kW of hydro power with the required hydraulic power. This case is represented in fig. 2. For hours less than H,, .the load duration curve can be satisfied at a lower cost by installing gas turbines, while it is the converse when one unit of installed capacity has to be used more than H,. When the cost of additional hydro power is higher, whether due to the cost of turbines or of additional hydraulic power, more gas turbines are installed and operated for a longer period. Similarly at the margin, the producer should be indifferent between developing the first hydro site further and developing the second one, ACT,

+ ACHP,(H,)

= ACT,

+ ACHP,(H,),

(2)

J.-T.

Bernard

and J. Chatel,

Marginal

cost pricing

361

principles

where H, is the maximum number of hours per year the first hydro power site operates which is also the minimum number for the site two. The higher cost of installing generating capacity at power site 2, represented by ACT,>ACT,, has to be compensated by the lower cost of developing additional hydraulic power. Instead of adding turbines and making investments to increase the available hydraulic power at a given power site, the producer has another option. He can install additional generating capacity at the said power site without changing the available hydraulic power, and supply the energy deficiency by increasing both generating capacity and the available hydraulic power at the next least cost site. Cost minimization implies that the producer should be indifferent at the margin between these ways of producing electric power. This is represented by the following equation: ACT, + ACHP,(H,)

= ACT, - f$ ACT, + 2 1

ACT, + ACHP,(H,).

(3)

1

The installation of one additional kW at hydro electric power site 1, to be operated during H, hours without additional hydraulic power at that site, decreases the amount of water available to the other turbines, so that H,/H, of a kW is left without hydraulic forces to be operated for H, hours. This deficiency has to be made up by installing H,/H1 x kW at the next cheapest power site, and by augmenting the hydraulic power at the latter site with the associated annualized cost ACHP,(H,) to generate H, x kWh. This avenue has also to be checked against the possibility of making”‘up for the power deficiency by using the next site, and so on until it comes to the point where the producer has to choose between increasing the capacity and the energy of its most expensive site or developing one more power site. Substracting ACT, from both sides of eq. (3) yields ACHP1(H,)

= ACHP,(H,)

+ H$H,(ACT,

- ACT,).

(4)

Since ACT, > ACT,, we have that ACHP,(H,)> ACHP,(H,), that is, lower cost hydro sites in terms of installing turbines are developed more intensively than higher cost ones in order to generate the same volume of energy, albeit at a different pace over the year. The expansion plan of Hydro-Quebec in the late seventies provides the information needed to evaluate the marginal equilibrium conditions for cost minimization specified thus far in this section. A sufficiently long period is considered in order to incoporate a menu of generating equipment which reflects its different uses, i.e., peak load facilities (gas turbines: La Citiere), energy limited facilities (addition of turbines at power site Manic 5),13 and 13The dam

and the initial

generating

facilities

(1252 MW)

were

developed

in the early

sixties.

362

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and J. Chatel,

Marginal

cost pricing

principles

some base load facilities (the huge hydro project James Bay phase 1 with 10,769 MW). Furthermore cost estimates of the next important project with respect to base load facilities (James Bay phase 2) and the next energy limited project (James Bay phase 1) are available. Table 1 contains the basic data for each of these projects.14 The problem to be addressed at this stage is to find the range of the load duration curve over which each type of plant has a relative cost advantage, that is, to find the range for the use of gas turbines H,, of energy limited facilities H, represented by Manic 5 (M5), and of base load equipment whose role is played by James Bay phase 1 (JBl) and James Bay phase 2 (JB2). The combination of the left-hand side of (1) and of the right-hand side of (3) yields the following equation: AC,+ H,O,= ACT,,

- +ACT,, m5

++

ACTjbl + ACHPj,,(H,).

(5)

In5

All cost variables in eq. (5) are observable except for the cost of increasing hydraulic power at power site JBl, ACHPj,,(H,), which is the marginal cost of increasing hydraulic power at that power site. But we know from table 1 the average cost of generating power at the next cheapest base load generating facility, JB2. This provides a way of evaluating the marginal cost of additional base load power. Eq. (5) has two unknown variables, H, and Hm5, which are the minimum and the maximum hours the energy limited equipment is operating. The other equation is (3). Unfortunately eq. (3) includes the unobservable variable ACHP,,(H,), which is the cost of increasing hydraulic power at power site Manic 5. The role of this equation is to determine the total hydraulic power at that power site. The total capacity (kW) of the turbines and the available hydraulic power determine the capac$y factor; the latter is defined as the number of hours each kW of capacity is running over the potential 8760 hours. 0n the basis of the current production level, the modified capacity factor of power site Manic 5 resulting from the on-going expansion plan can be computed to be

H,+Kn5 = 0.23. 2 x 8760

(6)

14At this stage their status is the following: La Citiere is completed and operational, James Bay phase 1, as’ a base load facility, is partly operational and will be completed in 1985, construction work at Manic 5 has started, but completion has been delayed due to electricity demand slowdown, and, finally, work at James Bay phase 2 and James Bay phase 1 (energy limited) has been indefinitely postponed for the same reason. Further additions of gas turbines at La Citiere are experiencing the same fate.

“Source: See appendix.

Construction years Construction cost (present value 1980 S) Capacity (MW) Economic life (generation/transmission) Annualized cost per kW Variable operating cost per kWh (1980 $) Transmission losses (%) 0 5

65 0

75/none 35

980

77787 467 x IO6

Manic 5 (energy limited)

35/none 24

284

77-80 84 x lo6

La Citiire (gas turbines)

0 3

75135 138

10269

71-86 18.4 x lo9

James Bay phase 1 (base load)

Table 1 Costs of power generating project (1980 $): Quebec-Hydro.”

0 4

75/none 40

1893

84-91 1.013 x 109

James Bay phase 1 (energy limited)

0 3

75135 111

1974

81-90 4.85 x lo9

James Bay phase 2 (base load)

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and J. Chatel,

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cost pricing

principles

Eqs. (5) and (6) can be solved simultaneously for H, and H,,. This approach rests on the assumption that Hydro-Quebec performs similar calculations to determine the use of its equipment, that is, the capacity factor of Manic 5 has been determined by a criterion similar to the one embodied in eq. (3). Solving eqs. (5) and (6) leads to these results: gas turbines have a cost advantage over the range one to 297 hours, energy limited equipment (Manic 5) from 298 to 3733 hours, and finally, base load power from 3734 to 8760 hours. A report published by Hydro-Quebecl’ indicates that gas turbines have a cost advantage over the range from one to 2OCL300 hours when compared to energy limited equipment. Furthermore the huge James Bay project phase 1 is designed to have a capacity factor of 70% when it will be fully operational. I6 According to our calculation, its capacity factor should be 71%. It can be seen that the estimates presented in this paper are almost identical to those of Hydro-Quebec. Given the .optimal plant mix determined by cost minimizing rules, it is possible to evaluate what would be the marginal cost to Hydro-Quebec of altering this optimal mix in order to accommodate one additional kWh over the year, that is, over any of the 8760 possible hours. This is the task of the next section, once transmission and distribution are introduced in order to identify at what voltage level the additional kWh has to be provided. 2.2. Transmission and distribution costs Keeping in mind the objective of section 2 which is the estimation of the added cost of supplying one more kWh at the time and voltage level desired by the customer, let us go back to fig. 1. It can be observed that the transmission network has two main components: (1) a set of very high voltage lines from 315 kV to 735 kV designed to carry power from generation sites to the main transmission network, and (2) a set of high voltage lines from 115 kV to 230 kV which transmitpower over the service area. The costs of the first set of lines have already been included in the generation costs. It is the additional cost of transmitting power over the second set of lines and over the distribution network which must now be analyzed. At this stage, a distinction must be made as to whether the additional kWh is originating from a new customer or from an old one. It is assumed that the costs of establishing connection and the investment expenses in meters could be recovered from a mix of connection charges and fixed monthly charges. The neglect of these expenses on the cost side assumes that the producer would incur the same marginal cost to transmit and distribute power whether the additional kWh is coming from an old or new user. lSHydro-QuBbec 16Frayne (1980).

(1980b).

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and J. Chatel,

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365

Transmission and distribution losses vary both with the demand for capacity at a point in time and the voltage level. On the one hand, the higher is the demand for capacity, the larger are the losses for a given voltage level; on the other hand, lower voltage levels increase losses for a given demand for capacity. When presented with an additional kWh to be delivered at the consumer level during off-peak hours, the utility can use the existing transmission and distribution network due to slack capacity. More than one kWh needs to be generated because of the ensuing losses. The same phenomenon is present in the peak period; however power losses are higher. Investment in transmission and distribution would reduce losses not only for the peak hour but also for every other hour over the year. At the margin, the utility should be indifferent during the peak hour between incurring higher generation costs with no change in the transmission and distribution network, and investing less in generation but supporting additional transmission and distribution expenses while taking into account savings during the off-peak hours. Before turning to the presentation of estimates of hourly marginal cost by voltage levels, here is a short description of the procedure followed to estimate the marginal cost of expanding the transmission and distribution network. The added transmission cost per kW of installed capacity has been computed by dividing the annualized” constant dollar investment expenditures on transmission lines and the associated transformers at voltage levels other than 735 kV,l’ over the 1971-1981 period, by&the increase in the generating capacity over the same period. lg This yields a marginal transmission cost of $18 per kW. The same rules have been applied for distribution while neglecting meter investment expenses. This leads to an added cost of $28 per kW which has been shared in the ratio 50150 between medium and low voltage distribution. Table 2 presents estimates of the costs of generating one additional kWh over the year at various voltage levels. It can be seen that the two independent estimates of the marginal costs are not identical as the cost minimizing approach suggests they should be. The incorporation of fixed operating costs in the next section will reduce these differences substantially. 2.3. Fixed enterprise costs and fixed operating and maintenance costs

Except for fuel costs of gas turbines, no operating

costs of the fixed or

17Transmission lines are assumed to have a 35-year life. ‘aThere is one exception: the 735 kV belt around Montreal is included. i9The increase in the capacity from 1971 to 1981 is 7832MW. It includes the 5225MW generating capacity of Churchill Falls although the latter site is not owned by Hydro-Quebec. However, it excludes the generating capacity of James Bay phase 1 which came on stream at the end of this period.

366

J.-T.

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Hourly Voltage

and J. Chatel,

marginal

Marginal

Table 2 cost by voltage

cost pricing

principles

level (1980 $).”

Peakb

2-291

298-3733

37348760

High 69 kV

(26.50 + 0.066)’ (33.62+0.063)d

0.066

0.0183

0.0167

and more

Medium 2,4kV

(30.36+0.076)” (34.06 + 0.068)d

0.076

0.0203

0.0182

to 69kV

Low 120, 220, 750 v

(33.72 + 0.084)’ (34.52 + 0.073)d

0.084

0.0221

0.0196

“Source: See appendix. ‘The first figure is the capital cost component and the second one is the variable cost per kWh. “Marginal cost with no additional investment in transmission and distribution. dMarginal cost with additional investment in transmission and distribution.

variable kind have yet been introduced. Hydro systems are known to have very low, almost zero, variable costs. This is supported by various regression results in which constant dollar total operating and maintenance expenditures are regressed on measures of output such as sales in kWh and sales in kWh by customer class. The best tit is obtained by simply using total installed capacity as the explanatory variable. This yields an estimate of $23/kW for fixed operating and maintenance costs, plus $215 millions as fixed enterprise costs which would be mostly accounted for by head office and research activities.” It is assumed that the latter could be covered by various fixed charges and therefore they are ignored for pricing purpose in this paper. The fixed operating component, on the other hand, is added to the peak hour costs appearing in table 2 and the results are presented in table 3. It shows that the two ways,of estimating costs yield results that are not too far apart in spite of the simplifying assumptions made here. Because of the small differences, only the estimates for no additional transmission and distribution investment are used in the following sections. 3. Consum& data

The last section provided estimates of marginal costs of electricity by voltage level and by time of use. The ideal situation would be to have access Z”The

regression

result

is

x=215x

106+23X,+U,, t=65, 81, R2=0.92 (6.1) (8.3) where I;= total operating and maintenance expenditures in constant 1980$, available capacity in kW (including Churchill Falls) at the end of the year.

and

X,=

total

J.-T.

Bernard

Peak

Voltage

and J. Chatel,

marginal

cost

Marginal

cost pricing

Table 3 by voltage level OM (1980 $).

including

principles

367

fixed

level”

High

Medium

Low

51.89 +o.o66b 57.89 +0.063’

59.45 + 0.076b 60.30 + 0.068’

66.04 + 0.084” 62.47 + 0.073”

“The first figure refers to the capital cost component while the second one is the variable cost per kWh. “No additional investment in transmission and distribution. ‘With additional investment in transmission and distribution.

to demand functions for each of these categories corresponding to the 1980 tariff structure. In particular, the relevant marginal prices could then be replaced by the estimates of marginal costs. Unfortunately estimates of such demand functions are not readily available, the difficulty being in part related to the fact that Hydro-Quebec has never practiced anything close to time-ofuse pricing in the past. In order to circumvent this difficulty, various data sources are combined to obtain estimates of demand elasticities. The purpose of this section is to point out the major steps in this respect. The tariff structure as applied by Hydro-Quebec “provides the basic framework for data gathering on electricity consumption. It is this information which must be transformed into demand functions that capture the reactions of users to changes in the marginal price of electricity. Four tariff categories cover most of the internal sales of Hydro-Quebec: residential and farm use, and small, medium and large capacity general use.21 For our purpose, the first category is identified with residential users, the next two with commercial users, and finally, the last one, with industrial users.22 The first two rows of table 4 display the number of customers in each class, and sales in kWh in 1980. The next three rows present the energy (%) consumed by time of use for each consumer class.23 Due to its production characteristics, electricity is not sold at a constant price per kWh, and this makes it difficult to identify the proper marginal price for a broad group of users. A tariff schedule usually has three ‘IThe grouping is based on the level of capacity at which electricity is delivered: residential and farm (less than 5OkW), small capacity general use (less than 100 kW), medium capacity general use (100 kW-5000 kW), and large capacity general use (5000 kW and more). “About 20”/, of the electricity sold under medium capacity general use is considered to be in the industrial class. a3This partition is borrowed from an internal report of Hydro-Quebec for 1978.

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Table 4 Electricity consumption and price by user classes (1980).”

Number of customers Consumption (lo6 kWh) Peak hours (%) (lOh-12h and 16h-2h Dec. 1 to Feb. 15; Mon.-Fri.: 300 h) Intermediate hours (%) (Nov. 1 to April 30 except peak hours: 4044 h) Base hours (%) (May 1 to Oct. 31: 4416h) Average price ($) per kWh Corrected average price ($) per kWh Low voltage energy (%) Medium voltage energy (%) High voltage energy (%) “Source:

See

Residential

Commercial

Industrial

2,145,864 29,519

250,112 18,344

11,398 31,509

6.16

5.18

1.95

58.03

46.66

44.05

35.20

41.56

48.00

0.0275

0.0314

0.0172

0.0230

0.0306

0.0172

100.00 0.0 0.0

75.0 25.0 0.0

0.0 40.0 60.0

appendix.

components: a lixed charge which is unrelated to consumption, a variable capacity (kW) charge, and a variable energy (kWh) charge. The marginal price which is faced by each consumer at each point of time depends very much on the circumstances prevailing at that time. Since aggregate data are used in this study, a price must be obtained for each consumer class which reflects the marginal prices faced byeach member of the class. This price has been derived in the following way: the fixed charge per customer has been deducted from total revenues to arrive at net revenues generated by the capacity and energy charges.24 It is this corrected average price per kWh which is taken as an indicator of the marginal price faced by members of a consumer class. Both the usual average price and the corrected average price appear in table 4. The fixed charges as a component of price are left aside to go along with the neglect of meter investment and fixed enterprise expenses on the cost side. For the three tariff schedules applicable to general uses (commercial and Z4The total annual fixed charge has been obtained by multiplying the annual charge by the number of customers in a class. Most of the commercial users are in the small capacity general use category and the fixed charge of the latter has been applied to all members of the class. Industrial users pay no fixed charge.

J.-T.

Bernard

and J. Chatel,

Marginal

cost pricing

369

principles

industrial customers), the power can be delivered at various voltage levels. To go along with estimates of marginal costs which vary by voltage level, information is needed on the power that is delivered at each voltage level by consumer class, and this appears in the last three rows of table 4. To complete the demand data, table 5 presents estimates of price elasticities by consumer class and by time of use. Since no estimates were directly available for Quebec consumers, they are drawn from another Canadian study.25 Two estimates are used to provide a better idea of the possible range of responses. Table 5 elasticities.”

Price Peak Low

Intermediate High

Low

Base High

Low

High

Residential Peak Intermediate Base

-0.10 0.0 0.0

-0.30 0.0 0.0

Peak Intermediate Base

-0.12 0.0 0.0

- 0.42 0.0 0.01

Peak Intermediate Base

-0.30 0.0 0.0

-0.90 0.15 0.05

“Source:

See appendix.

0.0 -0.25 0.0

0.0 -0.55 0.0

0.0 0.0 -0.20

0.0 0.0 -0.60

0.0 -0.55 0.01

0.0 0.0 -0.30

0.01 0.01 -0.80

0.15 - 1.00 0.05

0.0 0.0 -0.35

0.05 0.05 - 0.90

Commercial 0.0 -0.15 0.0

Industrial 0.0 -0.33 0.0

4. The effects of marginal cost pricing

Before turning to the results presented in table 6a (low price elasticity estimates) and table 6b (high price elasticity estimates), one should observe that prices based on marginal cost are in fact averages of marginal costs for hours in their respective period, i.e., peak, intermediate, and base. The main implication of this is that the capital cost component associated with the gas unit is spread evenly over the three hundred hours of the peak period; this amounts to assuming that all hours in this period stand an equal probability of being the actual peak and no other hour has any chance of occupying such a position. 25Protti

and McRae

(1980).

The effects

of marginal

Table 6a cost pricing:

p.4

P*

QA

0.023 0.023 0.023

0.3035 0.0220 0.0197

1999.5 17164.7 10411.8

1544.8 17336.8 10739.3

29576.0

29620.9

low

Q*

elasticity

estimates.a

AQ

AP

AR

AW

Residential P I B Subtotal

0.2805 - 0.0009 -0.0033

-454.7 172.1 327.5

422.86 -11.64 -27.91

63.77 0.08 0.54

44.9

383.31

64.39

-252.7 452.8 1278.1

206.58 -66.35 - 72.92

33.53 2.01 7.16

1478.2

67.31

42.7

-1386.1 -470.9 -61.1

239.41 17.36 1.96

163.07 0.45 0.006

Commercial P I B

0.0306 0.0306 0.0306

0.2960 0.0216 0.0194

Subtotal

1060.28 8559.31 8724.4 18340.0

807.5 9012.1 10002.5

0.2654 -0.0089 -0.0112

19822.1 Industrial

P I B

0.0172 0.0172 0.0172

0.2525 0.0190 0.0174

2504.97 13879.72 15124.32

1118.8 13408.8 15063.2

0.2353 0.0019 0.0002

Subtotal

31509.0

29590.8

- 1918.1

258.73

163.53

Total

79248.8

79033.8

- 395.0

709.35

270.62

“Notes: P =peak, I =intermediate, B = base; P,= average price (1980 $): table 4; P* =price based on marginal cost (1980$): tables 2, 3, 4; Q,=quantity of electricity consumed by period (gWh): table 4; Q*=quantity of electricity consumed under marginal cost pricing (gWh); AP =P*-P,; AQ=Q*-QA; AR=change in revenues (millions 198OS); AW= -$AQAP=change in welfare (millions 1980 $).

The effects

of marginal

Table 6b cost pricing: high

p*

P*

QA

0.023 0.023 0.023

0.3035 0.0220 0.0197

1999.5 17164.7 10411.8

922.1 17545.7 11425.7

29576.0

29893.5

Q*

elasticity

estimates?

AP

AR

AW

Residential P I B Subtotal

0.2805 -0.0009 -0.0033

-1077.4 381.0 1013.9 317.5

233.87 -7.03 - 14.39 212.45

151.11 0.17 1.67 152.95

0.2654 - 0.0089 -0.0112

-651.5 1781.0 4082.3

88.53 -37.53 -18.52

88.69 7.59 22.86

5211.8

32.18

119.14

-2281.7 4822.3 2085.2 4625.8

13.27 118.48 39.31 171.06

252.92 1.94 0.02 256.88

10155.1

415.69

528.97

Commercial P I B

0.0306 0.0306 0.0306

0.2960 0.0216 0.0194

Subtotal

1060.28 8559.31 8724.4 18343.9

408.7 10340.3 12806.7 23555.7 Industrial

P I B Subtotal Total

0.0172 0.0172 0.0172

0.2525 0.0190 0.0174

2504.97 13879.72 15124.32 31508.9

223.2 18702.0 17209.5 36134.7

79248.8

89583.9

0.2353 0.0019 0.0002

“Notes: Terms are defined in table 6a; the measure of the change adapted to take into account that demand functions are interdependent.

in economic

welfare

is

J.-T.

Bernard

and J. Chatel,

Marginal

cost pricing

principles

371

The first column of table 6a and 6b shows that commercial users pay substantially more per kWh than the two other classes of users. Our estimates of the cost of delivering electric power by voltage level would not support such a high price for that class of users.26 Price based on marginal cost would lead to price differentials which would be in the ratio of 14: 1 for peak versus intermediate period and in the ratio 15: 1 for peak versus base period for all three classes. The information with respect to the price changes (AP) from uniform average prices (PA) to prices based on marginal costs of delivering power to each consumer class (P*) indicates that prices over the peak period would rise substantially, while there would be a slight decrease in the intermediate and base period for both residential and commercial users. For industrial users, there would be an increase in all three periods. The insertion of P* in logarithmic demand functions incorporating the price elasticity estimates of table 5 leads to new quantities demanded Q*: dQ indicates the extent of the change. Price elasticity estimates differ in two ways: first, the high estimates of own price elasticities are slightly less than one and are about three times as large as the low estimates; second, some of the high estimates of cross-price elasticities are positive while the low estimates are zero. These estimates of price elasticities would lead to a significant reduction in the demand in the peak period and to an expansion in the off-peak periods. 27 For the low price elasticity estimates, these two opposite changes are almost offsetting, while the high estimates yield a 13% expansion in total electricity demand. The price adjustment induced by marginal cost pricing would cause a 30% increase in revenues under low price elasticity estimates and 17% for high estimates. These higher revenues, and the associated reduction in costs that results from changes in production, would lead to higher profits of $1.275 billions under low price elasticity estimates and of $1.211 billions under high price elasticity estimates. The higher profits are caused by a combination of factors such as time differentiated tariffs, use of a real rate of discount of 7.4% which is higher than the rate entering Hydro-Quebec’s evaluation, and use of economic depreciation rather than historical costs depreciation. The role played by each factor is not evaluated here. These higher profits could be used to cover some (or all) of the added metering expenses and of the fixed enterprise costs discussed in section 2. They could also find their way into the Government of Quebec treasury through the dividend policy ,already in effect. Since all costs have been accounted for in the present exercise, the residual is pure profit which can be 26This higher price for commercial users Qu&bec which requires the electric company power to each user class. Z70ne exception is the industrial demand estimates.

is also in contradiction with the mandate of Hydroto set price in agreement with the cost of delivering in the off-peak

period

under

the low price

elasticity

312

J.-T.

Bernard

and J. Chatel,

Marginal

cost pricing

principles

attributed in part to the cost differentials of developing the hydro sites which are operated by Hydro-Quebec. A cost minimizing approach leads to the development of low cost sites before higher cost sites.28 The marginal site yields no rent under such a scheme since price is set equal to its marginal cost: however lower cost sites have the potential for generating rent. Until now, it has been the policy of Hydro-Quebec to sell power at the cost borne by the electric utility and no rent has been collected by owners of hydro sites. Our estimates suggest that these potential rents have been dissipated in part through the sale of peak power at less than cost for all three consumer classes and through the sale of power to industrial users at less than cost in all three periods. Changes in prices, quantities, costs, and revenues from uniform average cost pricing to time differentiated tariffs are illustrated in fig. 3. It is seen that uniform pricing leads to too large an output for the peak period and too small an output for the off-peak one; furthermore some of the cost savings linked with the low cost site .Q, are passed on to peak users.

Fig.

3. The effects

of marginal

cost pricing.

The last column of table 6a and 6b shows the changes in economic welfare that would accompany a move from uniform average cost pricing to time differentiated pricing based on marginal cost estimates developed in section 2. This value of economic welfare change is $270.62 millions for the low price elasticity estimates and $528.97 millions for the high price elasticity estimates. This represents 11% and 22% respectively of Hydro-Quebec’s total income in 1980. It should be pointed out that these estimates of the 28Solow

and Wan

(1976).

J.-T.

Bernard

and .I. Chatel,

Marginal

cost pricing

principles

313

change in economic welfare would need to be adjusted downward to take into account the added metering expenses. Since the industrial users would contribute about half of the change in economic welfare, maybe there is room for restricting the application of time differentiated tariffs to this particular class. The number of users is small and the metering equipment already in place is capable of measuring hourly consumption. 5. Conclusion

Hydraulic forces which drive the turbines at various hydro power sites are scarce resources that should be priced properly if the objective is to induce their efficient use. On the basis of the theoretical framework presented in this paper, it has been estimated that proper accounting of the limited availability of hydraulic forces and of the costs of developing various hydro power sites would create cost differentials of generating electricity in the order of 15: 1 between peak and off-peak periods. If the current practice of average cost uniform pricing were replaced by prices based on the marginal cost of delivering power to consumers, a sharp decrease in peak demand and an expansion in the off-peak periods would follow. Such price and output changes would substantially boost Hydro-Quebec profits and would also generate a change of economic welfare in the order of $270 millions to $530 millions a year, without considering the added metering expenses. This is obviously a first round analysis which does not take into account the effects of the implied output changes on the functions performed by various hydro sites. The results presented here indicate that further work along these lines should be pursued. Appendix: Data A.l. A.l.1.

Cost data Generation

Annual construction expenses for the various projects are drawn from two sources: first, 1971-1982 for realized projects or projects under construction: Hydro-Quebec, Annual Report; second, 1981-1990 for completion of projects under construction or projects yet to be started: Hydro-Quebec (1980a, 1982). The generating capacity (kW) is obtained from the same sources. Interest during construction is subtracted for each year and the remaining expenses which go toward the payment of administration, labor, materials, equipment, and services peculiar to each project are converted into 1980 $ [Hydro-Quebec (1981a, 1981b)]. The annual expenses are then converted into present value of 1980 $, while taking into account the transfer into service of each generating unit. The real rate of interest for this purpose is 7.5%; this estimate is derived from Helliwell et al. (1973). The present value is then

314

J.-T.

Bernard

and J. Chatel,

Marginal

cost pricing

principles

converted into an annualized equivalent payment over the economic life of the project. Economic lives are drawn from Bernard et al. (1982). Variable operating cost for gas turbines is obtained from Energy and Resources, Government of Quebec (private communication). Transmission losses have been computed on the basis of information obtained directly from HydroQuebec. A.1.2. Transmission, distribution and associated power losses Annual investment expenses in transmission and distribution were obtained from Hydro-Quebec, Direction Comptabilite des Immobilisations. Hydro-Quebec, Direction Recherche Economique (1981a) provides price indices for these expenses. The economic lives are assumed to be 35 years for transmission and 25 years for distribution. See Bernard et al. (1982). The yearly change in generating capacity was obtained from Hydro-Quebec, Annual Report, annual. Hydro-Quebec gave us information on cumulative transmission and distribution losses by voltage level and by time period. A.1.3. Operating and maintenance expenditures Hydro-Quebec, Annual Report, annual. A.2. Consumption’ data The number of consumers and total electricity consumption come from Hydro-Quebec, Annual Report, 1980. The information with respect to electricity consumption by period (peak, intermediate, and base) and by voltage level for all three consumer classes has been obtained from HydroQuebec. Estimates of price elasticity of demand are adapted from Protti and McRae (1980) table C.4 and table C.6. A.3. Data sources Frayne, A., 1980, Trends affecting Hydro-Quebec rates policy, Service de la Tarification, HydroQuebec, Sept. Helliwell, J., G. Sparks and J. Frisch, 1973, The supply price of capital in macroeconomic models, in: A. Powell and R. Williams, eds., Econometric studies of macro and monetary relations (North-Holland, Amsterdam) 261-283. Hydro-Quebec, various years, Annual report. Hydro-Quebec, 1971-1981, Etat des variations de comptes de construction en cours, Direction comptabilite des immobilisations. Hydro-Quebec, 1980a, Plan des installations 1981-1990, Direction de la Planification, Nov. Hydro-Quebec, 1980b, Rapport sur les etudes d’avant-projet, Centrale de Pompage Delaney, Nov. Hydro-Quebec, 1981a, Historique des taux d’inflation, 1972 a 1981, Direction recherche economique, Dec. Hydro-Quebec, 1981b, Previsions des taux d’inflation, Direction recherche economique, Dec.

J.-T.

Bernard

and J. Chatel,

Hydro-Quebec, 1982, Plan des installations National Energy Board, 1983, Canadian 1981 (Ottawa) April.

Marginal

cost pricing

principles

1983-1992, Direction de la planification, electric utilities: Analysis of generation

315 June 1982. and trends:

References Acton, J.P. and B.M. Mitchell, 1983, Welfare analysis of electricity-rate changes, in: S.V. Berg ed., Innovative electric rates (Lexington Books, Heath and Co., Lexington, MA) 195-226. Anderson, D., 1972, Least cost investment models, The Bell Journal of Economics and Management Science 3, no. 1, 267-301. Berg, S.V., ed., 1983, Innovative electric rates, issues in cost benefit analysis, (Lexington Books, Heath and Co., Lexington, MA). Bernard, J.T. and J. Chatel, 1984, The role of energy limited equipment in an optimal plant mix, Energy Economics, forthcoming. Bernard, J.T., G.E. Bridges and A.D. Scott, 1982, An evaluation of potential Canadian hydro electric rents, Resources paper 78, Program in natural resource economics (University of British Columbia, Vancouver) Feb. Boiteux, M., 1949, La tarification des demandes en pointe, Revue Generale de l’Electricit8 58, 321-340. Translated as: Peak load pricing, The Journal of Business 33, no. 2, 1960, 157-179. Dreze, J.H., 1964, Some postwar contributions of French economists to theory and public policy, with special emphasis on problems of resource allocation, American Economic Review 54, no. 4, Supplement, part 2, 64. Lillard, L.A. and J.P. Acton, 1981, Seasonal electricity demand and pricing analysis with a variable response model, The Bell Journal of Economics 12, no. 1, 71-92. Neveu, G., 1978, Etude du cotit marginal de l’tlectricitt methodologie (Hydra-Quebec, Montreal), Revised Nov. 1978. Panzar, J.C., 1976, A neoclassical approach to peak load pricing, The Bell Journal of Economics 7, no. 2, 521-530. Protti, G.J. and R.N. McRae, 1980, The impact of rate structure change on electricity demand: A case study of Calgary Power Limited (Canadian Energy Research Institute, Calgary). Solow, R.M. and F.Y. Wan, 1976, Extraction costs in the theory of,exhaustible resources, The Bell Journal of Economics 7, no. 2, 359-370. Turvey, R., 1968, Optimal pricing and investment in electricity supply: An essay in applied welfare economics (Allen and Unwin, London). Wildi, T., 1978, Electra-technique (Les Presses de l’universite Laval, Quebec) (Les Entreprises Sptrika Ltte).