the marginal costs of electricity supply in victoria

The Marginal Costs of Electricity Supply in Victoria*

PETER HARTLEY CHRIS TRENGOVE Princeton University, and Monash University, and Monash University,

Princeton, NJ 08540, USA Clayton, Victoria 3168 Clayton, Victoria 3168

This paper dkcusss some of the determinants of the costs of StrppIying eIectricity by season, by time of day and by location. A model is constructed of the State EIectricity Commission of Victoria grid to illustrate the propositions. It k found that current tariffs bear Iittle relationship to the opportunity costs of supplying electricity.

In this paper we illustrate some influences on the marginal costs of supplying electricity using a simple model of the State Electricity Commission of Victoria (SECV) grid. More particularly, we illustrate how marginal costs are affected by short- run operating costs and long-run capital costs, the availability of hydroelectric capacity and restrictions on its time of use, and transmission losses. We also discuss, but do not model in a formal way, interactions between demand conditions and marginal costs, and the value of interruptibility to electricity supply authorities or, equivalently, the costs of not having sufficient capacity to meet high demands or cope with plant breakdowns. In the final section we compare electricity tariffs with the opportunity costs of electricity supply.

I Some Relevant Theory’ OptimaI Capacity and Congestion

To begin with we shall ignore the spatial

‘This paper is the result of work carried out for the Centre of Policy Studies’ (1982) report, ‘Energy Pricing Issues in Victoria’. We would like to express our thanks to the remaining authors of that study, as well as to Ron Griffin of the SECV and Rob Booth of CRA Ltd, for many helpful discussions. Thanks also go to Kerry Moloney for providing the computer programming input and to two referees for useful comments.

‘The primary focus of the paper is the illustration of some influences on the marginal costs of electricity supply. This section is not intended to be a survey of the extensive

distribution of demand and suppose there are jus t two components of cost. Let c1 be a constant, per period, marginal operating cost’ and cz be a constant, per period, marginal cost of expanding capacity. Suppose we identify electricity supplied in three different time periods, each of length one period, as being three products supplied by the system and assume the demand curves are as in Figure 1 and demands in the three periods are independent of prices charged in the remaining periods.’

The demand for capacity in period 3 is given by the vertical distance between the period 3 demand curve and the short-run cost curve, cl. For example, if the existing capacity were q,, period 3 customers would be willing to pay @, - c,) at the margin t o expand capacity. However, customers in periods 1 and 2 would not exceed available capacity if it were q1 and would not be willing to pay for increased capacity, which is, for them, a ‘free good’. Now suppose the current capacity were q1 instead of q,. Period 2 customers would also use all

literature on marginal cost pricing, but rather a brief discussion of some of the issues most directly relevant to our study. The interested reader can consult Rees (1976), Turvey (1%8) and the symposium in the Bell Journal of Economics (1976), and the references cited therein, for further details.

’Note that c, will in general depend on the length of the period.

’Pressman (1970) discusses peak load pricing when demands in different periods are interdependent.

‘ - confinued

340

1984 ELECTRICITY COSTS 34 1

FIGURE 1

available capacity if charged the short-run operating costs. c,, and would in fact be willing to pay @: - c,) at the margin to expand capacity. Similarly, period 1 demanders would be willing to pay up to @; - c,) to increase capacity. But any expanded capacity would be supplied jointly to the two groups of users and hence their demands for capacity expansion should be summed vertically to give the total system demand.‘

The optimal system capacity, q*, is given by the intersection of the demand for capacity expansion with the cost of expanding capacity (Figure 2). Capacity will be a free good in period 1 so the marginal cost of supplying output will be c,. On the other hand, there will be ‘congestion’ in periods 2 and 3 if users are only charged cl. Consumers would be willing to pay up to pf in period 2 and pf period 3 to gain access to the available supply of electricity, with the result that the opportunity cost of electricity in those periods exceeds the generation cost, cI. In a world of stationary demand and costs, the optimal ‘congestion tolls’, @? - c,) and (pf - cl), would generate just enough revenue to cover the cost of providing capacity to replace depreciation of existing plant.

‘When the peak and off-peak periods are nor of equal length, Williamson (1966) suggcsts the graphing of short- run marginal costs as the operating costs of supplying an incremental unit of output over an entire cycle (peak plus off-peak) and capacity costs as the annualized per cycle capital costs plus average maintenance costs over the cycle. Similarly, demand is graphed as the output per cycle which would be demanded at each price were the demand in quation to prevail over the entire cycle. The demand for capacity expansion then becoma the weighted sum of the demands in the peak and off-peak periods, with weights equal to the proportions of peak and off-peak demand.

FIGURE 2

So far we have assumed (homogeneous’) capacity that can be enlarged continuously, rather than in discrete lumps. In fact, although very small units of base load generating capacity may be technically feasible, their costs are prohibitive. Base load generating capacity in Victoria, for example, is currently expanding in 500 MW jumps.‘

In Figure 3, the marginal cost curve for capacity expansion becomes vertical at the limit of each increment to capacity (i.e., at qr and ql). Suppose the curve Dr represents the current aggregate demand for capacity expansion and q, is the current

’Wenders (1976) discusses peak load pricing when a range of plants is available to provide new capacity. These plants will typically have a hierarchy of capital costs and a reverse hierarchy of operating costs. He shows that the proportions of the cycle over which each plant would be operated would be chosen to balance out the higher fuel cost of peaking plant against its lower capital cost. If these periods of operation over the cycle do not correspond to the fluctations in demand, Wenders shows that off-peak consumers may also bear a capacity charge. An increase in demand in the lowest demand period leads to an increaud demand for base load capacity. This allows for some substitution of base load for intermediate load capacity in the intermediate and peak periods. Only if the length of the intermediate and peak periods corresponds to the period of operation of the intermediate plant will the cost savings from lower operating costs match the higher capital cost of base load plant.

‘MW denotes megawatt, or one million watts. Also used in this paper are kilowat (kW) and gigawatt (GW) for one thousand watts and one thousand million watts, respectively. Electrical energy is measured in kilowatt- hours (kWh), etc., and transmission voltages in kilovolts (kV).

342 THE ECONOMIC RECORD DECEMBER

capacity.’ Suppose D,, is the expected aggregate demand for capacity next period. The benefits of expansion next period by one unit will be abcf and the costs adef. It will be optimal to expand capacity only after dbg exceeds gec: In the meantime, aggregate ‘congestion charges’ in period 0 will be (p, - c,) , exceeding c,. and immediately after the expansion in capacity will fall below c2. The fact that it proves to be optimal to expand capacity in discrete lumps implies that congestion will increase in the short run as the existing capacity falls far short of peak demands and then, after system expansion, there will be very little congestion even at the peak.’

I I I 9 0 91

FIGURE 3

Intertemporal Trade in Electricity The above discussion implies that the

opportunity cost of electricity is likely to be higher when system demands are at a peak even when short-run operating costs are constant. However,

’See Williamson (1966) for further discussion of this model. When both peak and off-peak demands exhaust available capacity at a price equal to marginal operating cost, ‘congestion charges’ will be paid by both peak and off-peak customers but will vary by time of day. When there arc peak and off-peak customers the aggregate demand for capacity can be most w i l y obtained by the procedure outlined in footnote 4.

‘If new plant embodies a superior technology, with lower short-run costs, it will in general be optimal to bring it on stream earlier than this analysis would suggest. See Turvey (1968) for further discussion.

‘A more general model would allow for the possibility of intertemporal demand substitution, from before the date of capacity increase, to after that date. This will have the effect of attenuating the difference between pre- and post-expansion congestion charges.

a utility usually has available to it several generating plants with different ratios of capital to operating costs. If it is cost minimizing to use the capital intensive plant at all, such plant must necessarily display comparatively low operating costs and it will be cost minimizing to use it for as many periods as possible. Plant with lower capital costs (for example, gas turbines) may then be used to satisfy peak demands even though operating costs are higher. This configuration of plant use implies that operating costs, in addition to congestion costs. are likely to be higher in peak periods.

If consumers faced prices for electricity which reflected opportunity cost they would have an incentive to switch their demand from peak to off- peak times. Households could shift cooking and cleaning times. and make use of stored hot water, while industrial consumers might re-schedule production processes, or generate their own electricity from waste heat. However, such adjustments will have costs. Pricing electricity to reflect opportunity cost would not remove all time variation in demand levels.

A utility which has access to hydroelectric capacity can shift the supply of electricity across time periods by storing potential energy as water in dams. Moreover, the rapid start-up of the turbines increases the suitability of hydro capacity as a means to smooth out peak loads on the thermal system. Turbine capacity limits the maximum instantaneous supply of electricity from hydroelectric plant, but the major constraint is the amount of energy which can be supplied over the entire season.

II A Model of the SECV System’’ The Products Supplied

While the cost of supplying electricity to any user will be a function of both the time at which the user draws power, and his location in the State, it would be prohibitively expensive to calculate these costs for each of the (infinity of) possible timelspace alternatives. We instead consider discrete approximations to the ‘true’ system cost function. The geographical element is modelled by adopting a simplified representation of the transmission system (the grid), with regional demands concentrated at particular ’nodes’, and the time element is analyzed

“For further details of the model see Centre of Policy .Studies (1982, Chap. 11). The basic model is closely related to that discussed in Scherer (1977). See also Rowse (1980) and Turvey and Anderson (1977).

1984 ELECTRICITY COSTS 343

*Figures in parenthesis are the year of first operation for each station.

FIGURE 4 The Victorian Electrici!y Grid

by selecting a fured number of representative periods.

Our schematic representation of the SECV grid is shown in Figure 4. Because of data availability, the State is divided into regions corresponding to the Electricity Supply Regions used by the SECV (cf. Annual Report 1980-81. Appendix 6) . Figure 4 also lists the generating plants located in each region, and their year of first operation. Note that the heart of the SECV system is the collection of brown coal stations in the Latrobe Valley (node 1) which provide the State's base load power. Finally, the figure shows the lengths of each transmission link and the transmission voltages.

Ideally, the daily load curves for each region could then be examined and a number of representative seasonal load curves chosen. As we do not have load curves for individual regions we assume the load curve has the same shape throughout the

State." The relative demands for electrical energy in each region are obtained from the 1980-81 SECV Annual Report, Appendix 6, and these are used to weight the overall system load curve to obtain the regional time-variant demands. * * Four load curves are used; three to approximate week days (winter, summer and spring/autumn) and one for

"It appwrs that in fact the northern regions have a summer peak demand (irrigation and air conditioning) while the south has a winter peak (industry and domestic heating).

"Some allowance must be made for transmission losses since the demands appropriate to the model are those registered at the transmission nodes, prior to the distribution stage.


weekends.” The load curves are converted to load- duration curves showing the number of hours demand exceeds a given amount. Each load- duration curve is then approximated by a step function with a load-factor equal to that of the actual load curve.“ The representative load curve for winter 1980 is presented in Figure 5 . together with its corresponding load-duration curve and step approximation. It is to be emphasized that the demands represented in such curves are demands given current prices. A change in tariff structure will alter the load curve to an extent depending on own- and cross-price elasticities of demand at different times of the year.

FIGURE 5 Winter Loud and Loud Duration

‘The approximations to the ‘SpringIAutumn’, ’Summer’ and ‘Weekend’ load curves have 3, 3 and 2 steps, respectively .

”Load curves for the year 1979-80 (supplied by the SECV’s Production Coordination Department) were used to determine both the shape of the ‘average’ daily load curve in each of the four periods chosen and the relative magnitudes of the loads between seasons.

“If loadduration curves differed by region, then the choice of partition for the step functions would nnd to be adequate to approximate u// regional load-duration curves.

The Planning Period Given expected changes in technology and

demands and expected physical depreciation of existing plant over some ‘planning horizon’, we could attempt to build an explicit dynamic model of the system which would show how the marginal costs of meeting demand would change over time. However, for a planning period of N years, the number of decision variables in the analysis would be multiplied by N. Given the scope of this study it was decided instead to attempt an analysis in a ‘static’ framework. We implicitly consider two time periods - a short run and a long run. In the short run, power output from each generating station can be increased up to a capacity limit by using more fuel and employing more labour for maintenance. In the long run new capacity can be brought on if it is economic to do so. This enables us to approximate the marginal costs for an ‘average’ year within the period.

In our formulation, capital costs of proposed capacity expansions are taken into consideration, but interest and depreciation charges on existing plantI5 have no impact on the solution. In order to capture those elements of system design which depend on replacement and expansion of capital equipment it is therefore necessary to ensure that the planning horizon is sufficient to encompass decisions on the introduction of new plant. We calculate marginal costs in a situation where Newport D, the second stage of Yallourn W, and the first unit of Loy Yang can each be brought on stream as new plant to satisfy demand. This scenario does not correspond to the planning situation currently facing the SECV. At the time of writing. the three above-mentioned plants are either operational or partially completed. Our static model corresponds to an ‘average’ year in the early 1980s (with all costs in 1980 dollars), as viewed from a period in time prior to the construction of the new plant. costs of Supply

The main technical activities involved in electricity production are generation, transmission and distribution. The model only considers the generation and transmission activities, since, to a good approximation, distribution costs can be separately estimated and then added on to obtain the overall costs of supplying particular classes of customers.

”This is only valid if the net scrappage value of existing plant is zero.

1984 ELECTRICITY COSTS 34s

In order to model generation costs realistically it is not sufficient to assume a strict division between fixed costs (annual capital charges for new plant) and variable costs (depending on actual generated output). Many costs, for example, most labour costs, are incurred to make existing capacity available. Thus, the capacity limit for base load stations can be changed by increasing maintenance in the off-peak periods to reduce the probability of plant failure during peak periods. Futhermore, the stations are not totally indivisible units, and their level of manning (particularly for peak load stations) can be lowered if only partial usage is anticipated. There are also start-up and shut-down costslwhich depend on how often plants are used rather than the amount of electricity produced.

The model uses three types of variable to simulate costs of generation. The discrete variable, x,,, for each plant n, takes the value 1 if the plant is used to supply the system in any period and 0 otherwise. The continuous variable, En, represents the maximum output of the plant. Actual generations at time t are grit. The costs of maintaining and running a plant, or introducing it if it is new, then become

T

t = 1 + b n i n + C cnigntht

where a,, depends on the scrappage value of the plant if it is old, or construction cost if new, b,, is a function of those maintenance and administrative costs which are independent of plant usage but do depend upon available plant capacity, cnt are strictly variable costs (mostly fuel) and h, represents the number of hours in period t.

The capital charge, a,. is calculated as a constant annual payment satisfying

M L an

t = 1 K= C k,(1 + r)' = C

t = 1 (1 + r)I

where K denotes the real capital cost of the plant (including interest costs during construction), M is the number of construction periods. k, is the construction cost t periods before the plant is brought on stream, L is the economic life of the investment and r is the real interest rate (5 per cent in the base case). Since we ignore scrappage possibilities, the only positive a,, are those for the new plants. The calculated values, in millions of 1980 dollars, are 37.9 for Loy Yang, 46.7 for

Yallourn West 2 and 27.0 for Newport D." The remaining cost variables, b,, and cntr are shown in Table 1."

Thecosts of transmission links can also bedivided into operating and capacity costs. Annual costs of keeping the link in the system are mainly maintenance costs, though there will also be a capital charge for new links (and old links too if their net scrappage value is non-zero). To simplify the model we have assumed an unchanging grid configuration. That is, no decision variables associated with possible new links. or with the maintenance of old

"All calculations assume a thirty year operating life. The time profile of construction costs (1980 Smillions) is (S.20,60,110,100.90,60) for Loy Lang, (5.15,40,70,130.140,70,60) for Yallourn West 2 and (10,20,30,30,40.30,4,70,25,5) for Newport D. These values arc based on actual construction costs for Yallourn West and Newport D and estimated costs for Loy Yang. n e time profile of expenditures is. however, only roughly approximated. Also, historical costs are adjusted to 1980 values using the building materials price index which may not be an accurate measure of current costs. In the case of Loy Yang, capital costs have been calculated ignoring the difficulties which arise from the staggered construction and operating periods of the eight SO0 MW units-for an elegant solution to this problem see Swan (1983). Note also that the Loy Yang estimates have been excccded by actual construction performance.

"We assume that b, and cn, are strictly linear functions of capacity and output. respectively. This is sufficient to yield easily comprehensible but non-trivial results, but more complicated (and more accurate) assumptions could be utilized if so desired. In particular, nonlinear cost fundons could be approximated by several linear functions. The values in Table 1 were arrived at from data available in the SECV Annual Reports supplemented by information from industry sources. The costs, c,,, are largely bascd on 1980 fuel costs, and, while perhaps not accurate, at least capture the distinct hierarchy of plant operating costs which the SECV system displays, and which has such a strong influence on model results. The coefficients. b,, were determined by apportioning the cost of labour to each plant in proportion to its share of the total labour employed in all plants. (The Loy Yang values are based on projected fuel and labour usage, in 1980 prices). The assumed Snowy operating cost of I .6c/kWh may be misleading. The opportunity cost of Snowy water is probably its marginal value for generating electricity in NSW. Being unable to estimate this value, we take the overuge cost of Snowy water lo Victoriu as an approximation. As we note, this value can be raised somewhat without altering the optimal system configuration-though total, average and marginal costs and the shadow value of Snowy power are all affected by such changes.


TABLE 1

Generating Station In formation

n Station Gn bn Cnt A,, Sn Rnt

1-4 5-7 8-10 11,12

1 Hazelwood 2 Yallourn West 3 Yallourn 4 Morwell 5 Jeeralang 6 Newport 7 Richmond 8 Spencer Street 9 Loy Yang

10 Yallourn West 11 Newport D 12 Vic Hydro 13 Snowy

1500 I 750

490 190 500 190 39 95

500 2 750

500 485

1084

25 0.7 0.73 0.63 20 0.9 0.77 0.67 40 1.3 0.71 0.61 45 1.1 0.82 0.72 10 3.2 0.9 0.9 25 7.0 0.9 0.9 20 6.8 0.9 0.9 25 6.5 0.9 0.9 15 0.5 0.75 0.65 20 0.9 0.77 0.67 15 3.0 0.9 0.9 20 0.2 0.95 0.95 - 1.6 0.95 0.95

0.53 0.63 0.57 0.67 0.51 0.61 0.62 0.72 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.55 0.65 0.57 0.67 0.9 0.9 0.95 0.95 0.95 0.95

0.9 0.9 0.9 0.9 0 0 0 0

0.9 0.9 0 0 0

0 0 0 0

0.85 0.75 0.75 0.75 0 0

0.85 0.9 0.9

~~ ~~

Note: G, is rated capacity (MW), b, is intermediate-run cost (S/kW-year), c,, is variable cost (c/kWh), Ant is plant availability, R,, and S,, are reserve capabilities.

links, have been incorporated. Operating costs are transmission losses as a function of the power transmitted through the link." Table 3, showing the base case pattern of transmission, lists the percentage losses on each link. Constraints on the System

To calculate marginal costs we minimize the total cost of producing sufficient electricity to supply all regions over all periods subject to a variety of constraints. These are demand, capacity, reserve, and hydroelectric constraints.

Power supplied at time period t and at node i must at least equal demand at the node at that time, d;, . Transmission variables are included by specifying that power generated at the node plus power transmitted to the node be equal to outgoing transmissions plus the demand for electricity at the node. The Lagrange multipliers on the demand constraints give the marginal cost of satisfying that demand.

"As a first approximation, transmission losses are taken to be proportional to the square of the current transmitted on each link with the Same constant of proportionality for each link, chosen so that total losses approximated actual losses on the SECV system in 1980-81. The quadratic functions are then approximated by linear functions.

Output, g,,,- must not exceed the available capacity, Anrg,, of each unit, where the parameters A,, reflect the fact that full capacity will not normally be available for any one plant due to planned and unplanned servicing requirements, strikes, etc. In turn, available capacity cannot exceed maximum rated capacity, G,. The values of G, and A,, for the base case are shown in Table 1."

Extreme values of either demand or available capacity can occur, and the system should be designed to reflect the value which consumers of electricity are likely to place on relatively assured supply. The model of this study does not incor- porate an explicitly stochastic approach to the determination of reserve capacity." Instead, deterministic constraints of the form

"These figures were determined on the basis of the reported average utilization rate of various plants and an arbitrary though plausible scheduling of required hours of down-time for maintenance.

"A traditional measure used to express system reliability is the 'loss of load probability' (LOLP). The LOLP may be set to achieve an average of, say, one


are included. The parameters R,, and S,, represent abnormally low supply capabilities, and can be varied according to period if need be. Abnormally high demand is represented by the parameter Vr (0.3 in the base case).

In practice, generating units are not all equally suitable for providing reserve power. Gas turbines and hydro units can be more rapidly and cheaply started and shut down than can brown coal base load stations. Consequently, both plant capacities, in, and actual operating levels, g,,, appear on the left-hand side of the reserve constraints. Table 1 gives the values of R,, and S,,, in the base case and reflects this varying ability to supply reserve capacity. For the base load stations S,,r is set to 0.9 (adverse operating conditions) and R,r to zero to correspond with the difficulty of increasing their output in the short run. The reverse procedure is adopted with the peak thermal and hydro units.

The constraints on hydroelectric operation assumed in the base case included an 'energy' constraint on each of the two units. The model allows no more than 700 GWh per year to be produced from the Victorian hydroelectric stations (Vic Hydro) and no more than uxx) GWh per year from the Snowy Mountains (Snowy).'l

In the case of the Victorian hydro facilities, the water storages are dual purpose in that they are used for irrigation. In order to model this joint use, we assume that a minimum fraction of 0.55 of the 700 GWh Vic Hydro energy capacity must be devoted to the summer periods (8, 9 and lo)."

Y-mntinued

brownout every ten years, and will depend on the probability distributions of both demand and supply. With respect to supply variability, there is an important trade-off between the size of the largest units and the need for reserve capacity. Our deterministic approach is less satisfactory than one based on actual probability distributions, but there is a partial justification in that our model treats maximum unit sizes as exogenous. I f we were, say, to allow the model to select the optimal size of unit for the new Loy Yang station, instead of constraining its capacity to be 500 MW, then a stochastic formulation would be rather more desirable.

"The allowance for the Snowy may be somewhat generous in dry years. A stochastic model would need to take variations in precipitation into account.

"The actual institutional arrangement is that the irrigation authorities determine the amount of water to be released on each day, while the SECV decides at what time. during the day, the given amount is to be released.

III Model Results The Base Case

Table 2 shows the full set of generation variables, including the operating levels of each plant in each period. Under the base case assumptions the optimal system configuration involves operation of all existing stations-with the exception of the peak thermal stations Newport, Richmond and Spencer Street - together with the construction of the new stations Loy Yang and Yallourn West 2. All stations included in the system are to be operated at an available capacity level equal to their rated capacity, with the exception of Yallourn G, = 345 MW), Jeeralang Gr = 475 MW) and Vic Hydro (& = 221 MW).

Hazelwood, Loy Yang and Yallourn West 2 are operated throughout the year at full available capacity. Demand is sufficiently small in the off- peak weekend period (period 12) for Yallourn West 1 to be only partially utilized at that time = 357 MW). All other periods. with the exception of winter period 4 when the Yallourn station is only partially utilized @,,, = 16 Mw), involve full usage of available capacity on the six base load brown coal generating units. All of these (ten) periods also involve some hydroelectric generation. Although part of the system, the Jeeralang station is represented as being unused throughout the year. In effed it is providing reserve capacity but making no contribution to average generations."

Table 2 also shows the instance of the two types of system loss which are incorporated within the model. For example, in period 1 total generations are 3828 MW, 94.5 per cent of which actually enters the grid, the rest being used up within the stations. Of this 3618 MW. 5.7 per cent is absorbed in transmission losses, leaving 3412 MW to satisfy demand.'. Summing across the table, total demands are 22 002 GWh. the satisfadion of which involves the generation of 24 650 GWh.

"In this deterministic model then, the capacity factor for such a station (zero) is misleading, since normal operation will generally require some generation in order to cover abnormal supply/dcmand conditions when they arise. In fact, during 1980-81. Jceralang station ran at a capacity factor of 54 per cent in order to cover a number of adverse supply and demand conditions, such as the poor performance of the Hatelwood station.

'.Transmission losses in this model are likely to be biased downwards because average, rather than peak, demands are included and we assume a quadratic loss function.

TABLE 2

Base Case System Operation

Station Capacity in G, grit

Factor Winter Spring/Autumn Summer Weekends 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2

Hazelwood ON 62 I500 1500 1095 1095 1095 1095 945 945 945 195 795 795 945 945 Yallourn W1 ON 62 I50 750 511 577 511 517 502 502 502 421 421 421 502 357 Yallourn ON 31 345 490 245 245 245 16 210 210 210 176 176 176 210 0 Morwell ON 56 190 190 155 155 155 155 136 136 136 117 111 111 136 0 2 Jeeralang ON 0 4 1 5 5 0 0 o o o o o o o o o o o 0 m

Richmond OFF - 0 39 0 0 0 0 0 0 0 0 0 0 0 0 0

Loy Yang ON 64 500 500 375 315 315 315 325 325 325 275 275 275 325 325 Yallourn W2 ON 66 150 150 571 511 577 511 502 502 502 421 421 421 502 502 5

Vic Hydro O N 16 221 485 221 91 210 0 131 0 21 210 210 156 0 0 8 Snowy ON 21 1084 1084 592 513 123 0 513 319 16 621 363 0 % 0

Totals Annual (GWh) Generation 24 650 3828 3630 3360 2191 3261 3001 2660 3050 2792 2375 2118 2129 Entering grid 23 118 3618 3428 3149 2615 3088 2831 2488 2892 2634 2221 2548 1991 Transmission losses 1 176 205 190 161 148 158 143 132 141 117 96 133 94 (Percentages given below) 5.1 5.7 5.6 5.3 5.7 5.1 5.1 5.3 4.9 4.5 4.4 5.2 4.1 Demand 22 002 3412 3237 2982 2461 2929 2688 2355 2151 2516 2124 2415 18%

Note: G, is rated capacity (MW), in is maximum output (gross of planned and unplanned outages), g,, is operating level.

Newport OFF - 0 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 8 Spencer St OFF - 0 95 0 0 0 0 0 0 0 0 0 0 0 0 8

Newport D OFF - 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - By period (MW)

0 0 rn rn 5 rn z,

TABLE

3

Bas

e C

ase

Tran

smis

sion

Lev

els

Nod

es

App

roxi

mat

ion

Perc

enta

ge lo

ss

Win

ter

Spnn

g/A

utum

n Su

mm

er

Wee

kend

s Li

nked

St

ep (M

W)

1 st

2nd

12

34

56

78

91

01

11

2

1, 2

60

0 2.

3 7.

1 86

1 81

7 75

2 62

2 73

9 67

8 60

0 69

4 63

5 600

609

600

1, 3

80

0 2.

6 8.

3 16

65

1717

17

93

1749

14

61

1532

16

26

1165

12

35

1289

16

14

1222

2,

3

300

1.2

3.8

0 0

0 0

0 0

5 0

06

3

01

19

3,lO

50

0 3.

8 11

.5

0 0

0 25

2 0

0 19

4 0

0 16

15

3 13

3 8

3, 2

30

0 1.

2 3.

8 0

00

00

00

00

00

0~

3,

4

450

2.5

7.4

607

576

548

460

521

485

450

494

460

450

450

413

3.11

-

1.6

- 0

00

00

00

00

00

0~

4,

5

50

1.5

5.5

96

91

84

69

82

76

66

77

71

60

68

53

,+ 10

0 1.

5 4.

2 11

8 11

2 12

0 10

6 10

1 10

0 11

2 10

0 10

0 14

3 10

3 14

0 .e

4,

6

5, 6

6,

7

- 1.

9 -

35

33

31

25

30

28

24

28

26

41

25

43

2 50

1 .o

3.

9 0

0 17

21

0

6 30

4

12

50

20

50

7, a

-

2.9

-

0 0

0 0

0

0 0

0 0

19

0

23

6,

9

50

1 .o

3.9

00

00

00

00

00

00

-

3.6

- 42

39

36

30

36

33

29

33

31

7

29

0 9,

6

9, 8

10

, 3

500

3.8

11.5

36

8 21

0 0

0 28

1 71

0

474

272

0 0

0 10

, 9

100

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Table 3 gives the values of the transmission levels on each link. The use of two linear functions to crudely approximate the nonlinear loss function nevertheless allows some switching to take place across transmission paths according to the level of power to be transmitted. For example, periods 7, 10 and 12 involve partial usage of the link connecting nodes 2 and 3 in order to avoid larger transmission losses on the (1,3) link. The main qualitative change in the structure of transmissions depends on if and when hydroelectric power (in the north-east of the State) is generated. In periods 4, 7, 10, 11 and 12 power must be transmitted from the metropolitan area to the north-east because of insufficient generation in this area.

Table 4 gives the system marginal costs of supplying electricity for the base case. Over all locations, a marginal kilowatt-hour of electricity is most cheaply supplied in period 12 (weekend off- peak). As noted above, this period involves only partial utilization of the available capacity of Yallourn West 1. The next least costly period of supply is period 4, also involving partial usage of the Yallourn station. All other periods display some generation of hydroelectric power. With the exception of periods 8 and 10, the model sets the marginal cost of additional demand in node 12 (Snowy) at 2.49 c/kWh. The marginal valuation placed on additional energy capacity (additional water) from the Snowy, or the shadow price associated with the Snowy energy constraint. is 0.89 c/kWh. (The difference between the 2.49 c/kWh

,and 0.89 c/kWh equals the assumed Snowy operating cost of 1.60 c/kWh.) Moreover, this shadow price is equalized across periods when hydroelectricity is generated. If demand is altered at node 12 (the Snowy) during any one of these periods the system response will be the same. Of the stations which actually generate power, the Snowy is the most expensive (1.6 c/kWh) based on the hierarchy of operating costs. The positive shadow price of 0.89 c/kWh is due to other cost savings, related to the capacity costs, bn, which would occur were additional water available.

The anomalous marginal cost in period 10 is due to the fact that the irrigation constraint on Vic Hydro generation is binding. Additional demand in this period is less costly to service because a certain level of hydroelectric generation must already occur to satisfy irrigation needs. Put equivalently, reduction of demand in period 10 by one kilowatt-hour would allow something less than a reduction in costs of 2.49 cents, because of the

lack of freedom to reallocate newly available hydro energy to other periods.

Under the base case assumptions power is most expensive to supply in period 8, the summer peak. This is the only period for which the reserve constraint is binding, and its contribution to marginal costs is 2.29 c/kWh. If an additional kWh is demanded in period 8, apart from any additional generation which will be required (which will largely come from alteration of Yallourn capacity and generating levels), an additional reserve of 1.3 kW must be pr~vided.’~

The fact that the most costly period of supply occurs in the summer rather than the winter, when demand is greatest, is due to the plant availability factors assumed in the base w e (see Table 1) together with an allowance for interruptible demand during the winter peak.“ Although this result might appear rather surprising in the Victorian context, there is apriori no reason why this should not be the case. Naturally, if plant availabilities for the base load stations are revised to reflect altered maintenance schedules, so that more capacity i s available in the summer and less in the winter, then the most costly period will move.

Table 4 also quotes the total cost of supplying the annual 22 002 GWh of electricity demanded as $401.4 million, giving an average cost of 1.82 c/kWh. Multiplication of the quantities of electricity demanded at each location at each time by the relevant marginal cost of supply gives $545.2 million per year, or in other words, an ‘average revenue under marginal cost-pricing’ of 2.48 c/kWh. This would equal actual average revenue under marginal cost pricing only ifdemands were unchanged by the implied restructuring of tariffs. It is larger than the average cost of 1.82 c/kWh but there are other sunk costs which need to be covered so that it is difficult to say whether or not long-term supply is financially viable under these conditions.

”This capacity increment will come from the Jeeralang station at a cost of $30.6 (equal to $20 per kilowatt multiplied by 1.3 and divided by 0.85, the relevant supply reliability figure from Table 1 ) . Dividing this figure by the number of hours in period 8 in each year (83 1/3 multiplied by 8) yields the required figure, 2.29 c/kWh.

“For the purposes of meeting the reserve requirement, the winter peak of two hours has been adjusted downwards (by 220 MW) to allow for the possible short- term intmuption of one or two potlines at the Alma Point Henry aluminium smelter. See also Section III . sensitivity to reserve parameters.

1984 ELECTRICITY COSTS 35 I

TABLE 4

Base Case Marginal Costs

Supply Region Winter SpringIAutumn Summer Weekends 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2

Gippsland 2.57 2.45 2.43 1.39 2.45 2.45 2.27 4.86 2.45 1.63 2.27 O.% Eastern Metropolitan 2.75 2.62 2.60 1.49 2.62 2.62 2.43 5.04 2.62 1.75 2.43 1.03 Metropolitan 2.78 2.65 2.63 1.51 2.65 2.65 2.46 5.07 2.65 1.77 2.46 1.04 Barwon 2.99 2.84 2.82 1.62 2.84 2.84 2.56 5.28 2.84 1.84 2.56 1.07 South-Western 3.15 3.00 2.98 1.71 3.00 3.00 2.70 5.44 3.00 1.94 2.70 1.13 Mid-Western 3.11 2.% 2.94 1.69 2.% 2.94 2.67 5.38 2.94 1.91 2.67 1.11 Wimmera 3.17 3.02 3.00 1.72 3.02 3.00 2.72 5.44 3.00 1.95 2.72 1.13 Mallee 3.23 3.08 3.08 1.76 3.08 3.08 2.79 5.53 3.08 2.01 2.79 1.17 Northern & Midland 3.12 2.97 2.97 1.70 2.97 2.97 2.69 5.41 2.97 1.94 2.69 1.14 North-Eastern 2.68 2.55 2.55 1.56 2.55 2.55 2.55 4.97 2.55 1.84 2.55 1.08 Portland 2.82 2.69 2.67 1.53 2.69 2.69 2.50 5.12 2.69 1.80 2.50 1.06 Snowy 2.49 2.49 2.49 1.60 2.49 2.49 2.49 4.78 2.49 1.88 2.49 1.11

Total system cost 5401.4 million Shadow prices for hydro constraints Average cost 1.82 c/kWh Snowy energy 0.89 c/kWh Average marginal cost 2.48 c/kWh Vic Hydro energy 2.19 c/kWh

0.67 c/kWh Reserve cost 2.29 c/kWh Vic Hydro irrigation

Note: ‘Average marginal cost’ is the average of the marginal costs in the table, weighted by the quantities of electricity supplied. ‘Reserve cost’ forms part of the marginal cost of supply for the period in which the reserve constraint is binding.

Sensitivity to the Real Interest Rate An important parameter of the model as far as

the determination of capital costs is concerned is the real interest rate. Row 2 of Table 5 (row 1 summarizes Tables 2 and 4) gives results in an abbreviated format when the real interest rate is increased to 10 per cent from the base case value of 5 per cent. Annual capital charges for the three new stations are thereby increased to $82.2 million (Loy Yang), 5104.6 million (Yallourn West 2) and $62.3 million (Newport D), in 1980 prices. The higher capital costs cause construction of Yallourn West 2 to be forsaken and increase the utilization of existing stations. Richmond and Spencer Street are now both included in the system to provide reserve capacity (with Spencer Street’s capacity only partially available) and the Jeeralang power station is called on extensively, running at a capacity factor of 62 per cent.

Total costs are now $465.7 million, an increase of 16 per cent. The only period in which the base load brown coal stations are not fully utilized is the weekend off-peak period (period 12) when the marginal unit of power comes from the Yallourn station. All other periods require utilization of some Jeeralang power and (with the exception of

period 4) some hydroelectric power. Consequently, the marginal cost of an additional kWh demanded in node 12 (the Snowy) in periods 2 to 11 is 3.75 c/kWh. This figure is determined by the cost of power sent out from Jeeralang (3.42 c/kWh) and transmission losses. The irrigation constraint is now non-binding because of the reduced availability of cheap base load power.

The peak period has now been shifted to period 1, the winter demand peak. The incremental cost due to the need to provide reserve capacity is 26.0 c/kWh (raising the period 1 marginal cost considerably) and is significantly larger than the corresponding cost in the base case for two reasons. First, the marginal unit of reserve is provided by the Spencer Street station at higher operating cost than that provided by the Jeeralang station in the base case. Second, the capacity cost must be allocated over a smaller number of hours in the year, since period 1 is of a two-hour duration. as against the eight-hour duration of period 8.

Overall, the increase in the real interest rate creates an increased need t o save on f i e d costs a t the expense of other costs. Average marginal cost is increased to a massive 4.24 c/kWh. If the interest rate is increased further, to say IS per cent, costs


5 8 8 ? p p 8 8 $ 000000000

m n w n w w - m m O N 0 0 - - 0 0 0 0919Y=!09'IY09

are further increased to $538.2 million per year (or roughly 34 per cent higher than in the base case). However, there is no change in the system configuration. The discrete nature of the station inclusion variables in this model means that system operation will only alter in discrete jumps as fixed costs vary.

Sensitivity analyses may also be performed with respect to variations in operating costs. A particularly interesting experiment is to reverse the relationship between the costs of hydroelectric power and those of peak thermal generation. Row 3 of Table 5 gives results for the case where the operating costs of Jeeralang, Newport D and the Snowy are set at 2.2, 2.0 and 2.5 c/kWh, respectively. Yallourn West 2 is no longer required, and Jeeralang is operated at a 62 per cent capacity factor. Note that, although more expensive than Jeeralang power (available at 2.35 c/kWh in the Gippsland region), the Snowy energy capacity is fully utilized. This is because transmission losses and capacity costs, b,,, are sufficient to assign a shadow price of 2.58 c/kWh to Snowy generations, which exceeds the operating cost of 2.5 c/kWh. Sensitivity to Plant Availabilities

Ideally, that part of down-time which corresponds to planned maintenance ought to be endogen id s o that optimal system operation involves automatic allocation of that maintenance throughout the year. To illustrate the variation in costs which occurs with varied maintenance schedules, row 4 of Table 5 gives results for the system under the assumption that the base load stations' maintenance schedules are flat. Costs increase by 1.7 per cent to $408.2 million per year. Hydroelectric energy is now less valuable and irrigation less costly. In addition the peak is moved to the winter, as would be expected, since, apart from the interruptibility allowance, the only seasonal variations are due to demand variability.

In the case of the Victorian brown coal base load stations, plant capacity factors are crucial determinants of system cost. Table 5, row 5, gives results under the assumption that availability of the largest station, Hazelwood. is 0.62 during the winter periods and 0.52 in all other periods, thus lowering the capacity factor from 62 to 55 per cent. Total costs increase 3.1 per cent to $413.7 million per year. In addition, some Jeeralang generation is required.

Although hydro plants are extremely reliable with respect to instantaneous availability, annual energy output is constrained by the availability of

1984 ELEmRICITY COSTS 353

water. Row 6 of Table 5 shows how costs increase when hydro energy availability is reduced by 200 GWh for Vic Hydro and 500 GWh for the Snowy (roughly 25 per cent). There is an increase in system cost of 2.57 per cent, and the Jeeralang gas turbines must be utilized at a capacity factor of 5 per cent. On the other hand, an increase in water available for hydroelectric generation (300 GWh for Vic Hydro and 500 GWh for the Snowy or a 30 per cent increase in overall hydro energy) leads to a total system cost of $391.8 million (which is approximately a 2 per cent fall in costs).

The other constraint relevant to the operation of the hydro stations is the irrigation constraint. If this constraint is non-binding, then small variations in the amount of water which must be dedicated to the summer periods will not alter system operation. As the constraint is binding in the base case, an increase in the irrigation requirement can lead to an increase in system costs. If the fraction of energy to be generated from the ‘Vic Hydro stations during the summer is raised from 0.55 to 0.7, then a small increase of $0.7 million in costs results. Sensitivity to Reserve Parameters

The principal parameters associated with the reserve constraints are the supply capabilities, the factors used to inflate demands, and the interruptibility allowance, if any. Table 5, row 7, outlines system operations under the assumption that all supply capabilities are lowered by 0.05. Jeeralang is no longer sufficient to provide marginal reserve capacity and this is now supplied from Vic Hydro. Consequently, marginal costs for supply at the peak (period 8) are somewhat higher than in the base case and there is a reduction in the shadow price of hydroelectric energy. System costs are increased to $405.8 million. If, instead of altering supply capabilities, the excess demand factor, V,, is increased (from 0.3 to 0.35) the results are qualitatively very similar. Total system cost becomes $404.2 million (an increase of 0.7 per cent) and once again marginal reserve capability is provided from Vic Hydro.

The importance of the assumption of interruptibility during period 1 is shown in Table 5 , row 8. The assumption here is that there is no possibility of interruption. System cost is increased to $404.1 million and the peak is shifted to period 1. Marginal reserve capacity is supplied from Vic Hydro. One problem with the allowance for interruptibility is to decide just when it ought to be considered available. Presumably, demand might be inter-

rupted during any of the 12 indicative periods, but not for the entire period. Since the interruptibility option is a design variable of the system, rather than a constraint, it could well be included endogenously in the model. Sensitivity to Load Factor

We also look at the effect of an arbitrarily chosen change in the load curve. The new curve displays an increased load factor of 74.3 per cent compared to the base case load factor of 71.8 per cent. Row 9 of Table 5 shows the result of optimal system operation to meet this load curve, with the level of demand chosen so that total energy demanded is (approximately) equal to the 22 002 GWh assumed in the base case. There is then a reduction in system cost of about $3 million.

Clearly there are advantages to be gained from improvements in the load factor. But this brings us to a more fundamental aspect of electricity generation. The prices that consumers are at present charged bear virtually no relation to the timehpace differentiated marginal costs of supply presented here. Unless consumers were totally unresponsive to price changes, charging appropriate shadow prices would alter the structure of demands placed upon the system. This shift in demand, which our model ignores, is likely to improve the load factor, but more importantly, will necessitate a complete recalculation of optimal system operation and of marginal costs. The dynamic, iterative nature of the process becomes immediately obvious. Changes in prices will cause consumer reactions in the form of altered demands, and since optimal system operation depends upon the structure of demands to be met, will lead to another ‘optimal’ set of prices to be charged. Full (mathematical) application of this procedure would require a dynamic model incorporating, not only a range of assumptions and possibilities as to the future evolution of the system, but also some assumptions as to the demand responses of consumers throughout these future periods. In the context of such a model, straight- forward minimization of total costs of supply would no longer be appropriate. Instead, the preferred objective function would be the sum of producer and consumer surplus so that optimal operation of the electricity system would allow benefits to be captured, both through adjustments on the supply side to provide a given level of demand more cheaply, and through adjustments made by consumers purchasing a more suitable package of electricity when faced with a given structure of tariffs.


IV Some Implications of the Results Relation to Theoretical Dkcussions

The results in Section III illustrate the points made in the theoretical discussion in Sedion I. Fmt we observe that marginal costs are higher in the peak than in the off-peak period both because marginal operating costs are higher and because peak demands necessitate a higher system capacity than would otherwise be required. However, if prices were to reflect these marginal costs, we suspect that demand would shift from the current peak period to off-peak periods with consumers in these latter periods then also becoming marginal to system capacity and so reducing the capacity component of peak costs considerably. Second, we find that even though the availability of hydroelectric capacity does help the system smooth out costs it is not sufficient to prevent considerable -off-peak differences in marginal costs in some of the examples considered. Third, in most of our examples, the requirement that some water be released in the summer months for irrigation purposes raises SECV costs above what they would otherwise be. Fourth, we observe that transmission losses lead to geographical variation in marginal costs. This variation would be considerably increased if distribution costs were added to the generation and transmission costs examined in the madel since distribution losses (and maintenance costs) are much higher (relative to demand) in the sparsely populated rural parts of the network.

Relation to Price-Setting While the marginal costs of generation and

transmission calculated in Section III are very approximate, and we have not examined the costs of distribution, metering and billing, it would appear that current SECV tariffs bear little relationship to the opportunity costs of supplying electricity. The major difference between the pattern of marginal costs and tariffs is that, whereas the costs vary by location and time, tariffs vary by customer type and product use. The SECV customer categorization reflects to some extent the different average costs which different customers impose on the system, particularly in relation to distribution. In addition, customer categorization may be used as a proxy for the absence of time differentiated tariffs. However, even if some customers tend to take more power at the peak. the current tariffs give them no incentive to alter the time pattern of consumption and in that sense the tariffs are not time differentiated at all. Some

of the apparent anomalies in the current tariff structure, such as high charges for commercial lighting, appear instead to be related to elasticity of demand.”

Another major difference between the SECV accounting procedures and the calculations of costs in this paper lies in the SECV’s use of historical costs. The historical interest and depreciation charges associated with existing generation and transmission facilities are largely irrelevant to a determination of the actual cost of making that capacity available. Furthermore, the SECV makes considerable use of declining block tariffs. These may have the effect of making the marginal price of electricity lowest in the peak season when the marginal cost is highest.”

Finally, the results suggest that the marginal costs of supplying rural customers are higher than those for urban consumers. Since, generally speakiig, the prices charged are geographically uniform, there is a cross-subsidy from urban to rural customers embedded in the tariffs.” Moreover, it appears that irrigation water may have a shadow price associated with its value in electricity production. It is not clear that the price charged for irrigation water reflects the costs imposed on electricity consumers by the requirement that the water be used to generate electricity in the irrigation season.’O

In conclusion, this paper has discussed some of the determinants of the costs of supplying electricity and illustrated these by constructing a model of the SECV grid. It has also compared the current SECV

”There are few good substitutes for electricity in lighting, while electricity is likely to be a small component of the overall costs of a commercial establishment.

”Declining block tariffs might be defended as a means of raising revenue when average costs decline with output so that setting prices equal to marginal mts will not raise sufficient revenue to cover total costs. While such tariffs may discourage some consumers who would have pur- chasid if all units were priced at marginal cost, the number affected may (see Crockett, 1976) result in a lower reduction in consumer surplus than would occur with average cost-pricing.

I’We should note, however, that if private firms were permitted to supply power to the SECV and ECNSW systems and were paid the marginal value of any power supplied. a station based on, say, Riverina coal might be profitable and might supply power to rural Victoria at lower cost than the Latrobe Valley stations.

”Davidson (1%9) and Centre of Policy Studies (1983) are useful sources of information on the Victorian irrigation schemes and their joint use for hydroelectric generation.


tariffs with marginal costs and finds considerable divergences between the two. It would seem that electricity consumers, and potential private electricity producers, are not being given price signals which reflect the opportunity cost of Victorian electricity. However, we suspect this has more to do with the incentives inherent in the current institutional arrangement for supplying electricity in Victoria than with any lack of information within the SECV on how to calculate marginal costs and structure tariffs accordingly.

REFERENCES Centre of Policy Studies (1982), Energy Pricing Issues in

Victoria, a Report prepared for the Long Range Policy Committee of the Victorian Government, Government Printer, Melbourne.

+1983), Distribution of Costs and Benefits of Victoria’s Irrigation Systems, a Report on a study commissioned by the Public Bodies Review Committee of the Parliament of Victoria, Government Printer, Melbourne.

Crockett, J. H. (1976). ‘Differential Pricing and Inter- consumer Efficiency in the Electric Power Industry’, Bell Journal of Economics, 7 , 293-8.

Davidson. B. R. (1969). Awtralia- Wet or Dry? Melbourne University Press, Melbourne.

Pressman. I. (1970), ‘A Mathematical Formulation of the Peak Load Pricing Problem:. Bell Journal of Economics, 1, 304-26.

R a , R. (1976), Public E n t e p r k b n o m i a , Weidcnfdd and Nicolson, London.

Rowse, J. (1980). ‘Intertemporal Pricing and Investment for Electric Power Supply’, Bell Journal of Economics, I I , 143-65.

Scherer, C. R. (1977), Ertimating Electric Power System Marginal Costs, North-Holland, Amsterdam.

Swan, P. L. (1983). T h e Marginal Cost of Baseload Power: An Application to Alma’s Portland Smelter’, Economic Record, 59, 3 3 2 4 .

Turvey, R. (1968), Optimal Pricing and Investment in Electricity Supply, George AUen & Unwin, London.

-and Anderson, D. (l977), Electricity Economics: Essays and Caw Studies, Johns Hopkins University Press, Baltimore.

Wenders, J. T. (1976), ‘Peak Load Pricing in the Electric Utility Industry’, Bell Journal of Economics, 7, 2 3 2 4 .

Williamson, 0. E. (1966), ‘Peak Load Pricing and Optimal Capacity under Indivisibility Constraints’, American Economic Review, LVI, 8 1@27.

the marginal costs of electricity supply in victoria

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