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The determination of reserve generatingcapacity criteria in electricity supplysystemsMichael G. Webb aa Institute of Social and Economic Research, University of YorkPublished online: 09 Mar 2007.

To cite this article: Michael G. Webb (1977) The determination of reserve generatingcapacity criteria in electricity supply systems, Applied Economics, 9:1, 19-32, DOI:10.1080/00036847700000003

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Applied Econonzics, 1977,9 19-31

i The determination of reserve generating capacity criteria in electricity supply

I

systems

M I C H A E L G . W E B B

Institute o f Social und Economic Research, University of York

~ I . I N T R O D U C T I O N Electricity supply utilities are suppliers o f a heterogeneous product which varies in its cost

1 of production and its quality of supply. Important to both of these dimensions of the

1 product is the determination o f the 'optimal' generating plant reserve capacity. Since with limited resources amd imperfect knowledge it is not possible to plan for complete security of supply, the planning problem is that of determining for each successive period the .

1 'optimal' standard of security. Interruptions to electricity supply can have many causes. In I this paper the concern is solely with interruptions arising from possible insufficient

generating capacity. Planning o n the generation side of a n , electricity supply utility involves two sets of

problems which are distinguished by the time dimension to which they apply. The first is

1 the problem of determining the optimum use of the inherited stock of generating capacity, which is concerned with planning the day-today operation of the supply system so as t o minimize the resource costs of meeting the expected load on the system.' Short-run

I marginal costs are relevant in the solution of this problem. Security of supply in this

1 short-run problem is obtained in pure thermal supply systems by having some spinning spare plant (generators which are spinning but not synchronised t o the grid system).

I The second problem is concerned with planning optimal changes in the inherited capacity

and is thus concerned with long-run marginal and total costs. Security of supply in this long-run problem is obtained by planning an excess of generating plant over the expected simultaneous maximum demand (SMD)2 for specified weather conditions. The generating plant reserve capacity margin may be defined as the difference between the total installed

1 capacity and SMD, divided by the SMD.

'This is not necessarily the case. In a situation of fuel shortage the power stations may be operated to minimize the fuel requirements for meeting a given demand. 'System peak demand.

Printed in Great Britain O 19 77 Chapman and Hall L td.

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20 Mictlael G. Webb

In a pure thermal supply system (which could have a mix of plant such as coal-fired, oil-fired, nuclear and gas-turbines) a very simple least cost objective for the determination of optimal capacity additions, with a given demand forecast which it is assumed must be met, could be formulated as follows:

Minimum expected P V C (Kt + F, + 0, + T , + V, ) r = l

where Kt represents the capital costs of new generating capacity installed in year t ; i.; represents the total fuel costs in year t of all capacity used to meet the expected demand; 0, represents all other generating costs in year t associated with both newly constructed and inherited capacity; T, represents the capital costs o f new transmission capacity constructed in year t ; and V, represents all other costs in year t associated with the transmission system. While this objective ignores distribution costs and the fuel transportation problem etc., it will be sufficient t o illustrate the nature of the long-run reserve generating capacity planning problem.

The immediate point to 'note is that in terms of achieving an optimal stock of generating capacity this objective is deficient in that it makes no reference to security of supply. Consumers of electricity (as with telephones and other similar services) d o not merely demand electricity, but in addition they demand the right to consume it when they want it. Because of risk and uncertainty although the generating capacity which an electricity utility must plan for will be a function of SMD (because electricity is not storab!e) it will not equal SMD. There are a number of reasons for this. These include plant breakdowns, transmission losses, errors in demand forecasts, and the hobabil i ty that some capacity will not be available because it is being repaired or maintained.

Measuring in megawatts (MW) and using mean expected values, we have for available capacity if SMD is to be met:

A t = D , + L t + E ,

where A, represents the available capacity in megawatts sent out in period t ; D, represents the simultaneous maximum demand; L, the capacity allowance for transmission losses; and E , is a capacity allowance for demand forecasting errors. The available capacity at the time of SMD will be:

At = C, - B, -- M,

where C, is the total installed capacity measured in megawatts sent out in period t ; B, is a capacity allowance for breakdowns and late commissioning; and ibl, is a capacity allowance for repair and maintenance. It therefore follows that if SMD is t o be met the total installed capacity must be:

C, = A , + B , + M ,

Although security of supply has been introduced in this formulation the fundamental question of whether the plant margin is optimal has been side-stepped. In many electricity supply utilities this question is answered by considering whether the resulting capacity margin permits supply to be offered to consumers at a pre-determined risk of failure standard. This standard is often expressed in the form of the number of winters in one

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The determination of reserve generating capacity criteria in electricitjt supply systems 2 1

hundred that supply failures from lack of generation causes can be expected at the time of SMD. For the C.E.G.B. this standard is 3 per cent, while in Belgium it is 1 per cent and in Spain 5 per cent (Cash and Scott, 1969). This definition of optimality is not satisfactory to economists because the risk standard is chosen arbitrarily and not by reference to the resulting costs and benefits of any improvement in the security margin. It is with these costs and benefits that the next section of this paper is concerned.

11. C O S T S A N D B E N E F I T S O F T H E S E C U R I T Y M A R G I N

At a simple level the margin can be analysed as follows. Assume that the only cause of a power failure would be a breakdown in generating plant during the critical period, which we shall limit to the time of SMD. Assume further that the inter-connection of the supply system is such that the effects of this breakdown can be spread either over a large number of consumers with the duration of the loss of electricity to each consumer being only a few minutes, o r that the effect can be concentrated o n one o r a few large consumers with a duration of a few hours. The margin required to allow for the possible non-availability of generating capacity a t the time of SMD can be derived approximately from the reciprocal of the percentage availability of all plant installed on the system at the time of SMD. This availability figure can be obtained by estimating the winter peak availabilities of all plant on the system and combining them into a composite figure for the system as a whole. Suppose that this availability figure was 9 0 per cent, then the required margin would be

100 - - 1 x 100 = - I 1 per cent. 9 0

The question then remains of whether the provision of this margin is worthwliile. Consider first the case where the loss of electricity lasts for a short time but affects many

consumers. Assume that individual preferences are to count in the determination of this margin; that prices are everywhere equal to marginal costs and that there is perfect knowledge; that there are no external effects and that the distribution of income is judged t o be ideal (or that the utility is required to act as if it were ideal); that all inputs and outputs are perfectly divisible and that all second-order conditions are fulfilled, and finally that all production functions exhibit constant returns to scale. While these assumptions are obviously not realistic the analysis based on them does provide us with a useful insight into the problem of determining the size of the optimal reserve plant margin. In the case being analysed these assumptions imply that electricity prices across all consumer groups will equal marginal valuations of electricity. Since by assumption, each consumer is affected in a small way by the power cut there will be no difference between the expected utility of the income lost by the power cut and the expected value of that income. The consumers' marginal valuations will allow for the benefits derived from a secure supply. Thus it follows that the investment in capacity for the margin should proceed to tl:e point where t l ~ e present value of the incremental receipts from providing an increment in capacity for the margin equals the present value of the costs of this capacity.

Consider now the alternative case in which the loss of electricity would affect a few consumers for a relatively long time. In this case with downward sloping demand curves

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Michael G. Webb

with respect t o the price axis, the evaluation of the margin on the benefit side would require the use of consumers' surplus measures. In addition, in this case with each consumer being affected significantly, if we assume a diminishing marginal utility of income schedule for each consumer a distinction would have to be made between the expected utility of the generating margin and the expected value of the income from provision of that margin. With diminishing marginal utility of income in this case consumers would not be willing to pay an amount equal to the expected value of the income arising from the provision of the margin, but something less.

Cost of the security margin

In a thermal supply system with an optimal plant mix (that mix of generating plant of different technical types which permits expected demand period by period to be met at least discounted total system cost), new capacity of kinds other than gas turbine will usually generate some fuel cost savings (Webb, 1973). These savings act as a partial offset to the capital costs of the new plant, and in the determination of the optimal plant margin these latter costs must be calculated net of any such savings. T o these capital costs must be added any associated fuel and other operating costs.

i t is unlikely that at any moment the plant mix on any particular system will be optimal. But the problem under consideration is the determination of the optimum planning margin, and for this purpose it is reasonable to assume that the existing plant mix is optimal. In that event we can concentrate on the costs of gas turbine capacity. Since this capacity will operate at the bottom of the merit order it will not earn any fuel cost savings. This considerably simplifies the task of calculating the costs of the security margin.

These costs can be presented in a number of alternative ways. If our benefit figure is going to be expressed in terms of pence per unit then it is necessary that the cost figure be similarly presented. One way to d o this is to simply represent the cost of the plant in annual equivalent form A [ k ] , where k is the net cost of providing for a l/kW increment in capacity and A [ I represents the annual value o f the sum in the brackets. Assume that an accurate forecast can be made of the number of hours each year that supply would be at risk if this investment did not take place. Since this number of hours will vary from year to year, t o find their annual equivalent it will be necessary to take present values and spread back over the life of the new investment. Let PV(H) be the present value of these hours and A[PV(H)I their annual equivalent value. The unit cost of providing for an increment in the security margin is thus A [ k ] / A [P17(tl)] = m .

In a perfect market with complete information this cost information could be incorporated into tariffs (it is part of the cost of supplying output to a particular quality standard). The determination of the reserve margin could then be left to consumers expressing their preferences through market rates. However. in the absence of perfect markets, the determination of the optimilln margin will require the explicit calculation o f unit benefits for comparison with rn.

Benefits of' t l ~ e security tnargit~

The estimation of the benefits to consumers of an improvement in the quality of electricity supply poses formidable problems. In the industrial sector they will vary with the industrial

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The deterrnit~ation o f'reserve getleratilrg capacit.~ criteriu it1 electricitj~ srtppljl s~~stetns 33

process used by the consumer, the possibilities for rescheduling production, the duration and timing of the supply interruption, etc. However, much can be done. First, it is relatively simple to calculate the minimum value of the increased output from the improved security margin. Second, in many cases it will also be possible to measure the maximum value. Finally, the implicit value of the marginal unit of electricity in the security margin can be calculated and compared with a range of possible benefit figures (see Section 111).

Minimum value. If we ignore external effects and make the necessary assumptions for market prices to reflect willingness to pay, and if we assume that any supply failure would affect many consumers each in a small way, the minimum measure of willingness to pay would be the revenue foregone at the retail tariff level. Since retail tariffs vary accross main consumer groups and with the voltage level at which power is supplied, the calculation of even this mininlum benefit figure presents certain problems. It must proceed by identifying the consumers whose supply would be at risk if the incremental capacity was not constructed, the number.of hours each year for which their supply would be at risk, and the tariff under which they would purchase that supply.

In the case of many consumers each of whom is affected in a small way, if 11, represents the number of hours that supply would be a t risk in period t if the investment in the margin did not take place, and PI the follow-on unit price for consumer i in year I , the annual equivalent unit value of an improvement in the margin would be:

where P f = 0 whenever a consumer is unaffected by a power failure. An improvement in the margin is worthwhile if b > m. If the supply failure would affect

relatively few consumers significantly then the calculation of benefits would have to allow for consumer surpluses.

Maximum value. For a large consumer in all consumer classes this maximum value can be calculated as the minimum price such a consumer would be willing to pay for an alternative source of supply. Thus a large consumer may be prepared to invest in his own stand-by supply plant. In this event the maximum value for comparison with m should be calculated as the present value of the capital and operating costs of this plant annuitised over its expected life divided by the estimated number of hours for which supply from the public supply system would be at risk.

There are a nun~ber of problems associated with this approach. One of these is that the individual consumer considering the possibility of installing his own supply source is not only concerned with the duration of possible supply interruptions due to shortages of generating plant. He is concerned with failure due to all possible causes, including distribution and transmission faults. The consumer is thus insuring himself against a number of possible events, while we wish to ihfer from his behaviour the price which he is prepared to pay for insurance against only one of those possible events. Only in the unlikely event of a linear willingness to buy insurance schedule could the transference be made simply from the act of insuring against a range of possible outcomes to the implied value of insurance against anyone of those outcomes.

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Michael G. Webb

Marglnol value of 0 output lost

0 A Duratton of supply follures In hours per year

Fig. 1

The principal problem for the consumer considering the installation of his own generating plant is the estimation of the annual hours at risk (from the public supply) probability distribution. This will probably have t o be based on an estimate of subjective probabilities. The costs of an alternative source of supply will not be unique, but will vary with the capacity, technological type, fuel requirements etc., of the proposed in~ ta l l a t ion .~ Given estimates for this data, the annual equivalent costs can be calculated for a particular interest rate and estimate of the plant's life. Marginal costs will probably be a declining function of the number of hours each year for which own generating capacity is operated. This is shown by Curve aa in Fig. 1.

The benefits resulting from an investment in own generating capacity will relate to the annual value of output which is in consequence not lost and to the inconvenience etc. which would now not be suffered. An important issue concerns whether a series of supply interruptions lasting for one hour each on a number of successive days are to be considered as identical t o a single supply interruption of the same duration occuring in a particular working day, which is an empirical question. In principle the marginal value of output !ost per unit of electricity not supplied can be calculated, and it will probably be an increasing function of the number of hours of supply failure as shown by Curve bb in Fig. 1 .

Even if the information required for the construction of this diagram could be obtained its interpretation would not be straightforward. Investment in own generating capacity would not necessarily become worthwhile if the mean expected number of hours of supply interruption was equal o r greater than OA. This would be the case if the probability distribution of supply failures was normal shaped with a mean of OA hours and the two

'Note that there is a problem of interdependency. The desired capacity of the proposed installatian will vary with the number of hours each year for which supply from the public supply system is at risk. The greater is this number the more likely is it that the desired capacity will equal the maximum demand which the consumer places on the public supply system. With economies of scale marginal costs will be a declining function of the number of hours of supply failure.

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The determination o f reserve generating capacity criteriu irz electricity supply systems 25

Curves aa and bb were mirror images of each other. However, there is obviously no a priori reason to expect either of these conditions t o be satisfied.

For every year that the supply failure lasts for less than OA hours the independent source of supply involves the consumer in a cost penalty, and when it is greater than OA it leads to a cost saving. In these circumstances the question is simply what premium will it be worth paying for security of supply? This requires the identification of the minimum number of hours of supply failure (which must lie in the range OA) which the consunler is prepared to tolerate. This is a matter of judgement to be determined in accordance with the consumer's preference function. Given an estimate of this value it can be compared with the consumer's own estimate (subjective) of the number of hours per year for which supply t o him from the public supply is at risk. If this latter figure exceeds the former, the value of security of supply t o this consumer can be calculated on the basis of his own estimate of the number of hours for which his supply is at risk and the cost t o him of providing his own capacity as an insurance against a supply failure. This cost when expressed as either a present value o r annual equivalent cost over the lifetime of the plant provides a measure of the maximum willingness t o pay for an irnprovement in the security of supply system.

Once the maximum and minimum values of the incremental output from the security margin have been calculated, a weighted average of b could be calculated for each consumer class, using as weights the proportional consumptions of electricity during the risk period, by , say, large, medium and small consumers. The value of b across all consumer classes could be obtained by taking a weighted average of the bs for each consumer class, the weights being given by the proportions of the total units supplied during the risk period t o each consumer class. This method was used in Sweden in a survey conducted in 196718 to discover the values to consumers of electricity not supplied because of supply system failures (Costs of Ir.terruptions, 1969).

It may be possible t o estimate the maximum value by introducing interruptible supply clauses into tariffs (at the present t ~ m e the C.E.G.B. has over 1000 MW of load on such tariffs). By adjusting prices in the tariff until they reached the level at which the consumer was just willing to have such a clause included in his tariff the maximum amount which he would be prepared to pay for security of supply could be found. The summing of this amount across the affected consumers and taking present values would provide the money value of benefits which must be compared with the present value incremental costs of providing for additional security through an improvement in the margin. The optimum size of the margin would be given by the equality of these present value costs and benefits.

1 1 1 . S O M E E V I D E N C E O N T H E C O S T S A N D B E N E F I T S O F T I I E S E C U R I T Y M A R G I N

If the plant mix is optimal, the system incremental cost of ~mproving the security margin is the same for each of the plants which might be installed. Since we are concerned with the problem of the optimal planning margin, it is reasonable to assume that initially the plant mix is optilnal and thus to calculate the cost of an improvement in the margin by reference to the costs of gas turbine capacity. At the present time the capital cost of this type of plant to the C.E.G.B. is in excess of £100/kW, and to be on the conservative side we shall use this figure. If we assume an interest rate of 10 per cent and a plant life of 30 years, then allowing

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for interest during construction the cost per kilowatt per year is approximately E12. The operating cost of sucll capacity would be of the order of 1.0 p/kWIl. Assuming that these cost figures reflect social opportunity costs, their use in combination with social benefit figures for marginal units of electricity supplied would permit the calculation of the o p t i m ~ ~ m number of hours of supply interruptions from lack of generation causes each year. Given probability information on plant breakdowns etc., the optimal security margin could 1 be determined. The optimum number of 11ours of supply failure each year must be distinguished from the average number of hours each year that any consumer would be without electricity because of generation shortages. An example will make this clear.

Given the capacity cost figure of E12IkW p.a. and the operating cost of l.Op/kWh, if the marginal social value of a unit of electricity not supplied was X I .0 1 . the opt im~lm number of hours of supply failure would be twelve per year. Supposing that ten per cent of the total number of consumers would be affected by the supply failures. the average annual supply I interruption per consumer would last for 1.3 hours (the expected loss per consumer is given by C$, Li p (L i ) = 12 x 1/10 + 0 x 9/10 = 1.3 hours). Similarly if the supply failure affected only five per cent of the total number of consumers, the average expected loss of power per consumer would be 0.6 hours per year.

I t now follows that given evidence on both the number of hours each year that each consumer could expect to be without electricity because of shortages of generation capacity with the existing security margin, and the proportion of all consumers affected by the supply failure, the implicit marginal valuation of electricity in that margin could be calculated. We have previously noted that the C.E.C.B. has adopted a 3 per cent risk of failure standard. The adoption of this risk of failure standard can be expected to lead to a consumer losing a very small number of hours of potential supply each year because o f shortages of generating plant. In fact in the middle to late 1960s the number of consumer hours lost per connected consumer per year from this cause was of the order of 0.1 .4 If this figure could be taken as indicative of the long run average number of hours, a consumer could be expected to be disconnected because of shortages of generating capacity then, using the previously derived capacity cost figure of €12/kW and assuming that the power failure affects 5 per cent of all consumers, it follows that the implied (minimum) marginal valuation of electricity in the security standard would be &6/kWh. If the supply failure affected 10 per cent of all consumers the equivalent figure would be £l?/kWh, etc. Given that the follow-on rates in tariffs today are of the order of 1.75p, these figures are rather high. (However, note the public good aspect of the improved security margin.)

As previously noted, the estimation of the benefits to consumers of an improvement in the quality of electricity supply poses formidable problems. But various attempts have been made in a number of countries to estimate these benefits. The results of a number of these studies have been reported in a UNIPEDE study document (Report of the Croup of Experts, 1972). This study document supports the type of approach discussed in the present

'cash and Faux (1967) show that for 196516 roughly 5 per cent of all consumer hours lost were due to shortages of generating capacity, and 4 per cent to failures in the bulk supply system. Sheppard (1969) showed that in the mid 1960s the number of consumer hours lost per connected consumer per annum due to faults on the transmission system was 0.05. It therefore seems reasonable to use a figure of 0.10 as the number of hours lost due to shortages of generating capacity.

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The determination of reserve generating capacity criteria in electricitj] supply systems 27

paper to the determination of optimal planning margins. Unfortunately the basic equation I used in the document involves double counting. The equation is:

Cost perkW = X, V, + X2 V2 + (XI + X2 )V3 (per year or century)

where x , is the number of hours per century o r year o f voltage/frequency reductions; V, is the marginal value to consumers of kwh not supplied through voltage/frequency reductions; x 2 is the number of hours per century or year of disconnections; V2 is the marginal value to consumers of kwh not supplied through disconnections; V, is the marginal value to the supply industry of revenue and goodwill lost.

This equation clearly involves double counting by its reference to revenue in V,. This component of the social benefit foregone when electricity is not supplied is picked up in the first two terms of the equation, and should not also be included in the third term. The third

I term should be redefined to relate only to the value of the goodwill which is lost. I The study document reported on an analysis of the benefits of quality of supply in Great I Britain, in which it was concluded that the average value for all consumer classes of a unit

of electricity not supplied might be of the order of £0.50. The methodology used in the calculation of this figure was not satisfactory. For example, the figure for industrial consumers was calculated as a first approximation as being thirty-three times the average electricity price per kwh, since electricity accounted for approximately 3 per cent of total industrial production costs. This gave figures in the range of £0.30-0.90 per kwh not supplied, the higher figure being for industrial processes in which the proportion of total costs accounted for by electricity was particularly small: While the calculated figure may represent the value of output lost (although this is very doubtful, especially as what matters is the marginal value), it does not represent either the private or social cost of an interruption of electricity supplies. Considering the social cost, if all prices equal rnarginal social costs, the above formulation implicitly assumes that all cooperating factors of production have a zero social opportunity cost if electricity is not supplied. The appropriate measure of the social cost is the marginal value of the output lost minus the marginal social cost of the cooperating factors which are not then used. The use of this valuation method would result in the derivation of a lower value for the marginal unit of electricity not supplied.

I t is worth noting that even the relatively high marginal valuation figures quoted in the study document are substantially less than the implied (minimum) marginal valuation figures derived above. This conclusion is unchanged even if full allowance is made for inflation in the study document figures.

Although it is fully recognized that the figures presented in this section are based on weak foundations, prirna facie it would appear that the implied marginal valuation figure is of the order of a few pounds. Whili it would be extremely difficult to persuade the average consumer (especially domestic) that it was in both his own and the national interest t o have occasional power failures, the preceding analysis does suggest that this may be necessary. Further it suggests'that serious consideration sho~lld be given to trying to shift the cost of providing for very high security of supply from the public supply system to individual co1:silmers.

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I V . S O M E E V I D E N C E O N R E S E R V E C A P A C I T Y C R I T E R I A (see Tab le 1 )

Although the European and Asian data d o not relate to the same year, (the European data relates to 1963, except that for the C.E.G.B.) the essential difference in the type of criterion frequently adopted by relatively large and relatively small electricity utilities is clearly brought out. Whereas the large utilities often approach this problem using probability calculations, the small utilities usually rely on a rule of t l iu~nb method, that is, a reserve margin equal te the loss of the largest generating unit on the supply system. The fact that this latter method often leads to relatively large generating plant margins, as previously defined, is clearly brought out in the table. In terms of the discussion of this paper these utilities should consider the resulting costs and benefits of a change in the margin. For example, they might compare the cost saving frorn basing the margin on the second largest unit with the expected costs of any associated power failures (these costs may be minimized by using interruptable supply tariffs). Although these margins are often relatively large, the margins achieved in practice are frequently greater, as shown in Table 11. It should be noted that the C.E.G.B. is currently considering increasing its reserve capacity margin criterion to above 20 per cent.

Table I. Reserve capucity criteria

Gross plant margin Country (utility) Basic method (per cent in peak demand)

Belgium France (E.D.F.) Germany, F.R. Great Britain (C.E.G.B.) Hungary Netherlands Norway Portugal Spain Sweden

Probability Probability/Experience Experience Probability Experience Probability Probability/Experience Probability ProbabilitylExperience Probability

15 (+5 per cent inter-connection) 17 17 20

5 27-30 16 20-2.5 20 20

Asia

Bangladesh Largest unit or 10 per cent at minimum 38 (60 MW in 1972)

Korea (K.E.C.O.) 7 per cent of thermal + f of gas and diesel installation 15 (3 15 MW in 1972)

Pakistan (K.E.S.C.) Largest unit 43 (125 MW in 1972) Philippines (Agus grid) Largest unit 64 (50 MW in 1971) Thailand (E.G.A.T.) Largest unit 19 (200 MW in 1972) Vietnam (V.P.C.) Largest unit 29 (66 MW in 1972)

aSource: Cash and Scott, 1969.

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The determination of reserve generating capacity criteria in electricity supply systems 29

V . S O M E E V I D E N C E O N A C H I E V E D R E S E R V E C A P A C I T Y M ' A R G I N S

In Table 2 we show for a few selected countries the installed capacity, simultaneous maximum demand and reserve plant margin actually achieved in selected years. Considerable care is required in the interpretation of this table. The reserve capacity margin achieved in

Table 2. Reieive capacity in practice

Country (utility) . 1962 1967 1972

Bangladesh (B.P.D.B. East Zone)

Installed capacity (MW) 146 164 Peak demand (MW) 58 124 Reserve margin (per cent) 152 24

Korea (K.E.C.O.) ,

Installed capacity (MW) N A 917 Peak demand (MW) N A 778 Reserve margin (per cent) N A 18

Pakistan (K.E.S.C.)

Installed capacity (hlW) 129 26 1 Peak demand (MW) 8 3 165 Reserve margin (per cent) 55 58

Philippines (Agus grid)

Installed capacity (MW) ' 5 2 5 2 Peak demand (MW) 58 48 Reserve margin (per cent) 3 7 8

Singapore (P.U.B.)

Installed capacity (MW) N A 404 Peak demand (MW) N A 248 Reserve margin (per cent) N A 8 7

Thailand (E.G.A.T.)

Installed capacity (MW) 128 546 Peak demand (MW) 113 397 Reserve margin (per cent) 13 38

England and Wales (C.E.C.B.)

Installed capacity (MW) 34 21 1 45 020 Peak demand (MW) 2 9 5 2 0 3 5 8 1 8 Reserve margin (per cent) 14 20

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3 0 Michael C. Webb

any year will depend on a number of factors, such as the accuracy of the demand forecasts; the size of unit additions to the generating system; the water flow characteristics in mixed hydro-thermal supply systems such as that of E.G.A.T. in Thailand; the plant availability factors, the availability of adequate coal and oil supplies, etc. While the table tells us nothing about the cause of the observed margins (thus it does not tell us that much of the cause of the observed increase in the margin on the C.E.G.B. system was due to demand forecasts which were based on a too optimistic forecast of the growth of Gill'), the observed margins on some systems are so large as to suggest that an excessively high quality of service is being provided. Where the large size of the margin results from a movement to larger generating sets in order to capture potential economies of scale, the question must be considered of whether the savings from such sets on a lifetime discounted basis are warranted on a system basis when for a relatively large number of years a consequence of their introduction is generally low plant load factors. The higher are the discount factors, the more important is this point.

Large reserve margins as shown for some utilities in the table, are sometimes defended in electricity supply industries on the ground that the consequences for a country of over investment in the industry are less serious than those of under investment. In the absence of empirical data on the costs and benefits of providing for the security margin, and on the time duration of any possible power failure along with the identification of the affected consumers, this argument should not be accepted. Further, the argument is considerably weakened by the fact that in many electricity supply systems the majority of interruptions to the power supply are not caused by deficiencies of generating plant, but rather by failures in the distribution and transmission systems.

V I . C O N C L U S I O N S

The supply of products which are non-storable at economic cost levels poses many interesting economic problems. Foremost among these is that of what is termed peak load pricing within the context of marginal cost pricing. In this paper we have considered another of these problems, that of the provision of 'optimum' reserve capacity margins. This problem is of importance in a number of industries, such as electricity supply, water, gas and telephones. The approach adopted in this paper was to apply the concept of willingness to pay to the problem of both identifying and measuring the costs and benefits associated with a change in the size of the reserve capacity margin. Although power cuts are unpopular, in view of the high costs to a nation of providing the reserve capacity margin, it is argued that the determination of the optilnum size of this margin should be related to an attempt to measure its associated costs and benefits rather than simply trying to meet some arbitrarily established reserve capacity criterion.

R E F E R E N C E S

Cash, P. E. and Faux, F. (1967). Generation - Central Electricity Generating Board System in England and Wales, in The Economics of the Reliabilify of Supply, The Institution of Electrical Engineers Conference Publication No. 34, Part 1, London.

Cash, P. E. and Scott, E. (1969). Security of Supply in Planning and Operation of European Power Systems, I.E.E.E. Transactions on Power Apparatus and Systems, P4S -88.

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The determination o f reserve generating capacity criteria in electricity supply systerns 3 1

Costs of Interruptions in Electricity Supply, (1969). Report from the Committee on Supply interruption Costs.

Report of the Group of Experts on the Quality of Service from the Consumer's Point of View (1972). International Union of Producers and Distributors of Electrical Energy.

Sheppard, H. J. (1969). Reliability of Supply in Distribution Systems, paper presented at international Symposium on Intermediate Voltage Transmission and Distribution Systems, Liege.

Webb, M . G. (1973). The Economics ofNationalised lndustries. Thomas Nelson, London.

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