Public Disclosure Authorized Mohan Munasinghe Optimal ...documents.worldbank.org/curated/en/...traditional power system design and planning has been based on the overall principle

World Bank Reprint Series: Number 201

Mohan Munasinghe

Optimal Electricity Supply:Reliability, Pricing,and Systemi Planning

Reprinted with permissioil from Energy Economics, vol. 3, no. 3 (July 1981), pp. 140-52. Copyrighted by IPCScience and Technology Press, Ltd., Guilford, U.K.

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Optimal electricity supply

Reliability, pricing and system planning

Mohan Munasinghe

This paper provides a state-of-the-art sumnmary of r ecent developments in electricity

supply reliability, pricing and system planning, with emphasis on the close inite;-

relations/hips among these aspects. Economic theory indicates that net social

beniefits wou7ld be maximized if price was set equal to marginal cost while the

marginal system costs of improving reliability were equal to the averted marginal

otutage costs. A ttentionz is focused on the measurement of outage costs and a

reliability optimizing model is utsed to develop an operational criterion for system

planniing in which the sum of system costs and outage costs is minimized. This

approach subsu7nes the traditional criterion of minimizing only the system costs

at an arbitrary target level of reliability. The results of a case study to test the new

methodology are summarized and the use of reliability indices anqd techniques of

estimating outage costs are also discussed.

Electricity is one of the most essential forms of energy shortages of both local and foreign exchange resources.

in modern societies. Therefore, it is not surprising that Traditionally, the main emphasis has been placed on

investments in the electric power sector are estimated enhancing technical and financial efficiency in areas

to be about US$400 billion (1979 dollars) in the USA, such as least-cost long-range system expansion planning,

and US$450 billion in the developing countries, during optimizing short- and medium-term system operation,

the next decade. and better utility management. These supply side

Already, there is a general worldwide rising trend in considerations have been tackled with a remarkable

the real unit costs of supplying electric power, which degree of success, basically by engineers, using mainly

is likely to continue, owiilg to several factors. These technically and financially oriented solutions. More

include the shift towards more costly coal and nuclear recently, the influence of economists has resulted in

generating plant, following the oil crisis, the increasing greater attention being paid to the objectives of economic

scarcity of cheaply exploitable hydroelectric sources, efficiency, based on the national viewpoint. These

and the limited possibilities for realizing further signifi- developments have had a growing and significant practical

cant economies of scale, especially as systems continue impact on the demand side, clhiefly through the appli-

to expand into areas of lower population density. cation of marginal cost pricing principles. On the supply

The massive investment needs for power imply that side also, the acceptance of economic arguments is

even small efficiency improvements in the sector will reflected in the use of the true economic resource costs

lead to significant savings, which are especially impor- represented by shadow prices, instead of purely financial

tant in the case of developing countries experiencing or accounting costs.The current emphasis on economic efficiency, especi-

Mohan Munasinghe is with the Energy Departrrient, ally in the area of marginal cost pricing and improved

The World Bank, 1818 H Street, NW, Washington, tariff policies (on the demand side) is beneficial and

DC 20433, USA. long overdue. However, the related topic of electric

This paper is based on work carried ou. for World Bank research power systemn reliability, or quality of electricity services,

projects 670-76 and 671-86. The views of the author do not has hitherto received detailed attention only from the

necessarily reflect those of the World Bank. The author wishesto thank Rorneshl Dias-Bandaranaike and Mark Gellerson for supply side, in terms of engineering models. On the

helpful ideas. demand side, the socioeconomic impact of the reliability

Final manuscript received 1 December 1980. of electricity supply on consumption has been examined

140 0140-9883/81/030140-13 S02.0C ( 1981 IPC Business Press

Optimal electricity supply: M Munasinglhe

in a much more general and descriptive manner. Thus, Theoretical backgroundtraditional power system design and planning has beenbased on the overall principle of minimizing the supply The principal concerns of electric power sector policy-costs required to meet a certain load, at a given level makers are investment and pricing decisions. The invest-of reliability. In the last few years, there has been ment decision has traditionally been treated within theincreasing recognition of the fact that even the most framework of the least-cost system expansion plan. Insophisticated least-cost power system expansion planning recent times sophisticated system planning models andmodels are usually optimized with respect to standards techniques have been developed, based on the criterionof supply reliability which are themselves derived from of minimizing the cost of supplying a given long-rangepast practice, and vague notions as to the quality of demand forecast, at some acceptable reliability levelservice which would be acceptable to the electricity (or quality of supply).' The optimal size, mix and timingconsumning public. of new capacity additions are treated in this way, and

related models also provide for optimal (least cost)Using optimal reliability levels operation of the system.The theoretical foundations of optimal electricityUntil recently the idea of investigating the demand side pricing date back as far as the pathbreaking efforts ofeffects relating to the economic worth of reliability had Dupuit and subsequently Hotelling; Ruggles provides areceived little attention, principally because of the comprehensive review of work in this area up to the 1 94Os2difficulties of measuring the benefits of improved quality T'he development of the theory, especially for applicationof service. This new approach to reliability attempts to in the electric power sector, received a strong impetusredress the above mentioned weakness, by considering from the work of Boiteux, Steiner and others, from thethe reliability level as a variable to be optimized, rather 1950s onwards.3 Recent work has led to more sophisti-ihan an arbitrarily imposed standard. In order to achieve cated investment models which permit determinationthis goal a social cost-benefit approach must be adopted of marginal costs, developments in peak load pricing,to evaluate the inherent tradeoff between the increase consideration of the effects of uncertainty and thein power system supply costs required to achieve a costs of power shortages, and so on.4higher level of reliability, and the corresponding decline While the close relationships between optimal invest-in outage costs, ie, the economic costs incurred by ment and pricing policies have been recognized for someelectricity consumers due to power shortages. In other time, these links were systematically analysed only inwords, the optimum reliability level, which maximizes some of the more recent studies. By explicitly incorpora-the net social benefits of electricity consumption, should ting effects due to the stochasticity of supply and demand,be determined at the point where the marginal increase and introducing the notion of shortage costs, in welfarein system supply costs, due to a reliability increase, are maximizing models of electricity consumption, it hasexactly offset by the marginal decrease in outage costs. been shown that the optimal conditions for price andThe adoption of such an approach would result in capacity levels must be simultaneously satisfied.5 In thissignificant net economic gains, in most countries. context, determining the optimal capacity level is

This paper highlights the interrelationships between equivalent to establishing the optimal level of reliability,optimal reliability, pricing and system planning, and the since in general, greater excess capacity implies betterimportance of developing reliability standards which a,re reliability and vice versa. Problems relating to thebased on explicit economic criteria. By means of a corn- dichotomy of having to choose between short- andbined economic-engineering approach, it is possible to long-run marginal c)sts, and the correct allocation ofshow that an optimum long-run power system expansion capacity costs among peak, intermediate and off-peakplan and a corresponding range of reliability levels may consumers have been illuminated in recent work.be determined (given a set of prices), which maximize net Wit may summarize this complex analysis in simplesocial benefits. In particular, this approach leads to a plan- terms, as follows: the optimal price is the marginal costning criterion based on minimization of total costs, ie, of supply. Simultaneously, the optimal reliabilitythe sum of system and outage costs, which reflects the (capacity) level is defined by the point at which thenational viewpoint. This planning rule effectively sub- marginal cost of increasing reliability is exactly equalsumes the traditional criterion of minimizing only the to the corresponding reduction in marginal outage costs.system cost, which is more consistent with the viewpoint The short-run marginal cost (SRMC) is defined as theof a private utility. Such a balanced treatment of both the cost of meeting additional electricity consumption, withsupply and demand side effects of reliability requires capacity fixed, while the long-run marginal cost (LRMC)accurate estimates of both system costs and outage costs. is the cost of providing an increase in consumptionAs described here, the former category of costs may be (sustained indefinitely into the future) in a situationdetermined from straightforward engineering-economic where optimal capacity adjustments are possible. Whenconsiderations normally associated with power system the system is optimally planned and operated (ie, capacitydesign and planning. However, the estimation of outage and reliability are optimal), SRMC and LRMC coincide.costs is more difficult, and hence, new models and detailed However, if the system plan is suboptimal, significantmethods are also presented for analysing the various ways deviations between SRMC and LRMC will have to bein which electricity is utilized by different categories resolved within the pricing policy framework. Finally,of consumers. if there are substantial outage costs outside the peak

ENERGY ECONOMICS July 1981 141

Optimal electricity supply: M. Munasinghe

period, then the optimal marginal capacity costs may be values. The random nature of supply and demand is

allocated among the different rating periods (ie, peak, captured by the reliability parameter R and its effects on

intermediate and off-peak) in proportion to the corres- shortage (or outage) costs, OC, and the system supply

ponding marginal outage costs.* costs, SC. As explained more fully below, the choice of

an appropriate (multidimensional) reliability index Rwhich can be easily related to both OC and SC is an

Reliability optimizing model and methodology important requirement for application of the model.

For practical purposes, the joint optimal price and Consider a power system in which the expected value

reliability conditions are used in an essentially uncoupled of electricity demand over a long period of (r + 1) years

form. Application of the marginal cost pricing rule has is represented by D, where t varies from 0 to T. D is a

been attempted in several countries (most notably France), function of other variables and may be written:

and while interpretations vary among practitioners, theapproach is gaining wide acceptability.b The optimal Dt -Dt (Pr, t t t) (l)

reliability rule is more difficult to apply, especially where P is the electricity price, Y is the income variable

because outage costs are difficult to estimate. A frame- which represents the level of economic activity, R* is

work for using this rule for system expansion planning the value of reliability expected by consumers, and Z is a

is summarized below, and problems of implementation vector of other independent variables affecting demand.

are discussed. Initially, it is assumed that the values of arguments Pt, Yt

The task of the planner is to ensure that the supply and Zt on the righthand side of Equation (1) are

of electricity services(S) will exceed the demand(D) at onouse fixed.speif Pquallow us tu p

all times in the future. Even if planned supply exceeds the joint optimal pricing and reliability conditions at this

planned demand in expected value terms during a given stage. This constraint may be subsequently relaxed, as

time period t, ie, St > Dt, there is a stochastic element described later.

in both supply and demand. Therefore actual dema~nd The economic costs suffered by electricity consumers

Dw may exceed actual supply S. , SO that consumers due to electric power shortages associated with each

will suffer shortage costs. system plan may be represented as a function of the

We might represent this most simply as: generalized reliability level Rt, forecast demand, and

St-Dt = St-Dt + Ut reliability expectation:

where Ut is a random variable (eg, with a zero mean and OC, = OCt (Rt, Dt, Rt) (2)

standard deviation a2 ) which represents the stochasticnature of both supply and demand. This is shown in Corresponding power system supply costs, incurred as a

Figure 1, where a shortage condition (or excess demand) consequence of providing electricity services may be

exists in the shaded region. written:

The system would have a higher level of reliability SCt = SCt (Rl, . . . , R,; D1 , . . . , DT) (3)

(Rt), the smaller the probability of shortages. Clearly,the reliability would be higher (lower) when the planned The supply costs described in Equation (3) correspond

safety margin, St - Dt, was larger (smaller), and when to least-cost system designs. Note that SC should include

uncertainty, a2 , was smaller (greater). To clarify the the capital and operating expenses as well as the kW and

presentation and keep the optimization model as opera- the kA7h losses in the system, appropriately valued (at

tional as possible, it is developed in terms of expected the marginal cost of supply), but net of the marginal

supply costs of kWh not delivered due to outages. Finally,since reliability expectation depends on past reliability,we may write:

-IR-*= R-*(Rt- 1, * Rt-,) (4)

a. <A simple expression for the net benefit (NB) of elec-

Region of tricity consumption to society (in present discountedshortages value terms), is:

X \ T

NB = E (TBt - OCt - SCt)I(l +r)t (5)

0 (S, - D,) Excess supply (S, -D)

Figure 1. The condition for shortages: §, - L < 0; or where TBt = TBt (Dt) is the total benefit of electricity

equivalently: Ut < - (St - Dt); when Ut - N(O, a2 ) falls consumption in the absence of outages, and r is the

in the shaded area. appropriate discount rate. Because of the long lifetimeof some investments, the discounting time horizon

* It has been suggested that capacity costs should be allocated to T may be chosen to be greater than the planning time

different rating periods in inverse proportion to LOLP, but this horizon r to eliminate end-effects.would be unsatisfactory because aggregate reliability indices suchas LOLP are poor proxies for prorating outage costs. In order to identify the marginal conditions which

142 ENERGY ECONOMICS July 1981

Optimal electricity supply: M Munasinghemaximize NB, we formulate the Lagrangian: Equation (6) indicates that the net benefits to society

T will be maximized at the point where the marginalL = (TB, - C - SC,)/(l + r)t outage costs associated with a change in reliability aret= O exactly offset by the corresponding change in supply-Xt [R *-Rt(Rt . ccsts. Although this equation relates to reliability in- t t *time period j, in practice, changes in reliability are

-It [Dt -Dt (R*)] likely to be implemented over several time periods.t A) Therefore, a more useful form of Equation (6) would be:The three first order conditions of relevance are: T

(a/i)-(aoc-laR[) -RAR)I(l + r) i(Ul/aRj)= ((aOCj1aRj)1(1 + r) j=o lT

+ E r)tl - E (aSct/Rj)- ARj/( /(l + r)t = 0 (7)+ aCtaj1 J + t= 0 SC)t= 0

T where ARj is a small change in reliability during periodj.+ E Xt (aRt/IaRj) = o For practical application of this rule, let us consider nt= o alternative long-range system expansion programmes,(aL/aRJ) = - (aOc'/aRl)/(l + r)' where the reliability level of the ith programme in yeart is R'. Suppose that expansion plan (i + 1) is derived

+ ,j (aDi/aR)X-i = 0 from plan i, by a small change in reliability given by:(UL/aDj) = [(aTBj1 aDj) AR'= R'+ -R

-- (aOCj/aDj)]/(l + r) i for i = 0, 1,. . . , nT Examining Equations (4) and (7), the corresponding

+ E (aSCt1aDj)/(l + r)t -II = 0 change in net benefits may be written:t=O

for j = 0, 1, .. . , T ANB1 =NB1 +1 -NB - AOC1 - ASCi (8)

Combining these three equations yields: where

(aOCj/aRj)/(l + r)I AOc' = , (3ocJ/R)) ARj/(l + r)T j=o

-E(SCt13Rj)1(1 +Tr)t) andt=O

T [aCSCi = E E (aSC'jaRj1) AR1/(1 + r)t+ E (aR */aRj) t[-(aOCt/aRt) j=o t=O

To interpret Equation (8), it is assumed that the change+ (aDW/aRt) {(MTBtIaDt) from system expansion plan i to plan (i + 1) involves an-(aOCt/aDt)} ]/(l + r)t overall unambiguous improvement in reliability, ie, thateach component AR' is non-negative. In general, thisT implies correspondingly that AOC' S 0 and ASC'> 0.

-ZE (aSC,/13D,/(l +r)- O In this case, Equation (8) yields:

The first term {. . .} captures the direct impact of I ANBI = I AOC'l - I ŽSC'ireliability changes on OC and SC, while the rest of the Therefore, in order to maximize the net economicequation represents the corresponding indirect effects benefits of supplying electricity to society, the relia-via the reliability expectation. To simplify inter- bility level should be increased in successive system planspretation of the above condition, we might assume to as long as the corresponding decrease in incrementalfirst order that (aR-3aRj) * (aOctIaR*) and (aRt! outage costs exceeds the increase in incremental supplyaRj) - (DtlaRtf) are negligible. In other words, the costs, and vice versa. Equivalently, since the total benefiteffect of changes in reliability level R on both OC and TB is assumed to be independent of reliability R, the netD, via the reliability expectation R *, are small. This benefit NB is maximized when the present discountedassumption would be especially valid if the range of value of the sum of outage costs and supply costs isvariation of R is not very wide. Therefore minimized.

Next, define the scalar reliability index RI which-(aOCj1/aRj)/(l - r) characterizes the it" system expansion plan, as follows:

- T(aSC,aRj)1( + r)t 0 (6) R- - [OEtl+r)t]/[zTE/(l +r)tl


Optimal electricity supply: Al. Munasinghe

l I use of a marginal cost pricing rule, or some simpleTC^Q / financial requirement such as an adequate rate of return

TC I / on fixed assets, may require previously unforeseen

oc / changes in future electricity tariffs, to compensate for

N the new supply costs. Such a shift in prices would

I / I directly affect load growth. Furthermore, the new

target reliability levels implied by the first round

I I optimum expansion path i = m, may themselves affectI l I reliability expectation, and thus have a secondary

sc I I impact on demand and outage costs [see Equations (1)

I and (2)].' RI /m I R I In such a situation, the impact of the new sets of

0 R R R" Rm Rn 1.0 R price and expected reliability levels on the demand

Figure 2. Outage costs, supply costs and total costs as forecast and outage costs estimates should be considered,

functions of the reliability level. when iterating through the model again. In general, thisprocedure would shift the whole total cost (TC') curve

where OE is the electric energy not supplied because of as shown by the broken line in Figure 2, leading to a new

outages and TE is the total energy that would have been optimum plan m'. In this fashion, the direct and indirect

supplied in the absence of outages. feedback effects of reliability on demand may be con-

Figure 2 shows a typical graph of outage costs (OC) sidered iteratively until a set of self-consistent price,

and supply costs (SC) associated with different system demand and reliability levels was determined (see also

expansion programmes and reliability levels. The total feedback loops in Figure 3).

cost TC = SC + OC is also plotted. As R increases SC

rises more and more rapidly; clearly a perfectly reliable

system (R = 1.0) is not attainable. Correspondingly OC Practical methodology for implementation

falls towards zero as R increases towards unity. The Figure 3 is a flow chart of the reliability optimizing

optimal reliability level (Rm ) is at the minimum point methodology presented in this paper. To begin with, a

of the TC curve, when the slope of SC is equal to minus framework and set of models are developed to analyse

the slope of OC, corresponding to Equation (7).nths formuain the reiblt mesr is defined the economic costs incurred by different categories of

In aher gnrmalize The refore, te selei of * consumers (eg, residential, industrial, etc) due to electric

the optimum system plan and the associated reliability power shortages of varying intensity. Concurrently, a.lev is .mad on the basis of e omic tenefity disaggregate long-range (eg, 20 years) load/demand

e iforecast is estimated, based on a predetermined evolutionanalysis, and is quite independent of the actual index of of electricity prices, within the area to be served by the

reliability. However, from a practical point of view, t pX

is important to develop reliability indices which not e

only characterize future system performance in a satis- cost) power system plans are prepared to meet this

factory manner, but are also meaningful at the consumer future load, at several different levels of reliability. The

level, and could be easily used to determine the costs of expected annual frequency (ie, the number) and duration

shortages incurred by users. From this viewpoint, of power failures associated with each alternative system

load-point indices of the frequency and duration type design or plan, as well as the time of occurrence of thesed o i c shortages, and the average numbers and types of con-

would bt most conv emeasure t use. bsis, sumers affected by them, is estimated for the entirewould be the most convenient measures to use. It iS frcs pro.

also important to know the times when outages occur, forecast period.

Since outage costs are generally a non-linear function of By substituting the estimated outage frequency and

ouaeduration, ideally, the probability distribution of duration results in the consumer outage cost models, itoutage is possible to determine the total future outage costs for

duration should be computed. However, in practice, a each system plan. On the supply side, the investment and

knowledge of the mean duration at specific times may operating costs of each alternative design may also be

be sufficient, eg, during the periods of peak, inter- estimated. Then a cost-benefit model is used to compare

mediate and off-peak demand, the outage costs with the corresponding power system

costs attributable to each alternative plan. At this stage,

some preliminary feedback of forecast frequency and

Price variations duration data, as well as disaggregate outage costs and

Next, let us relax the assumption regarding the original system costs from the dost-benefit module, may be used

fixed price P,. Consider the situation where the stream to further improve system design. Finally the optimum

of system supply costs SC' associated with the optimum long-run system expansion plan and a range of associated

expansion plan i = m, on the first round, necessitate reliability levels are established, which maximize the net

significant changes in the assumptions regarding the social benefits, or equivalently, minimize the total costs

evolution of prices pt which were themselves used to (ie, system costs plus outage costs) to society.

determine the initial demand forecast. For example, the Two further possibilities exist for includinig feedback


Optimal electricity supply: M Munasinghe

Iterative feedback loop (p,R) Estimate of marginal SmR- supply costs and new -L price and reliabilityexpectation projections

Design feedbackSystem models -- 71

Revised and data \,p, R* forecast n alternative SC 2

I system expansion - SC lI w ~~~~plans and costs---- \I-

IX-SCn Cost-benefit analysis Optimal systemOriginal p,R Load - demandnOrgia a, models, data, 1 rR Rn (maximize A\E9 expansio,nplanp,R forecast and forecast at minimum of and range of

Oi n a oc TC SC + OC ) reliability levelsOriginal R * n alternative OZ|/.O-igin-a,l outcige cost - C2f? forecast pr°tions

/ O COCnII

l Outage cost J

Revised models ndRforecast dat

Iterative feedback loop (R*)

Figure 3. Flowchart for the implementation of the mekhodology.Note: p = price; R * = consumer's reliability expectation; R = reliability level; SC = supply costs; OC outage costs; TC = total costs;and NB = net benefits. Maximizing NB yields the optimal system plan m and the corresponding reliability Rm at the minimum valueof TCm = SCm + OCm.

effects. The principal return path is via the impact of'electricity prices on the load forecast, ie, if the newoptimized system plan requires changes in the original LRMCDYNassumptions regarding the future prices which were used a,to make the initial demand projection. A similar, but >less important feedback effect due to the influence of / -changes in the reliability expectation of consumers, on ' - / LRMC(R)both the demiand and the outage costs, may also be P -

incorporated into the analysis. Therefore, if necessary, Do Diit is possible to iterate through the model several times,to arrive at a mutually self-consistent set of price, demand Quantityand optimum reliability levels. Figure 4. Evolution of demand and reliability.

Figure 4 illustrates the new procedure in a differentway. Suppose that in the starting year the optimal price grows, capacity is added to expand output, while pricepo has been set equal to the LRMC(R°), at the market and reliability are optimized iteratively, as describedclearing point A. The LRMC(R 0 ) curve is derived from earlier. Thus, when reliability is optimized, price andthe system plan with the optimal reliability level R 0, demand growth are assumed to be fixed, and when pricekeeping R0 fixed. Thus initially both pric'e and relia- is optimized, reliability and demand are assumed to bebility are jointly optimized. unaffected. Through successive iterations, the mutually

Now if the demand curve shifts from Do to DI self-consistent set of optimal price, reliability andafter some time, the optimal price is not necessarily demand levels would be reached at point B.p' on the same LRMC(R°) curve; using this staticLRMC corresponds to the traditional method of . .system planning with a fixed target reliability level te ef oarial rlia tR0 . The optimal reliability may have changed to R 1 system expansion plannngand the appropriate curve is LRMC(IR 1) with optimal At this stage, several important features of the reliabilityprice Pl. Thus, as demand increases, the dynamic optimization approach presented here, should be empha-optimal long-run marginal cost curve LR.MCDyN sized: first, this method adds an entirely new dimensionlies along AB. to the traditional process of system expansion planning.

In practice B is unlikely to be a well defined point Usually, the power authorities examine several alternativebecause although the LRMC curve is generally known long-range power system plans which are designed to meetfrom known supply side (technological- economic) a basically fixed load forecast (although some variationconsiderations, the slope and position of the demand in the growth of demand may be considered, for sernsi-curve are not. tivity testing), at some predetermined, desired level of

Therefore, since B is a poorly defined and shifting reliability and subject to other political, environmentaltarget, a trial and error approach is required. As demand and legal constraints. Then, the plan wlhich has the lowest



value of total costs is chosen. This cost minimization ditions. The purpose of an electric power system is to

approach is equivalent to the maximization of net benefits supply power to consumers at some required rate, at the

criterion used in cost-benefit analysis, provided that the time and place of their choosing, while maintaining an

benefit streams of the alternatives being compared are acceptable quality of service (ie, voltage and frequency

identical. levels must lie within specified limits).

In the new approach described in this paper, the Thus, an ideal electric power system which unfailingly

reliability level is also a variable to be optimized. There- supplies power to consumers, wlhenever required, is by

fore, the system planner must design a number of definition a perfectly reliable one. Conversely, a system

alternative systems to meet the future demand (which never able to deliver electricity to users could be termned

is initially assumed to be fixed) at each of several target totally unreliable. All real world power systems lie

reliability levels, but still subject to the other constraints between these two extremes, and furthermore, as the

mentioned above. Then these alternatives are compared, system reliability level is improved, there is an inherent

and the one which minimizes the total costs (defined as tradeoff between the increased costs of supply, and the

the sum of the outage costs,and the sysitn costs) is reduction in the inconvenience and costs imposed on

chosen as the optimum one. In other words, the con- consumers due to power shortages. Therefore, it is

ventional system planning criterion of minimizing only important to develop criteria and methods of assessing

the system costs is subsumed witlhin the new procedure, and ranking systems according to reliability level.

where the total social costs are minimized. As in the case of any other product or service,

Second, another level of sophistication in system electric power shortages occur when the demand exceeds

expansion planning is possible with the new model, by the supply, due to the failure of planners to correctly

considering variations in the demand forecast. The main predict all the uncertainties in supply and demand. The

focus in this method is on the reliability level, which is stochastic nature of demand manifests itself through

optimized subject to an initially given forecast of load unforeseen increases in the load level, eg, the sudden

growth, ie, assuming a fixed evolution of electricity buildup in the air-conditioning load due to unusually

prices. Ideally, from an economic point of view, both warm weather. Similarly, the randomness of supply is

price and reliability should be optimized simultaneously, characterized by the unexpected failure or outage of

as discussed in greater detail earlier. However, electricity the various components which make up a power system,

tariffs in the real world are most often fixed, and there- eg, the unavailability of water for hydroelectric

fore it is more practical to assume a given evolution of generation.t

prices when the first round of optimum reliability levels From the consumers' viewpoint, power shortages

are determined. Any resulting changes in the pricing manifest themselves in a. number of ways: complete

assumptions can be fed back iteratively into the model interruptions of supply (or blackouts); frequency and

to improve the optimum. voltage reductions (or brownouts); and instability effects

Third, the framework for evaluating outage costs as such as erratic frequency fluctuations and power surges.

well as system costs in ihis new approach, is basically While all these phenomena are likely to inconvenience

economic, and more appropriate in the context of the and impose costs on electricity users, the consequences

national economy, or society, as a whole. The goods and of supply interruptions are the most severe, and probably

services used as inputs to the electric power system (eg, also the easiest to define. For example, a blackout will

labour, land, physical assets, materials, etc) are considered disrupt productive activity, and prevent the enjoyment

as scarce economic resources which could be used in of leisure, whereas a voltage reduction may have lesser

alternative production, and they are valued accordingly. effects such as the inconvenience caused by the dimming

In particular, if markets are highly distorted, shadow of lights. Mains frequency variations would effect a

prices may be used. Such an approach is particularly power system's own automatic control equipment, as

appropriate in the case of a publicly owned power utility, well as other synchronous devices such as electric clocks,

often the case in the developing countries. In contrast, the while power surges could cause damage to equipment, but

traditional system planning approach is more compatible these consequences are difficult to isolate. Therefore,

with the financial or accounting viewpoint of a private although the term outage cost (which is used throughout)

utility. Finally, the model may be suitably disaggregated is meant to encompass the expenses incurred by con-

to permit optimization of an interconnected system at sumers due to all types of shortages, in practice the

various levels of aggregation ranging from the global (eg, principle emphasis will be on the impact of supply

in terms of system-wide generation reliability), to the interruptions. Moreover, the effects of random or

specific (eg, in terms of distribution reliability for small unexpected interruptions will be stressed, since they

geographic areas). are likely to impose much greater hardships on users,

than known or planned power cuts.

Reliability Meeting system failures

The concept of reliability in engineering may be simply The main safeguard against the incidence of shortages is

defined in terms of the probability that a component, or .. ..

a system, will perform its intended functions satisfactorily, tr

over some period of time, subject to actual operating con- t For a deTailed definition of a component outage see Ref 7.


Optimal electricity stupply: M. Munzasinghethroughout the system to meet unexpected contingencies. possible to compute the long-run expectation that aOnce a failure has occurred, in the short run, voluntary large and complex system would be in a given state ordecreases in demand, voltage and frequency reductions, condition (eg, unable to meet the load), by usingand either operator controlled or automatic load shedding relevant load data in conjunction with informationmay occur. The connecting and disconnecting of regarding the probable availability of the individualgenerators and loads to the system also give rise to system components (eg, a generator), appropriatelytechnical problems involving sequencing, matching, and 'combined' according to the axioms of probability.synchronization, but these are usually handled routinely. Familiar reliability indices such as the loss-of-load-If the load is not curtailed in an orderly manner, uncon- probability (LOLP), and loss-of-energy-probabilitytrolled system failure is likely to occur, accompanied by (LOEP) were estimated usinlg this approach.9effects such as instability, eg, frequency fluctuations Th-e latest generation of probabilistic tools for powerand power surges, the tripping of and damage to genera- system reliability analysis are based on the idea of over-tors and lines, finally culminating in widespread and laying the combinative technique with the concept ofunpredictable blackouts. the system viewed as a stochastic process which evolvesBulk transmission reserve capability is ensured by over time. With this latter approach, the system isfollowing basic design principles, Suchi as having adequate commonly modelled as a discrete-state, continuous-thermal margins (ie, to prevent overheating), steady transition Markov process.1 0 At any given moment thestate, dynamic and transient stability against disturbances system may change from one state to another, due to(eg, the buildup of large voltage oscillations following a events such as component outages, or actions designedlightning stroke), avoiding bottlenecks in power flows, to restore normal operation. Once all the possible statesand providing alternative pathways to feed load centres are identified, and the rates of transition between thesethrough the use of ring systems, etc. In an interconnected states (which are determined by the correspondingsystem, it is important to avoid prolonged and extensive contingencies or restorative control actions) are known,blackouts caused by the progressive overloading and the system may be analysed. The transition rate matrix,cascading failure of many lines, following the initial which specifies the transition rates between all possibleoutage of a single link (eg, due to a three-phase fault to pairs of states, provides a useful mathematical summaryground). The design of distribution networks also of the Markov process. The latter may also be visuallyprovides a certain measure of redundancy by adopting depicted by meanis of a state-space diagram, with atechniques suchi as allowing extra safety margins for number of closed boxes representing the system states,substation capacity and power flow along feeders, as and a series of lines joining the boxes representing thewell as the use of switches to isolate faulted sections of possible transitions. Anong the advantages of this typeline, and to temporarily connect customers to circuits of model is that it facilitates: the estimation of thewhich are not affected by the outage. expected frequencies and durations of outages: theThere are two different (but interrelated) approaches modelling of the impact exogenous shocks, eg, suddenfor maintaining the quality of supply to consumers. The load; and the treatment of non-independent eventsfirst viewpoint which deals with the assessment of system (eg, failure and repair of different system components).security is essentially short-term, with the objective of The LOLP criterion (also called the loss-of-load-guiding system operations on an hourly or daily basis.8 expectation), is the reliability index which is commonlyThe second, more relevant, approach is concerned with used, especially in generation planning. System failurereliability evaluation for use in the long-range planning is most often defined in terms of inability to meet theand design of power systems and in the long-run potential daily peak load. Therefore, in the context of a genera-tradeoff between system costs and outage costs. tion study, the LOLP may be interpreted as the average

number of days over some long period of time, duringwhich the peak demand is expected to exceed theReliability analysis available generating capacity. For example, the targetReliability concepts are required to establish target LOLP frequently used in the USA is one day in 10reliability levels for purposes of system design, as well as years, while in European countries the correspondingto analyse and compare the future levels of system standard varies from one day in 15 years to one day inreliability with these target values. Historically, the 2.5 years. In the case of transmission and distributionearly use of reliability criteria in system planning relied planning, time is measured continuously, rather than inon simple rule-of-thumb, deterministic approaches, such terms of the daily load cycle, and therefore the LOLPas the concept of ensuring an adequate reserve margin is given in terms of the long-run average fraction of totalor use of a single or double-worst-fault design criterion time the system is expected to be in a state of failure(ie, the capability of the system to meet the load, after (defined as an interruption of supply, or sometimes athe loss of the largest or the two largest generating units voltage reduction or component overload).respectively). The LOLP is often supplemented by the expected-However, in light of the basically probabilistic character loss-of-load (XLOL) index, which indicates the expectedof system reliability and component outages, the next magnitude of the unsupplied load, given that a failurestage of sophistication in reliability analysis led to the has occurred. Another index which measures the magni-development of combinative (probabilistic) methods. tude of system failure is the loss-of-energy expectationWith these combinative concepts and models, it was or LOEE (also called the expected unserviced energy).


Optimal electricity supply: M. Munasinighe

The LOEE is the expected amount of energy not supplied actually takes place, or simply because one is expecteddue to outages in the long run, but expressed as a fraction to occur. During an outage, direct outage costs are likelyof the total energy demanded. The expected frequency to be incurred since normal productive activity is disrupted.or mean recurrence time between outages, and the Indirect outage costs are incurred in the absence of anexpected duration of such events when they occur, are outage itself, because consumers may adapt theira more recently discovered pair of reliability indices behaviour patterns in ways that are less efficient, or(FAD), which are widely used in transmission and more costly, but less susceptible to outage disruptions;distribution system planning, but rather infrequently in or, they may purchase alternative (standby) sources ofgeneration studies. energy. Although indirect outage costs cannot be attri-buted to any particular outage, they depend on theComparing outage indices general level of reliability, and represent real resourcecosts which should be considered, when attempting toEach of the indices has its strengths and weaknesses, and estimate the economic costs associated with alternativedoes not give a complete description of outages. For reliability levels. Generally, direct outage costs are relatedexample, although it is a measure of the probability of more to the short-term impact of unexpected outagessystem failure, the LOLP does not indicate the expected whereas indirect outage costs arise from longer-termmagnitude of the load lost during such a contingency, considerations of outage expectation, including theand furthermore, since it is a long-run concept, the effects of planned power cu.s. In practice, it wouldimpact of operating procedures and criteria which could often be difficult to estimate outage costs associatedmodify the risk of failure, is effectively ignored. On the with a particular level of reliability because such costsother hand, the XLOL provides the expected magnitude may consist of a combination of direct and indirectbut neither the probability nor the average duration of components.

an outage. Like the LOLP, the FAD measure does not All outage costs associated with a given level ofgive the mean size of the failure, but since it is commonly reliability depend, ceteris paribus, on both the expectedspecified at the load-point or particular point of con- and the actual levels of reliability. The nature of thissumption, the number of affected customers and the depe-ndence can best be illustrated by considering themagnitude of the interrupted load may be deduced. following two situations:The problem with these reliability measures is that, 0 If a low level of reliability is expected (RL*), thenbecause the underlying models, the methods of compu* consumers are likely either to adjust their activities,tai'on, and their interpretation may be all different, or to purcliase alternative sources of energy in orderthe various indices are generally neither comparable, nor to reduce direct outage costs. Such behaviour modifi-consistent (in the sense that they could yield different

rankings of systems, by reliability level). Often, even the Total nutage costs, ie, the sum of direct and indirectsame index may be calculated in more than one way. For outage costs, also depend on the actual level ofexample, it is possible to derive the LOLP using a reliability. If this level is low, direct outage costs areconventional model in which each generator is represented still significant despite the indirect (and preventative)in two or more discrete states, or alternatively, by outage costs incurred by consumers. In this case,modelling the whole generating system as a normal total outage costs will likely be high. With high actualdistribution.11 Similarly, the FAD measure of outages reliability, direct oLItage costs will be smaller, andmay be interpreted differently, depending on whether it thus total outage costs will be less than in the caseis defined at the load-point as mentioned earlier, or of low actual reliability.specified as a system-wide generation/transmission * If high reliability is expected (R H*), individualsindex. 12 Finally, if the LOLP and LOEP criteria are probably do little to adjust their behaviour andcompared, the former index will rank a system which has therefore, few indirect outage costs are incurred. Ina long-lasting failure on a single day above a system with such circumstances, total outage costs will betwo very short failures on separate days, whereas the relatively high if the actual reliability level is low,latter measure is likely to reverse the order of ranking. and such costs will be smaller if actual reliability isTwo broad categories of mathematical techniques are high.used to calculate the values of power system reliability The effects that the relation between expected and actualindices. One class of analytical methods relies on the reliability have on outage costs is demonstrated graphi-direct (or analytical) manipulation of the basic proba-bility axioms.13 In contrast, the Monte Carlo methods cally in Figure 5. Consider a field of curves, each of wtictuse the computer to first simulate various random events is a graph of total outage costs against the actual level ofin a manner analogous to throwing dice (eg, mean time reliability, but parametrized by a given level of expectedto failure, or repair time of components), and then reliability. In general, at a given level of actual reliability,estimate system reliability levels.J4

outage costs are higher when the difference betweenactual and expected reliability is greater. Also, outagecosts will typically decrease with increasing reliability,Outage costs for any given level of expected reliability. Overall, totalOutage costs may be defined as direct or indirect accord- outage costs wil] likely be highest in the case of highing to whether they are incurred because an outage expected reliability and low actual reliability (R*H R ).


Optimal electricity supply: M AMunasinghe

In conclusion, by ignoring possible feedback effects

between changes in reliability and expectations, some

D-- relatively small errors in outage cost estimation are

likely to be introduced, However, since little is known

\ I\a priori about the extent of such feedback effects,

v - \ sophisticated attempts to correct for thenm could easily

, Iresult in even greater errors.

'aB R- - -- -- -RL Estimating outage costs

IIn the literature there are two schools of thought con-

cerning how outage costs should be estimated. One

A - -- - - -- - approach is to estimate these costs on the basis of

I I RH* observed (or estimated) willingness-to-pay for planned

I I Ielectricity constumption.' 5 The other approach, used

I here, estimates such costs in terms of the effect of

I_ X I I- outages on the production of various, goods and services.16

O R L R RCH Attempts to estimate outage costs according to

Actual reliability level willingness-to-pay are actually part of a more general

Figure 5. Relationship between total outage costs and literature on optimal pricing for public utilities under

the levels of actual and expected reliability. conditions of uncertainty, ie, stochastic demand and

supply. In this approach, the variable to be maximized

Lower total outage costs are likely to occur in the case 6f is net welfare which is generally set equal to the expected

low expected, and actual reliability levels (RL*, RL), area under the demand curve corresponding to planned

lower still when there is low expected, and high actual electricity consumption, minus the sum of the expected

reliability (RL*, R) and finally, lowest when there is costs of supplying electricity, plus the expected costs

both high expected, and actual levels of reliability (if any) of rationing available electricity among

(RH*, RH). consumers, if an outage occurs. Thus outage costs are

In reality, reliability expectations might lie anywhere measured by the expected reduction in net welfare, or

between RL and RKI-, assuming that these are the the amount those who are deprived of electricity would

limits, and thus there will be many curves relating the be willing-to-pay for it, minus the costs saved by not

reliability level to outage costs. At each level of relia- applying it.

bility, the curve that indicates the lowest possible outage Studies that estimate outage costs on the basis of

costs is the one for which the actual and expected willingness-to-pay assume that electricity provides direct

reliability levels are equal. Thus it is possible to trace an satisfaction to its consumers. Outage costs are therefore

envelope curve that indicates the outage costs which estimated in terms of lost consumers' surplus. Other

would result if individuals could correctly anticipate the studies treat electricity as an intermediate input used to

actual level of reliability, and take rational steps to

minimize the resulting outage costs. Such an envelope

curve is represented by the bold line in Figure 6.

In practice, it will be difficult to determine how changes

in actual reliability affect consumers' expectations of

reliability. Thus it may be necessary to estimate outage

costs based on the assumption that such expectationsremain essentially uinchanged over a range of actual

reliability levels. With this simplified approach; outage

cost averting adaptions (such as the purchase of a standby \

generating plant) would be assumed to occur only after

the level of reliability fell below some critical value, °which would vary for different consumers. For example, 7a

RL.

as shown in Figure 4, if reliability level is reduced from 2

RH to R', outage costs will appear to increase by AD,

given the assumption that reliability expectations remain

unchanged at the high level RH *. H-lowever, the increase

in outage costs may be only AC if consumers' expecta- RH

tions, and hence their behaviour, have adjusted to the

lower level of reliability R* (once the critical reliability -

level R' has been passed). In reality expectations would o

take time to adjust and therefore tlle resulting increase in Actual reliability level

actual outage costs would lie somewhere between AC Figure 6. Envelope curve of total outage costs (heavy

and AD. line).


Uptinial electricity supply: M. Munasinghe

produce various goods and services required by con- can be measured in terms of the resulting reductionsumers, rather than an end product, wlhich itself provides in the present value of the stream of net social benefits.satisfaction to consumers. Outage costs are therefore When an outage disrupts production, the net benefitsmeasured primarily by the costs of lost production due derived from such activities are reduced, ie, direct outageto outages. costs are incurred, since the costs of inputs are increased,The studies that estimate outage costs on the basis of and/or the value of outputs is reduced. Specifically, anwillingness-to-pay have several important shortcomings. outage can cause raw materials, intermediate products, orFirst, it seems clear that observed willingness-to-pay for final outputs to spoil, and it can also result in productiveplanlned electricity consumption is not an accurate factors being made idle. The loss leads to an opportunityindicator of what one would be willing-to-pay to avoid cost equal to the value of the final product nowan unplannled outage. Such an unplanned outage is apt unavailable, minus the value of additional inputs notto disrupt activities which are complementary with now needed. However, if the value of the output is notelectricity consumption, and therefore, actual outage easily determined, as in the case of household and publiccosts may be greatly in excess of observed (long-run) sector outputs which are not directly sold on the nmarket,willingness-to-pay; and second, these studies measure then it is necessary to use the cost of producing thelosses of consumers' surplus on the assumption that load spoiled product or output as a minimum estimate ofshedding takes place according to willingness-to-pay, the resulting cost of the outage.ie, those with the lowest willingness-to-pay are the firstto have their electricity cuLt off. Case study

Thus lost consumers' surplus is the triangle-shaped area A case study was carried out to test empirically the newdefined by the downward sloping demand curve, the metudy described out the longrange distriwhorizontal price line, and the vertical line repre3enting methodology described above. The long-range distri-the quantity of electricity supplied in spite of the bution plan of the city of Cascavel sn Brazil wasoutage. However, in many instances it is not reasonable optFirzed accordimg to the procedure summarized into assume that load shedding takes place accordingto a Figure 2. For simplicity, only the distribution systempredetermined order. For example, if the outage is caused reliabiit was varied, whabil ofstheby adisribtio sysem ailre rater tan geeraion generation and transmission system was held constant;by a distribution syster failure (rather than a generation although it does not affect the results of the case study,system failure), the ability to order load shedding maybeysteve limired the cadsehersing loss note that varying the latter would have yielded a betterbe severely Iii-nted. If sucli iS the case, the resulting loss opiu.Tedtsrlangothdmndfectin consulmers' surplus is a trapezoid-shaped area defined optimum. The details relating to the demand forecastin conshimers smurplusve a thaprcezoid ad area dfin- and design of alternative distribution system plans haveby the demand curve, the price line, and the infra- been described elsewhere. 1 The more novel aspects ofmarginaJ units of electricity not supplied. The implication the analysis relating to the measurement of outageis that actual outage costs will exceed outage costsestimated on the basis of the marginal consumers' costs are summarized below.surpus lst.The results of a survey of residential consumers andsurplus lost. an analysis of their outage costs confirmed the resultinh te e ri erof a detailed theoretical model presented elsewhere, 1 9of outage costs requires exact knowledge of various and showed that: the chief irnpact of unexpectedconsumers' demand functions for electricity. Given the outages on electricity using households, was the lossproblems associated with this,' 7 it is likely that any o aestimates of outage costs obtained will be subject to evnn hrs when '.elerict wa consiredu essentiaconsiderable error. Given these criticisms, outage costs (for television, reading etc) whereas domestic activitieswould be more appropriately measured in terms of the which were interrupted during the daytime, could beeffects of outages on various kinds of productive activity. w ithrreltel litte icneience; anreschieduled with relatively little inconvenience; and

over this period, the monetary value of lost leisureProduction as a measure of outage cost could be measured in terms of the net wage or incomeProduction is a process in which capital and labour are earning rate of affected households, as confirmed bycombined with other inputs (raw materials and inter- their short-term willingness-to-pay to avoid outages.mediate products) to produce a time stream of outputs. Estimated residential outage costs were in the rangeUnder conditions approximating those of perfect com- of US$1.30-2.0/kWh lost. The principal advantage ofpetition, the net social benefit of a marginal unit of this method was its reliance on relatively easy tooutput in a given time period equals the value of the obtain income data.output minus the value of inputs. For infra-marginal In general industrial consumers suffer outage costsunits of output, producers' and consumers' surplus must because materials and products are spoiled, and normalbe included when measuring the net benefits of produc- production cannot take place. This results in an oppor-tion. When market distortions are present in the economy, tunity cost in the form of idle capital and labour, bothappropriate shadow prices have to be used to value inputs during the outage and any restart period following theand outputs. The aggregated net social value of a time outage. If there is slack capacity, some of the lost valuestream of marginal outputs equals the present value of added may be recovered by using this productivethe resulting stream of net social benefits. Thus the capacity more intensively during normal working hours.opportunity cost of supplying low reliability electricity !n addition, the firm may operate overtime to make up



lost production. B.ased on these considerations, a survey main industrial zone, while other areas of the city were

of the 20 principal industrial users of electricity in served at a lower reliability level. The range of global

Cascavel was made to determine outage costs for outages optimal reliability levels was 0.9987 > R > 0.9983.

of various durations (ie, 1 minute to 5 hours). The The effects of the new optimum reliability levels,

results indicated that there were wide variations in the on the demand forecast and outage costs, via the price

effects of outages on industrial consumers, eg, US$1.0- and reliability expectation feedback loops shown in

7.0/kWh lost, depending on the type of industry, the Figure 2, were not investigated, because of lack of

duration of the outage, and the time of day durinig information on how the original prices and expected

which it occurred. This approach helped to rank industries reliability levels should be revised. However, the results

in terms of sensitivity to outages, eg, for emergency load were found to be relatively insensitive to an arbitrary

shedding purposes. 10% change in the demand forecast.

An outage which affects public illuminiation imposes Finally, the residential outage costs of US$1.3-

a cost in the form of forgone community benefits such 2.0/kWh lost (depending on the duration) in Cascavel

as security and improved inotoring safety. One can may be compared with corresponding results of other

argue that these forgone benefits are worth at least as studies: US$0.4-0.7 (Sweden, 1948); 0.7-1.5 (Sweden,

much as the net supply cost wlhich the community would 1969); and 0.5-1.5 (England, 1975). Similarly Cascavel

have incurred for public illumination during the outage industrial outage costs of US$1.0-7.0/kWh lost

periods, eg, the annuitized value of capital equipment correspond to values of US$1.0-2.0 (Sweden, 1]948);

and routine maintenance expenditures. 0.1-3.0 (Sweden, 1969); 0.2-8.0 (Chile, 1973); and

Two hospitals (80 beds and 200 beds) were surveyed 1.0-9.0 (Canada, 1976) (all values in 1977 dollars).

to estimiiate the opportunity costs of productive factorswhjch are made idle (eg, electricity using equipment,labour etc) and intermediate products, such as blood and Conclusionsmedicines, which might spoil because of outages. The The principal purpose of this paper was to emphasize

prirncipal outage costs of US~i5.5 per hospital bed per the close interrelationships between optimal reliability,

hour of outage were found to occur during the night pricing and system planning in the electricity seetor.

period (ic, 1900-0600 lours), due to idle labour and For maximization of the welfare from electricity con-

capital. Estimating the outage costs resulting from sumption, price should equal marginal cost, and

possible loss of life is a task exceeding the scope of this reliability should be increased until the marginal increase

study. The existence of standby batteries for the intensive in system costs was equal to marginal outage costs

care and surgical equipment suggests that death will be thereby averted. By focusing attention on the hitherto

avoided in most cases; the cost of these batteries is small. relatively neglected area of outage costs, a broader

Outage costs for government offices and commercial approach to system planning was developed in which

customers were found to be minimal, because in most the sum of system costs and outage costs is minimized.

cases reliance on electricity using equipment such1 as This methodology, which also yields the optimal reliability

calculators and photocopiers was smiall, thus permit- (capacity) level, effectively subsumes the traditional

ting work to continue by daylight. Furthermore, there system planning criterion of minimizing only the system

was sufficient slack during the normal hours of work for costs subject to an arbitrary target reliability level.

jobs delayed by any ouiage to be made up. Supermarkets The theoretical methodology presented here was

and hotels reported minor amounts of spoilage for long applied to the case of a typical urban distribution

outages, ic, over five hours; however, such outages are system. The same basic approach could easily be used

extremely rare. Rural consumers around Cascavel could to optimize a total system plan, ie, at the generation

be neglected since their energy c(onsumnption was less and transmission level as well. In particular, fine-tuning

than 2% of the total, througlhout the plan period. the procedure permits the level of distributioin reliability

The residential and industrial categories incurred the to be varied by small areas, to yield a better optimum.

highest losses. The cost-benefit comparison of the outage This approach indicates that the optimal reliability

costs and system costs for Cascavel indicated that as level will be higlher for areas in which outage costs are

global reliability improved, outage costs decreased fairly greater, implying that optimal price would also be larger.

steadily, whereas supply costs were practically constant Because of the wide variation in electricity ccnsump-

until a critical level of reliability was reached, after tion patterns, power system characteristics, etc, in

which these costs increased sharply. The outage cost different countries, the results of the case study cannot

results disaggregated by cell and by consumer category be easily extrapolated to a worldwide scale. For purely

indicated that the high population density areas in the indicative purposes, note that the net saving or welfare

city centre and the industrial area suffered the highest gain due to system optimization in the case study

outage costs. Therefore, several additional rmixed or discussed is about 5% of the estimated total distribution

hybrid network expansion plans 4, 5, and 6, were designed, system investment costs, or approximately 0.4% of the

based on the principle of providing the highest reliability total value added in the urban area, during the study

service to areas with the highest outage costs, and so on. period. If even half these percentage values were taken,

This feedback procedure yielded the best system expansion on a conservative basis, the net potential savings on total

plan which provided high reliability service in the city electric power sector investments in the capital scarce

centre area with a high population density, and the developing countries alone, would be over (constant


Optimal electricity supply: M Munasinghe

1979) US$1 billion per year, during the next decade, Kleindorfer, Public Utility Econofmics, St MartinsFurter orkneed tobe one in efiingthePress, New York, 1979; and Turvey and Anderson,Further work needs to be done, lil refining -the op cit, Ref 4, Chapter 14.conceptual framework for measuring outage costs, and 6 See for example: M. Munasinghe and J. J. Warford,improving the methods of estimation. In particular, the Electricity Pricing in Developing Countries, Johnsrelationship between oLitage expectation and adaptioni Hopkins University Press, Baltimore, MD, 1981; andof consumer behaviour must be investigated in the M. Munasinghe, 'Principles of modern electricitycontext of indirect versus direct outage costs, and long- pr1cing', Proceedgs of the IEEE Vol 69 Mahversus short-run effects. The impact of various pricing 7 IEEE Standard, No 346 - 1973, IEEE, New York, 1973.policies on optimum reliability levels, via the demand 8 For details see: A. R. Debs and A. S. Benson,forecast, slhould also be examined. More case studies 'S>curity assessment of power systems', in Systemsare required, whiclh would cover varioLus aspects of Enginieering for, Power: Status and Pfospects,rem require , wc o covervaiou .aspcs f a USERDA Conference, Henniker, New Hampshire,system planning, eg, generation and transmission, in a August 1975, NTIS, No CONF-750867, pp 144-number of different countries, eacli having a different 1 76; and L. P. Hajdu and R. Podmore, 'Securitymix of consumers, as well as varied socioeconomic and enhancement for power systems', ibid, pp 177-195.physical conditions. 9 R. Billinton, R. J. Ringlee and A. J. Wood,Power System Reliability C'alculations, MIT Press,Cambridge, MA, 1973.

10 See C. Singh and R. Billinton, 'Frequency andReferences duration concepts in system reliability evaluation',I Denis Anderson, 'Models for determining least-cost IEEE Tronsacti(. !75 on Reliability, Vol R-24, Aprilinvestments in electricity supply', Bell Journal of 1975, pp 3 1-36.Economics, Vol 3, Spring 1972, pp 267-301 and 11 See for example: R. N. Allan and F. N. Takeiddine,Robert L. Sullivan,Power System Planning, McGraw- 'Genleration modelling in power system reliabilityHill, New York, 1977. evaluation', Reliability of Power Supply Systemts,2 P. Dupuit, 'De l'utilite et de sa mesure', La Reforma lEE Conference Publication No 148, London,Soziale, Turin, 1932; H. Hotelling, 'The general February 1977, pp 47-50.welfare in relation to problems of railway and 12 See for example: R. N. Allan and F. N. Takeiddine,utility rates', Econometrica, Vol 6, July 1938, 'Network limitations on generating systems reliabilitypp 242-269; N. Ruggles, 'The welfare basis of evaluation techniques', Paper No A78070-5, Proceed-the marginal cost pricing principle', Review of ing of the IEEE Power Engineering Society Win tel-Economic Studies, Vol 17, 1949-50, pp 29-46; Meeting, New York, January-February 1978; andand N. Ruggles, 'Recent developments in thle theory G. E. Marko, 'A method of combining high speedof marginal cost pricing', Review of Econiomic contingency load flow analysis with stochasticStudies, Vol 17, 1949-50, pp 107-126. probability methods to calculate a quantitative3 See for example: M. Boiteux, 'La tarification des measure of overall power system reliability', Paperdemandes en pointe', Revze Generale de l`Electricit, No A78053-1, Proceedings of the IEEE PowerVol 58, 1949, pp 321-340; P. Steiner, 'Peak loads Engineering &iciety S,nimner Meeting, Los Angeles,and efficient pricing', Quarterly Journlal of Econio- July 1978.mics, November 1957, pp 585-610; M. Boiteux and 13 R. Billinton, Power SysiL'n Reliability Evaluation2,P. Stasi, 'The determination of costs of expansion of Gordon and Breach, New York, 1970.an interconnlected system of production anrd distri- 14 P. L. Noferi, L. Paris and L. Salvaderi, 'Monte Carlobution of electricity', in James Nelson, ed, Marginal methods for power system reliability evaluation inCost Pricing in Practice, Prentice-Hall, Englewood transmission and generation planning', ProceedingsCliffs, New York, 1974; 0. Ii. Williamson, 'Peak of thle Annual Reliability and Maintainabilityload pricing and optimal capacity under indivisibility Symposium2, Washington, DC, January 1975,constraints', Thle A inericaz Economic Review, Vol pp 460-469.56, No 4, September 1966, pp 810-827; and 15 See G. Brown Jr and M. B. Johnson, 'Public utilityR. Turvey, Optimal Pricing an2d In vestmlentt in pricing and output under risk', Amnerican Ec'onomicElectricity Suipply, MIT Press, Cambridge, MA, Review, Vol 59, March 1 969, pp 119-1 28; M. A.1968. Crew and P. R. Kleindorfer, 'Peak load pricing with4 See for example: 'Symposium on peak load pricing', a diverse technology', Bell Journal of Economics,Bell Journial of Econiomnics, Vol 7, Spring 1976, Spring 1 976, pp 207-231; Sherman and Visscher,pp 197-250; R. Turvey and D, Anderson, Elec- op cit, Ref 4; and Crew and Kleindorfer, op cit, Ref 4.tricity Economics, Johns Hopkins University 1 6 See: M. L. Telson, 'The economics of alternativePress, Baltimore, MD, 1977; M. A. Crew and levels of reliability for electric generating systems',P. R. Kleindorfer, 'Reliability and public utility Bell Journial o1 Economics, Vol 6, Autumn 1975,pricing', American2 Economic Review, Vol 68, pp 679-694; Turvey and Anderson, op cit, Ref 4,March 1978, pp 31-40; R. Sherman and M. Visscher, Chapter 14; M. Munasinghe, 'The costs incurred by'Second best pricing with stochastic demand', residential electricity consumers due to powerAmerican Economic Reviewv, Vol 68, March 1978, failures', Journal o0 Consumer Research, Vol 6, Marchpp 41 -53;M4arginal Costin2gand PricingofElectrical 1980, pp 361--369; and Munasinghe and Gellerson,Energy, Proceedings of the State of the Art Con- op cit, Ref 4.ference, Canadian Electrical Association, Montreal, 17 L. D. Taylor, 'The demand for clectricity: a survey',Canada, May 1978; Mohan Munasinghe and Mark Bell Journzal ofEconomnics, Vol 6, Spring 1 975,Gellerson, 'Economic criteria for optimizing power pp 74-110.systems reliability levels', Bell Journal of Economics, 18 M. Munasinghe and W. Scott, 'Long range distri-Vol 10, Spring 1979, pp 353-365; and bution system planning based on optimum economicM. Munasinghe, 'Electric power pricing policy', reliability levels', Paper No A78576-l, ProceedingsStaff Working Paper No 340, World Bank, Washington, of thle IEE Power Engineering Society Sun2merDC, June 1979. Meetin2g, Los Angeles, July 1978.5 See for example: Michael A. Crew and Paul R. 1 9 Munasinghe, op cit, Ref 16.


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Public Disclosure Authorized Mohan Munasinghe Optimal ...documents.worldbank.org/curated/en/...traditional power system design and planning has been based on the overall principle