World Bank Reprint Series: Number 147

Mohan Munasinghe

A New Approachto Power System Planning

Reprinted with permission from IEEE Transactions on Power Apparatus and Systenms, vol. PAS-99, no. 3 (May/June1980, pp. 1198-1206. Copyrighted by the Institute of Electrical and Electronics Engineers (IEEE).

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1198 IEEE Transactions on Power Apparatus and Systems, Vol. PAS-99,No. 3 May/June 1980

A NEW APPROACH TO POWER SYSTEM PLANNING

Mohan Munasinghe, Senior M'eunber, IEEEEnergy Department, Thie World Bank

Washington D.C. 20433

Abstract - The conventional method of power system pansion planning models are usually optimized with res-planning relies on the minimization of system costs pect to standards of supply reliability which are them-subject to meeting given levels of demand and reliabil- selves derived from past practice, and vague notions asity, as well as other constraints, An economic criter- to the quality of service which would be acceptable toion for system optimization is presented here which the electricity cownsuming public (3), (4).subsumes the traditional approach by treating the re-liability level as a variable to be optimized. The Until recently, the idea of investigating the de-theoretical model io:hich is developed compares the costs mand side effects relatit, to the economic worth of re-with the worth of reliability, and leads to an opti- liability, had received !iLttle attention, principallymized power system plan in which net social benefits because of the difficulties of measuring the benefitsare maximized, or equivalently, the sum of the costs of improved qualit,y of service (5)-(8). If the relia-incurred by consumers due to power outages and the sys- bility level is considered as avariable to be optimized,tem costs is minimized. This approach is more relevant rather than an arbitrarily imposed standard, then ain the national economic context, whereas the tradi- social cost-benefit approach maybe adopted, to evaluatetional system planning technique emphasizes the finan- the inherent tradeoff between the increase in powercial viewpoint of aprivate utility company. Techniques system supply costs required to achieve a high level ofof estimating outage costs and the results of a case reliability, and the corresponding decline in outagestudy which validates the new methodology are also costs, i.e., the economic costs incurred by electricitysummarized. consumers due to power shortages. In other words, the

optimum system plan and reliability level which maxi-INTRODUCTION mizes the net social benefits of electricity consump-

tion, -hould be determined at the point where the mar-During the twentieth century, the electric power ginal increase in system supply costs, due to a reli-

industry has emerged as one of the most vital, as well ability increase, are exactly offset by the marginalas capital intensive sectors of the economy, in prac- worth measured in terms of the corresponding decreasetically every country. The US, which is the largest in outage costs.(about 560 GW installed capacity), and one of the mostenergy intensive (approximately 10,000 kWh per capita In this paper, a combined economic-engineering ap-per year), economies in the world, devoted almost US$30 proach is used to demonstrate, theoretically as well asbillion to electric power sector investments in1978 (1). operationally, that an optimum long-run power systemCorresponding investments in the developing countries expansion plan and a corresponding range of reliabilityare expected to also average about, (constant 1976) levels may be determined, which maximize net socialUS$25 billion per year over the next decade, account- benefits. Such a balanced treatment of both the supplying for over 20 percent of all public sector invest- and demand side effects of reliability requires accu-ments (2). rate estimation of both system costs and outage costs.

The former category of costs may be determined fromAlready, there is a general worldwide rising trend straightforward engineering-economic considerations nor-

in the real unit costs of supplying electric power, mally associated with power system design and planning,which is likely to continue, owing to factors such as However, the estimation of outage costs is more diffi-the shift towards more costly hydro, coal and nuclear cult, and hence, in order to do so, new models andgenerating plant, following the oil crisis, and the methods are summarized for analyzing the various wayslimited possibilities for realizing further significant in which electricity is utilized, by different cate-economies of scale, especially as systems continue to gories of consumers.expand into areas of lower population density. Themassive investment needs for power imply that even Figure 1 is a flow chart of the new power systemsmall efficiency improvements in the sector will lead optimizing methodology presented in this paper. To be-to significant saviogs, which are especially important gin with, a framework and set of models are developedin the case of developing countries experiencing short- to analyze the economic costs incurred by differentages of both local ar_ foreign exchange resources. categories of consumers (e.g., residential, industrial,

etc.), due to electric power shortages of varying in-Traditional power system design and planning has tensity. Concurrently, adisaggregate long-range (e.g.,

belln based on the overall principle of minimizing the 20 years) load/demand forecast is estimated, based ontiP1r costs required to meet a certain load, at a a predetermined evolution of electricity prices, within

g-iven level of .celiability. In the last few years, the area to be served by the electric power utility.there has been increasing rec;nition of the fact that Next, several alternative (least-cost) power systemeven the most sophisticated lea4t-cost power system ex- plans are prepared to meet this future load, at several

different levels of reliability. The expected annualfrequency (i.e., the number) and duration of powerfailures associated with each alternative system designor plan, as well as the time of occurence of theseshortages, and the average numbers and types of con-sumers affected by them, is estimated for the entireforecast period.

By substituting the estimated outage frequency andFd y the IEEE Power Sysem Eng. duration results in the consumer outage cost models, itF 79 1 5-53, A paper recommrended and approvgd by teE PwrSsmEn psietodemnehe total future outage costsneerng ommtte ofthe EEEPowr Egiser,ng Society for presentation at the is possible to determine the oa uueotg otneering Committee of the IEEE Power EngglFbgSceYf°rPrNetts°itsb for each system plan. On the supply side, the invest-IEEE, PES Winter Meeting, New York, NY, February 4-9, 1979. Manuscript sub-foeahstmpln Onheupysi,teivs-

nitted August 29, 1978; made available for printing December 27, 1978. ment and operating costs of each alternative design may

0018-9510/80/0500-l 198$O0.75 © 1980 IEEE

1199

iterative feedback loop (price and reliability expectation) I

L Demand Alternative (Least-Cost) Estimate of PowerForecast Power System Designs System Costs

Forecast of Fr- Cost-Benefit Optimum Powerquency and Duration - Analysis of Pow- Syatem Planof Outages and Con- er System Design and Range of Re-sumers Affected Alternatives liability Levels

Economic Models Estimate ofof Outage Costs Future Economic -,

Outage Costs

L.. - iterative feedback loo_(reliability expectation) _

Figure 1. Schematic of the Main Steps Involved in the Methodology

also be estimated. Then a cost-benefit model is used be emphasized. First, this method adds an entirelyto compare the outage costs with the corresponding pow- new dimension to the traditional process of system ex-er system costs attributable to each alternative plan. pansion planning. Usually, the power authorities exam-At this stage, some preliminary feedback of forecast ine several alternative long-range power system plansfrequency and duration data, as well as disaggregate which are designed to meet a basically fixed load fore-outage costs and system costs from the cost-benefit cast (although some variation in the growth of demandmodule, may be used to further improve system design. may be considered, for sensitivity testing), at someFinally, the optimum long-run system expansion plan and predetermined, desired level of reliability and subjecta rangeof associated reliability levels are established, to other political, environmental and legal constrairts.which maximize the net social benefits, orequivalently, Then, the plan which has the lowest value of totalminimize the total costs (i.e., system costs plus out- costs is chosen (9). This cost-minimization approachage costs) to society. is equivalent to the maximization of net benefits cri-

terion used in cost-benefit analysis, provided thatTwo further possibilities exist for including feed- the benefit streams of the alternatives being comparedback effects. The principal return path is via the im- are identical.pact of electricity prices on the load forecast, i.e.,if the new optimized system plan requires changes in In the approach described in this paper, the reli-the original assumptions regarding the future prices ability level is also a variable, to be optimized.which were used to make the initial demand projection. Therefore, the system planner must design a number ofA similar, but less important feedback effect due to alternative systems to meet the future demand (which isthe influence of changes in the reliability expectation initially assumed to be fixed), at each of several tar-of consumers, on both the demand and the outage costs, get reliability levels, but still subject to the othermay also be incorporated into the analysis. Therefore, constraints mentioned above. Tnen these alternativesif necessary, it is possible to iterate through the are compared, and the one which minimizes the totalmodel several times, in order to arrive at a mutually costs, defined as the sum of the outage costs and theself-consistent set of price, demand and optimum reli- system costs, is chosen as the optimum one. In otherability levels. words, the conventional system planning criterion of

minimizing only the system costs is subsumed withinTHEORETICAL BACI:GROU[.D the new procedure, where the total social costs are

minimized.The discussion in the previous section indicates

that the procedure for optimizing reliability levels Second, another level of sophistication in systemshould be both theoretically rigorous and operationally expansion planning is possible with the new model, byuseful. That is, it should bring together supply and considering variations in the demand forecast. Thedemand side effects within a consistent economic-engi- main focus in this method is on the reliability level,neering framework that would be relatively simple to which is optimized subject to an initially given fore-apply, and would use readily available information. cast of load growth, i.e., assuming a fixed evolutionAccordingly, the economic theory for the optimization of electricity prices. Ideally, from an economic pointmodel presented below is drawn mainly from the area of of view, both price and reliability should be optimizedcost-benefit analysis, whereas the engineering aspects simultaneously, as discussed in greater detail below.are strongly influenced by the practical approach used However, electricity tariffs in the real world are mostin power system planning. In brief, a range of opti- often fixed, and not necessarily at optimum levels. Inmum reliability levels may be determined, by identify- our model, it is more practical to assume a given evo-ing the system expansion program which maximizes the lution of prices when the first round of optimum relia-net benefits of electricity consumption, or equivalent- bility levels are determined. Any resulting changes inly, as shown below, minimizes the sum of system and the pricing assumptions can be fed back iteratively in-outage costs to society, over the planning period. to the model to improve the optimum.

At the outset, several important features of the Third, the framework for evaluating outage costsreliability optimization approach presented here, should as well as system costs in this new approach, is basic-

1200

ally economic, and more appropriate in the context of D = D (P , Y t, R* z (l)the national economy, or society, as a whole. The it it it titgoods and services used as inputs to the electric power where P is the electricity r>ice, X is the income vari-system, e.g., labor, land, physical assets, materials, able which represents the level of economic activity,etc., are considered as scarce economic resources which R* is the expected value of reliability, and Z is acould be used in alternative production, and they are vector of other independent variables affecting demand.valued accordingly. In particular, if markets are Initially, it is ass.xmed that the demand forecast ishighly distorted, shadow prices may be used (10). Such determined by the exogeneously given evolution overan approach is particularly appropriate in the case of time of the values of arguments on the right-hand sidea publicly owned power utility, which is a situation of equation (1).that occurs very often in the developing countries. Incontrast, the traditional system-planning approach is The economic costs suffered by electricity consu-more compatible with the financial or accounting view- mers due to electric power shortages may be representedpoint of a private utility. Finally, the model permits as a geographically localized function of the targetoptimization of an interconnected system at various reliability level, forecast demand, and reliability ex-levels of aggregation ranging from the global, e.g., in pectafion:terms of system-wide generation reliability, to the oC- oCi (Rt D R*) (2)specific, e.g., in terms of distribution reliability jt jt it' it' jtfor small geographic areas.

Power system supply costs, incurred as a consequence of

Before developing the optimizing mod2 l, we further providing electricity services, may be written:examine the question of simultaneous price and relia- i = i ibility (or equivalently, capacity) level optimization SCL SCt(R (3)mentioned above, because it is important from the the-oretical poirit of view. In fact, the issue of optimal It is assumed that if the system planners need to con-levels of capacity and electric power system reliabll- sider several alternative designi associated with anyity has received attention recently as part of the more single reliability configuration Ri, them in this case,general economic literature concerning public utility they would select the plan with the lowest present dis-pricing under conditions of uncertainty (stochastic de- counted value (PDV) of total costs (see below for amand and supply) (1l)-(13). Such studies indicate that, definition of PDV) The supply costs described inideally, both price and reliability should be jointly equation (3) correspond to such least cost system de-optimized to achieve maximum net social welfare. How- signs, where appropriate. SCi should include the capi-ever, as stated earlier, we recognize that electricity tal and operating expenses as well as the kW and thetariffs are often not readily subject to change. Thus kWh losses in the system, appropriately valued (at tnefrom a practical point of view, it is appropriate to marginal cost of supply), but net of the marginal sup-attempt to "optimize" reliability in the presence of ply costs of kWh not delivered due to outages. The ar-fixed or given tariffs, at least on the first round. guments on the right-hand side of equation (3) indicateMoreover, as discussed earlier, this method of optimiz- that because power system investments are lumpy, in gen-ing reliability (given the tariff level) can be used in eral, the supply cost in any given time period could being relrabilitie fhivn the tariff optiml)zeanbe re biiy associated with several components of reliability andan iterative fashion to Jointly optimize reliability demand, spanning many geographic areas and time periods.and tariffs.

BASIC SYSTEM OPTIMIZING MODEL A simple expression for the netbenefit of electric-ity consumption (in present discounted value terms),

We begin by formulating the hierarchical model of associated with system expansion plan i, is:an electric power system required to serve a large re- T Ngion consisting of N smaller geographic areas, over a NB = E EZ [(TB jt-OC jt) -SC tM(l+r) (4)long interval of time, which itself may be divided into t=o J=i'r distinct periods. Consider M alternative long-run where TB = TB (D ) is the total benefit of elec-investment plans (i.e., expansion paths), arising from jt jt jtdifferent power system lesigns prepared by the system tricity consumption in the absence of outages, and r isplanners. Let the set R which characterizes the glo- the appropriate discount rate. Because of the longbal reliability level for the whole region, and is as- lifetime of some investments, the discounting time hor-sociated with the i th power system expansion plan, be izon T is usually chosen to be greater than the plan-defined as: ning time horizon Z , to eliminate end-effects. For

R = R 1 = ,i..lN; t = lt,.,r ; for i =M; the period r to T, TB and OCit may be held cons .int,it while only,operating aA maintenance costs are inrtuded

where the superscript i and the subscripts j and t as- in the SCt stream. Since the lifetime of some systemsociated with the variable R, denote values of that var- components could even exceed T, it may be necessary toiable corresponding to system expansion plan i, in geo- deduct the residual depreciated value of such itemsgraphic area J, and during time period t, respectively. from the cost stream, in the final year T; the largeThe same convention regarding notation, will be used discount factor will minimize the effect of this cor-throughout this paper. rection.

Generally in any given area J, there are limits to Now, consider the case where system expansion plar.the variation of the reliability level in a4jacint time i + 1 is derived from plan i by a small physical chang,eperiods, and furthermore, the values taken y R t over in the latter. At one extreme, a change in the genera-time will be inter-related, because of the lumpiness of tion expansion plan may alter the reliability levwlpower aystem investments. globally, in all the geographic areas served by the

power system, whereas at the other extreme, a modifica-Next, the set representing global demand for elec- tion in local distribution system design would affect

tricity services is defined by; only the reliability level in a single area. Using

D D J 1,.. ,N; = D1 . , t ; equations (1) to (4), the resultant change in net bene-- t fit is given by:

Each component of demand is a function of othervariables and may be written:

1201

i i 1 tion (6) yields:

N ANB1 - jAocCi - lASCi! (7)t J r_- (TB -0 oc).AD -2oCi it iD t it jt jt.AR4 t Therefore, in order to maximize the net economic bene-

iR t fits of supplying electricity to society, the reliabil-t ity level should be iacreased as long as the corres-

Ai i ponding decrease in incremental outage costs exceeds2) SC R 2)SCt - t .AD] / (l+r)t (5) the increase in incremental supply costs, and vice ver-i AD sa, Equivalently, since the total benefit TB is as-aR sumed to be Independent of reliability R, the net bene-

i R+l i fit NB is maximized when the present discounted valuewhereARjt - R+t Rjit, A Djt D D AR t and so o. of the sum of outage costs and supply costs is minimized.

i R i OUTAGE SIMULATIONS AND OPTIMUM RELIABILITY LEVELSRit

The respective terms (a Sci . ARi) and (asci . AD), In this section, the characteristics of the modelt and the methodology are further explored (see also Fig-a Ri aD ure 1) by simplifying the theoretical model. First,

the measure of reliability R, which was introduced ear-are not strict mathematical vector expressions; they lier ina rather abstract way, will be defined more pre-symbolically represent the partial change in supply cisely. Second, ways of meaningfully aggregating varia-costs associated with changes in the set of reliability bles such as R, OC and SC will be developed, after theylevels alone, i.e., holding demand constant; and the have been estimated at the disaggregate level. One spe-partial change in supply costs due to the variations in cific reliability measure could be written:the set of demand levels, induced by the changes in the i i icorresponding set of reliability levels. The secondary R t a (ft , d t); where f and d are the mean fre-impact on demand and outage cost due to a change in thereliability expectation, which is itself induced by the quency and duration of outages, respectively. However,change in the reliability level, could be considered as for the exposition of the model it is more convenient tobeing already included in derivatives of the form: use the simpler measure: R t - 1 - (OE i / TE i) wherea D aOc i jt jt jt-it and aOt OE is the electric energy not supplied because of out-

aRi R i ages, and TE is the total energy that would have beenjt ajt supplied, if there had been no outages. The abovemeasure is analogous to the loss-of-energy-expectationEquation (5) may be greatly streamlined by assum- (LOEE) criterion used in generation system planning.ing that a Dit = 0, at least to first approximation so

i For a given plan i, and area J, the local reliabil-a Rity Rit may be plotted against time t. Figure 2 depicts

three such evolutionary paths of local reliability, forthat d jt0, and D=O also. On the basis of equa- a given demand forecast, starting from the existingtion (1), the above assumption has two implications. level a arnd extending over the planning horizon, i.e.,First, the direct impact of reliability level changes 0 to r . Each path corresponds to a system expansionon demand via the reliability expectation R* is negli- plan i which seeks to achieve the desired local reli-gible. Such a supposition is especially true when the ability level ai. In general, the paths will vary a-range of variation in R being considered is relatively bout the target ialues because of capital indivisibili-small. Furthermore, in purely practical terms, the ties (or lumpiness). A similar figure may be plottedproblems of estimating such direct feedback affects of for each of the N geographic areas served by the powerreliability on predicted demand are likely to far out- system. Furthermoie, by appropriately specifying theweigh any resulting advantages from the small refine- i TEment in the numerical results. Second, the indirect scalar index: Rt O- E it E TE/t ;i isimpact of reliability level changes on demand due to possible to graphically depict the evAlution of globalany associated price change is also ignored. However, reliability for the whole system over time (i.e., Ri).both these assumptions may be modified later, by iter- tating through the model on subsequent rounds, as dis- icussed later in this chapter. 1RtA

On the basis of the foregoing discussion, a sim- 3plified form of equation (5) can be written: < X tA NBi ,- AOCi - Asci (6)a

where AOCi= x E E( oc0 * R. i )/(l+r) ,and \t i it

a Ri

it

tj

In order to interpret equation (6), it is assumedthat thth clLu Erom system expansion plan i to plan 0Timei + 1 involves an overall unambiguous improvement inreliability, i.e., that each component of Ri is non-negative. iIn general, this implies correspondingly Figure 2. Evolution of the reliability levelthat A OC < 0 and ASC' >. 0. In this case, equa- along alternative expansion paths.

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The impact of the global reliability level on the indices which not only characterize future system per-present value of outage and supply costs may be sum- formance in a satisfactory manner, but are also mean-marized by the following scalar measures: ingful at the consumer level, and could be easily used

to determine the costs of shortages incurred by users.t = 1t l From this viewpoint, load-point indices of the frequen-r cy and duration type, referred to individual consumers

OCi = 2 t/(lr)t; on a disaggregate basis, would be the most convenienti j it measures to use, e.g., R t (fi , d; ). In particular,it jt ijtSC' E SCO/(,+0r)t , and the impact of operating criteria on system reliability

t should be considered wherever possible.

total costs: TC;L - 0 + SCi Generally, the more disaggregate and complete the

The model developed in the previous section indicates information regarding thereliability indices, the great-that the optimum expansion path is is the one in which er would be the accuracy of the corresponding estimatesTCi is minimized. It should be re-emphasized that prior of outage costs. For example, since outage costs areto the stmplifying aggregations described above, values generally a non-linear function of outage duration,of R, OC and SC are assumed to have been estimated at a ideally, the probability distributionof£outage durationvery disaggregate level, tor example, by starting uith should be computed. However, in practise, a knowledgevalues of the underlying frequencies and durations of of the mean duration at specific times, may be guffic-outages. ient, e.g., during the periods of peak, shoulder, and

off-peak demand. Such a procedure would improve theA typical set of results might appear as shown by accuracy of the outage cost estimates in two ways:

the solid curve in Figure 3. Starting with the low first, because outage duration could vary by time-of-reliability run t1, increasing the overall reliability day, depending on the load, availability of repairlevel results in decreasing social costs TC, down to crews, etk , and therefore, the actual values of dura-a minimum at IRm, beyond which further improvements in tion would bemore tightly clustered around the expectedreliability are not justified, because marginal costs value, if the day was sub-divided into smaller periodsexceed marginal betefitss of time; and second, since even the costs associated

with an outage of fixed duration would tend to vary byIn this formulation, the reliability measure is time-of-day. On the other hand, given the many other

definee in a very generalized way. Therefore, the sources of error in the estimation of outage costs, itselectlon of the optimum system plan and the associated would be difficult to justify devoting a great deal ofreliability level is made on the basis of economic effort to estimating probability density functions ofcost-benefit analysis., and is quite independent of the outage duration.actual index of reliability. However, from a practical It should also be noted that because of the largepoint of view, it is important to develop reliability number of variations possible, especially at the dis-

TC \/

SN

;> oc

SS

cn

035 c

C;I I I

.) \I I, , II >

Global Reliability Index

Figure 3. Outage Costs (OC), System Costs (SC), and Total Costs (TC), plottedagainst the global reliability index

1203tribution level, each global alternative expansion path new sets of price and expected reliability levels oni is likely to have a unique set of indices R asso- the demand forecast and outage cost estimates, mayciated with it. On the other hand, more than one such be determined, by iterating through the model again.path may correspond to a single value of the global in- In general, this reiteration would shift the whole totaldex Ri, which is a highly aggregate sca3ar quantity. cost curve as shown by broken line (TC') in Figure 3,In light of the points discussed above, two slightly leading to a new optimum plan m'. In this fashion, thedifferent conceptual interpretations o6T the method of direct and indirect feedback effects of reliability onoptimization, are possible.. From the fist viewpoint, demand may be considered iteratively, until the optimumeach lgng-range system design and corresponding index set of self-consistent price, demand and reliabilityset R may be considered as a strictly distinct one. levels was determined (see feedback loop in Figure 1).Therefore, the system planner designs several such al-ternative expansion paths which span a sufficiently However, the implementation of such an iterativewide spectrum of reliability levels, and then directly procedure would require agreat deal ofadditional infor-determines the optimum one which has the minimum value mation such as the probable evolution of pricing policy,of the sum of outage and supply costs. the elasticities of demand with respect to price for

various types of electricity consumers, the effects ofIn the other approach, the optimization procedure changing outage expectation on outage costs, and so on.may be broken down into two stages. Initially, several Therefore, although the simultaneous optimization ofspecific levels of the global, scalar Index Gt. (falling price and reliability is theoretically satisfying, inwithin a suitable range) would be selected, and the al- practise only a single iteration through the model isternative systems would be designed so as to be tightly likely to be attempted, assuming exogeneously fixedclustered around these reliability values. For example, prices and demand.if there are m target reliability levels, as well as abundle of n different system plans associated with each ESTIMATION OF OUTAGE COSTSlevel, then a total of (m x n) alternative expansionpaths would have to be considered. In any particular Electric power supply shortages manifest themselvesbundle or cluster, the global supply costs (SCi) icould in various ways, ranging from power surges, frequencyvary quite widely, but the total outage costs (OC ) are variations and voltage level drops (brownouts), tM loadassumed to be very similar. The first stage of this shedding and outright interruptions of supply (black-approach essentially consists of choosing the cheapest outs). All these effects impose certain economic costsalternative system design from each bundle; this tech- on consumers, of which the most important and also thenique closely parallels the conventional system plan- simplest to identify are the costs of interruptions.ning process. In the next stage, these m least-cost The term "outage costs" is used here to encompass allalternatives would be compared, to determine the opti- the economic costs suffered by society when the supplymum long-range system expansion plan, which minimized of electricity is not perfectly reliable, or when itthe total social costs (TCi). is not expected to be perfectly reliable, except where

the context indicates otherwise. Such costs can beThe first viewpoint discussed above is theoretic- labeled as either direct or indirect outage costs, re-ally more correct because no assumption is required, spectively, according to whether they are incurred be-regarding the equality of values of OC' for different cause an outage actually takes place, or simply becauseexpansion plans in the same cluster. However, the an outage is expected to occur. For example, duringsecond approach follows more naturally from the pro- an outage, direct outage costs are likely to bc incurr:edcedure used in traditional system expansion planning. since normal productive activity is disrupted. In con-In practice, the two interpretations would tend to trast, indirect outage costs are incurred in the ab-merge; since the system designing process is discrete, sence of an outage itself, because consumers may adapti.e., it does not move from one path to the next in a their behavior patterns to some expected reliabilitysmooth or continuous manner, and time constraints pre- level in ways that are less efficient, or more costly,vent simulation of too many alternative system designs, but less susceptible to outage disruptions; or, theyengineering judgment must be often relied upon to cut may purchase alternative (standby) sources of energy.down on the number of least-tost expansion paths to Although indirect outage costs cannot be attributed tobe considered. By choosing sensible paths for the in- any particular outage, they depend on the general leveldex Ri which do not intersect, and along which Rt of reliability, and represent real resource costs whichvaries reasonably smoothly, it is possible to avoid should be considered, when attempting to estimate thesituations where paths with lower values of Ri would economic costs associated with alternative reliabilitybe associated with higher expenditures (SCi). Because levels. Generally, direct outage costs are relatedof the possibility of such variations, it would be more to the short-term impact of unexpected outagesbetter to speak in terms of a target band of optimum whereas indirect outage costs arise from longer-termreliability levels around dOi, rather than a unique considerations of outage expectation, including thevalue. effects of planned power cuts.

In conclusion, consider the situation where the Within the economics literature there are twostream of system supply costs SCm associated with the schools of thought concerning how outage costs shouldoptimum expansion plan i = m, on the first round, be estimated. One approach is to estimate these costsnecessitate significant changes in the assumptions re- on the basis of observed (or estimated) willingness-garding the evolution of prices, which were themselves to-pay for planned electricity consumption (11), (12).used to determine the initial demand forecast. For The other approach, which is the one used here, esti-example, the use of a marginal cost pricing rule, or mates such costs in terms of the effect of outniges onsome simple financial requirement such as an adequate the production of various goods and services (6),(8),rate of return on fixed assets, may require previously (13), (14).unforeseen changes in future electricity tariffs, tocompensate for the new supply costs. Such a shift in The main shortcoming of the first approach is thatprices would directly affect load growth. Furthermore, observed willingness-to-pay for planned electricitythe new target reliability levels implied by the first consumption is not qn accurate indicator of what oneround optimum expansion path i = m, may themselves would be willing-to-pay to avoid an unplanned outage.affect reliability expectation, and thus have a secon- Such an unplanned outage is apt to disrupt activitiesdary impact on demand and outage costs (see equations which are complementary with electricity consumption,(1) and (2)). In such a situation, the impact of the and therefore, actual outage costs may be greatly in

1204

excess of observed (long-run) willingness-to-pay, following variations in primary distribution capacity:(a) High reliability system: Under normal conditions,

Therefore, it would be more appropriate to measure the system will have sufficient capacity to deliveroutage costs in terms of the effects of outages on var- power at peak load within the American National Stand-ious kinds of productive activity. When an outage dis- ards Institute (ANSI) favorable voltage range (i.e.,rupts production, the net benefits derived from such ac- 114 to 126 volts at the service inlet). Under emergen-tivities are reduced, i.e., direct outage costs are in- cies, the system will have sufficient capacity and in-curred, because the costs of inputs are increased, or ter-connections between circuits to pick up the load ofthe value of outputs is reduced. Specifically, an out- a faulted circuit at peak load and deliver power with-age can cause raw materials, intermediate products, or in the.ANSI tolerable voltage range (i.e., 110 to 127final outputs to spoil, and it can also result in pro- volts at the service inlet).ductive factors being made idle. The spoilage effect (b) Medium reliability system: Undernormalconditions,leads to an opportunity cost equal to the value of the the system will have sufficient capacity to deliverfinal product not being made available as a result of power at peak load within the ANSI favorable voltagethe outage, minus the value of additit&.l inputs not range. Interconnections between circuits are providedused because the final product was not produced. How- which will permit the picking up of loads from a fault-ever, if the value of the output is not easily deter- ed circuited under of-peak loading conditions, andmined, as in the case of household and public sector delivery of power within the ANSI tolerable voltageoutputs which are not directly sold on the market, then range. Two variations, A and B, of the medium relia-it is necessary to use the cost of producing the spoiled bility system would be considered.product or output, as a minimum estimate of the result- (c) Low reliability system: Under normal conditions,ing cost of the outage. When productive factors are the system will have sufficient capacity to deliver pow-made idle because of an outage, an opportunity cost er at peak load within the ANSI tolerable voltage range.results in terms of foregone output, the magnitude of No interconnections will be provided for this system.which depends on the nature of the production process,and the producer's decision whether or not to make up Outage statisticri and load duration data for Casca-any of the resulting lost output by working overtime. vel were analyzed to determine the future frequency and

duration of outages fi the three alternative distribu-CASE STUDY tion systems. Only permanent outages greater than about

5 minutes which are significantly affected by the basicA case study involving the optimization of the system designwere conisidered. For the high reliability

long-range distributior, system plan in a developing system, the outage duration iS the time it takes for acountry city, was used to empirically test and validate trouble lineman to locate the fault, switch loads andthe new approach described above. The principal tools isolate the faulted section. For the low reliabilityby which the methodology was implemented, consisted of system, the outage duration is the time it takes to lo-3 computerized models that were specifically used to cate and repair the damage. The medium reliabilitydetermine: Ci) the demand forecast; (ii) the alternative system is a mixture of the low and high reliabilitydistribution designs; and (iii) the outage costs and systems: during peak conditions, consumers must awaitsystem costs. The analysis was characterized by the switching and repairs, but during off-peak, they onlyhigh level of disaggregation required for distribution have to await switching. Past outage statistics forsystem planning. Twenty-four categories of consumers 1975-76 and analysis of load characteristics permittedwere identified: 4 residential income classes, 10 in- future outage frequencies and durations to be forec,stdustrial sectors, 3 commercial categories (including by city cell. For each system design, the system costsgovernment offices), 5 types of public illumination, and the energy and power losses were also determined.hospitals and schools. The city was overlaid with arectangular grid which divided u3 the urban area into For residential consumers, during an outage, elec-247 distinct cells (0.5 x 0.5 km ), and the planning tricity-dependent housekeeping chores could be effec-time horizon spanned a 21 year period (1976-1996). The tively rescheduled without much inconvenience, andtechnical and engineering considerations by which the cooking activity was not disrupted since it is done al-supply side costs were determined are summarized below most entirely by gas in Cascavel. However, leisure(4), (15). activities were significantly affected by outages since

the enjoyment of leisure in most households was con-First, a demand forecast was made assuming a con- strained to occur over a realatively fixed period ofstant future real price level, disaggregatedbyconsumer time in the evening, especially for wage earners, andcategory, by geographic cell, and by year, over the plan the use of electricity could be considered essential toperiod. For each consumer type, electricity consumption the enjoyment of certain leisure actlvities (e.g., TVwas correlated with one or more other explanatory vari- watching, reading, dining, etc.) during these nightables which were relativei; easy to predict. For resi- time hours.dential consumers, a non-linear relationship betweenkWh use and household inco,me was used together with the The results of a surve, of residential consumersprojected growth of the population and income, to fore- and an analysis of their outage costs confirmed the re-cast electricity consumption. In each industrial sec- sult of a detailed theoretical model presented elsewheretor, the future load was based on the value added per (14), and showed that: (i) the chief impact of unex-kWh, and projected growth of value added. Similarly, pected outages on electricity-using households was thethe key relationships for commercial users, hospitals loss of a critical 90 minute period of leisure, duringand schools were kWh consumption per unit area of floor the evening hours when electricitywas considered essen-space, per hospital bed, and per student respectively. tial, whereas domestic activities whichwere interruptedThese loads were allocated among the different geograph- during the daytime, could be rescheduled with relative-ic cells, for the plan period, starting with the exist- ly little inconvenience; and (ii) over this 1-1/2 hourting pattern of consumers in 1976 available from the period, the monetary value of lost leisure could bebilling records of the local electric utility company, measured in terms of the net wage or income earningand using the Cascavel long-rangeurbandevelopment plan rate of affected households, as confirmed by theirand zoning regulations to determine the future distri- short-term willingn.ss-to-pay to avoid outages. Esti-bution of demand. mated redidential outage costs were in the range of

US$1.30 - 1.70 per kWh lost or not consumed due to out-Initially, three alternative distribution systems ages, The principal advantage of this method for esti-were designed for meeting future demand, based on the mating the leisure costs of outages to residential con-

sumers was its reliance on relatively easy-to-obtain ting work to contivue by Fiu lth,nt. Fu: !e,nnore, there

income data. was sufficient slact .i.rrin, lie no^ 1a lhours of work

for jobs delayed by .any outage to be made up. Super-

Ingeneral, Industrial consumerssuffer outage costs markets and hotels roported minor amounts of spoilage

because materials and productq are spoiled, and normal for long outages, i.e., over Fivte hours; however, such

production cannot take place; the disrupted production outages are extremetv xaro. Rural consumers in the

results in an opportunity cost in the form of idle cap- vicinity of t.-a o 1 could 1ho '-. since their

ital and labor, both during the outage and any restart energy consumption was lena than 2'. of thLe total), through-

period foll.'twing the outage. It there is slack capa- out the plan period.

city, some of the lost value added may be recovered byusing this productive capacity more intensively during The residential an" iTnduastrial ..-- itogories incurred

normal worlking hours. In addition, the firm may operate the highest losses. The . bo b.hneftit comparison of the

overtime to make up lost production. Based on these outage costs and tiv.ntor. costs for Cascavel indicated

considerations, a survey of the 20 principal irdustrial that as global reliability inproved, outagv costs de-

users of elertricitv in Cascavel was made to determine creased fairly steadil,v whereas sttpply costs were

outage costs for outages of various durations (i.e., 1 practically constant: until a critical level of reli-

minute to 5 hours). The results of the analysis indi- ability was reached, afbtr whiih these costs increased

cated that there were wide variations in the effects of sharply (see Table 1 and Figure 3). The outage cost

outages on industrial consumers, e.g., US$1 - 6 per kWh results disaggregated by cell and by consumer category

lost, depending on the type of industry, the duration indicated that the high populat.iotn density areas in the

of the outage, and the time of day during which it occur- city center, and the indimtrial area suffered the high-

red. This approach was helpful to rank industries in est outage costs. lhoreforo several additional mixed

terms of sensitivity to outages, e.g., for emergency z hybrid network e;i.. ...on plans 4, 5, and 6, were

load shedding purposes. designed, based on the principle of providing the high-

est reliability service to areas with the highest out-

An outa-;e which affecrs public illumination imposes age costs, and so Onl 'A-i; feedback procedure yielded

a cost in the form of foregone community benefits such the best ;!S-tF-r {-x1 'in-4o plan 4, in which the city

as security, improved motoring safety, etc, One can ar- center area witli pop;,11t:>ion density, and the

gue that these foregone bcunefits are worth at least as main industrial zone, receivedcl hiigh reliability service

much as the net supply cost which the community would while other areas of the citv were served at medium B

have incurred for public illumination during the outage reliability levol. The ruwic' of P,lobal optimal relia-

per'.ods, e.g., the annuitized value of capital equip- bility levels was '. R > R > [.9982.

merc and routine maintenance expenditures: electricity

costs are not included since they are not incurred dur- The effects e- the new optimum reliability levels,

ing nutages. Two ihospitals (80 beds and 200 beds) were on the demand forecast and outage costs, via the price

surveyed to estimate the opportunity costs of both pro- and reliability expEctation foedhack loops shown in

ductive factors which were made idle (e.g., electricity Figure 1, were not investiFat-d, because of lack of in-

using equipment, labor etc.) and intermediate products, formationonhow the nriv.nal prices and expected relia-

such as blood and medicines, which might spoil because bility levels should be revised. ffo%jever, the results

of outages. The principal outage costs were found to were found to be relatively insensitive to an arbitrary

occur during the night period (i.e., 1900-0600 hours), 10.: change in the diemand forecast. A range of discount

due to idle labor and capital. The average cost was rates between 10% and 1;" were used, but these changes

estimated to be about USc 5.5 per hospital bed per hour also did not have much impact on the results. Finally,

of outage. Estimating the outage costs resulting from t e results were hardly affected by variations of the

possible loss of life is a task exceeding the scope of ^.-adow wage rate in the range 0.8 to 1.0 times the nom-

this study, and therefore, such costs are not consider- inal wage rate.

ed here. The existence of stand-by batteries for the CONCLUSIONS

intensive care and surgical equipment suggests that

death will be avo-lded in most cases; the cost of these One principel conclusion of this paper is that

batteries is very small. the long-range crnpanoion plan of a power system may be

optimized in terms of rellabilitv, by using the econo-

Outage costs for government offices and commercial mic criterion for svstem plarnning, in which the sum of

customers were found to be minimal, because in most both outage and system costs Is minimized. The theore-

cases reliance on electricity using equipment such as tical methodology presentel herewas validated by appli-

calculators and xerox machines was small, thus permit- cation to the case of a tvpical urban distribution sys-

Table 1: Global Characteristics of tl.e Alternative Dirtribut.ion yfitem Plans 1/

Outage Cost: Supply Cost Total C ost:OC+ Outage Cost/kWh

S§ystem Plan Reliability:a .(106 US$ SC (106 UI$) SC (1 LI$) Lost:OCK(USS/kWh)

Basic Designs

1 (Low Rel.) 0.9935 12.01 4.60 16.61 1.12

2A (Med. Rel. A) 0.9969 6.18 4.68 I1.86 1.19

2B (Med. Rel. B) 0.9981 3.96 4.62 8.58 1.26

3 (High Rel.) 0.9988 2.27 6.15 h;4 1.18

Hybrid Designs

4 (M,ed.flHigh Rel.) 0.9982 3.56 4.79 8.35 1.17

5 (Med./High Rel.) 0.9983 3.54 5.22 8,7P8 1.29

6 (Med./High Rel.) 0.9984 3.1 5 5.39 8.54 1.19

1/ Present discounted values of quantities over the period 1976-2006, as defined in the text; discount rate.'12%

tem. The same basic approach could be easily used to 7. M. Webb, "The Determination of Reserve Generatingoptimize a total system plan, i.e., at the generation Capacity Criteria in Electricity Supply," Appliedand transmission level as well. One of the main prac- Economics, March 1977, pp. 19-31.tical requirements would be to develop meaningful load 8. M. Munasinghe and M. Gellerson, "Economic Criteriapoint indices, especially of generation and transmission for Optimizing Power System Reliability Levels,"reliability, which incorporate the effects of operating The Bell Journal of Economics, Spring 1979.procedures and constraints into the long-term reliabil- 9. R. L. Sullivan, Power System Planning, McGraw-Hillity models. Fine-tuning the new procedure permits the International Book Co., New York, 1977.level of distribution reliability to be varied by small 10. M. Munasinghe and J. Warford, "Shadow Pricing andareas, to yield a better optimum. This approach 'ndi- Power Tariff Policy," Marginal Costing and Pricingcates that the optimum reliability level will tend to of Electricity, State of the Art Conference onbe higher for areas in which outage costs are greater Marginal Cost Pricing, Montreal, April-May, 1978.and therefore, on the basis of fairness alone, electri- 11?. R. Sherman and M. Visscher, "Second Best Pricingcity tariffs should also behigher in such neighborhoods. with Stochastic Demand," American Economic Review,March 1978, pp. 41-53.

Because of the wide variation in electricity con.- 12. M. A. Crew and P. R, Kleindorfer, "Reliability andsumption patterns, power system characteristics, etc., Public Utility Pricing," American Economic Review,in different countries, the results of the case study March 1978, pp. 31-40.cannot be easily extrapolated to a worldwide scale. 13. R. Turvey and D. Anderson, Electricity Economics,However, for purely indicative purposes, we may make use Johns Hopkins Press, Baltimore, 1977, Chapter 14.of the fact that the net saving due to system optimiza- 14. M. Munasinghe, "The Leisure Cost of Electric Powertion discussed earlier, is about 5% of the estimated Failures," World Bank Staff Working Paper No. 285,total distribution system investment costs, or approxi- The World Bank, June 1978.mately 0.4% of the total value added in the urban area, 15. M. Munasinghe and W. Scott, "Long Range Distribu-during the study period, In this case study, the main tion System Planning Based on Optimum Economicsaving arises from reduced system costs, because the Reliability Levels," Paper No. A78576-1, Proc. IEEEexisting reliability level is too high. But in other PES Summer Meeting, Los Angeles, July 1978.instances the net saving may arise from a large decreasein OC, accompanied by a modest increase in SC, to raise ACKNOWLEDGEMENTSthe reliability above the existing level. Whether thesavings arise from either an increase or decrease in the The author is grateful to Walter Scott and the staffprevailing reliability levels, even if half the percen- of Compania ParanaensedeEnergia Eletrica for their as-tage values of the case study were taken, ona conserva- sistance in carrying out the engineering aspects of thetive basis, the net potential savings in the electric case study, and to Mark Gellerson for helping with thepower sectors of the capital scarce developing countries economic analysis of outage costs. The contributions ofalone, would amount to about (constant 1978) US$450 mil- Monica Scott and David Teitelbaum in computer program-lion per year, during the next decade. ming are also acknowledged. This work was carried out

as a part of World Bank research study No. RES 670-67.Further work needs to be done, in refining the The views expressed are those of the author and not nec-conceptual framework for measuring outage costs, and essarily those of the World Bank.improving the methods of estimation. In particular, therelationship between outage expectation and adaptationof consumer behavior must be investigated in the con-text of indirect versus direct outage costs, and long- Mohan Munasinghe was born in Co-versus short-run effects. The impact of various pric- lombo, Sri Lanka in 1945. Heing policies on optimum reliability levels, via the - received the B.A. Honors anddemand forecast, should also be examined. In order to M.A. degrees in Engineering fromfurther test and strengthen the new methodology, more I Cambridge University, England incase studies are required, which would cover various -, 1967, the S.M. and E.E. degreesaspects of system planning, e.g., generation and trans- ' in Solid State Physics from themission, in anumber of different countries, each having Massachusetts Institute of Tech-a different mix of consumers, as well as varied socio- < nology, Cambridge, MA, in 1969,economic and physical conditions. Ethe Ph.D. degree in Electrical

e i ad pEngineering from McGill Univer-sity, Montreal, Canada in 1973,REFERENCESa and the M.A. Jegree in Economicsfrom Concordia University, Mon-1. "Twenty-Ninth Electrical Industry Forecast," Elec- treal, Canada in 1975.trical World, September 15, 1978, pp. 61-76.

2. E. A. Moore, "Electricity Supply Forecasts for the During 1969-1970, Dr. Munasinghe was with the SriDeveloping Countries," "Energy, Water and Telecom- Lanka Insmtitute of Scientific and Industrial Research,municatior.s Department, The World Bank, Washington, and also Visiting Lecturer, Electrical Engineering De-DC, December 1978. partment, University of Sri Lanka. From 1972 to 1975,3. A. D. Patton and A. K. Ayoub, "Reliability Evalua- he was a Research Associate and Consultant at the In-tion," System Engineering for Power: Status and ternational Institute of Quantitative Economics, Mont-Prospects, NTIS No. CONF-750867, USERDA Conference, real, Canada. Since 1975, he has worked as an econo-Henniker, New Hampshire, August 1975, pp. 275-289. mist-engineer in the Energy, Water and Telecommunica-4. M. Munasinghe, The Economics of Power System Relia- tions Departmient, World Bank, Washington, DC, He is alsobility and Planning, The Johns Hopkins Press, Balt- Visiting Professor, Economics Department, American Uni-imore, 1979. versity, Washington, DC, and Vice President and Director,5. R. B. Shipley, A. D. Patton and J. S. Denison, "Power Canifex International Socio-Economic Development Centre,Reliability Cost vs. Worth," IEEE Tr., Power App. & Montreal, Canada. He is the author of over 30 technicalSyst., Vol. PAS-91, Sept./Oct. 1972, pp. 2204-2212. papers inJournals of Physics, Electrical Engineering and6. M. L. Telson, "The Economics of Alternative Levels Economics, and abook, "The Economics of Power System Re-of Reliability for Electricity Generation Systems," liability and Planning: Theory and Case Study."Bell Journal of Economics, Autumn 1975, pp. 679-694.

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