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INDUSTRY AND ENERGY DEPARTMIENT WORKING PAPERENERGY SERIES PAPER No. 17

Incorporating Risk and Uncertaintyin Power System Planning

June 1989

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The World Bank Industry and Energy Department, PPR

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Incorporating

Risk and Uncertainty in Power System Planning

by

Enrique 0. Crousillat

June 1989

Copyright (c) 1989The World Bank1818 H Street, N.W.Washington, D.C. 20433U.S.A.

This report is one of a series issued by the Industry and Energy Departmentfor the information and guidance of Bank staff. The report may not bepublished or quoted as representing the views of the Bank Group, nor does theBank group accept responsibility for its accuracy or completeness.

Abstract

Power system plcnners face the challenge of determining the type andtiming of major investments under conditions of great uncertainty inpredicting the future trends in the major planning parameters such as exchangerates. Failure to match reasonably closely the power development program withthe actual least-cost expansion program for meeting demand imposes asubstantial cost penalty on the host economy which could disrupt theimplementation of macroeconomic policies for public investment, pricing,balance of payments and growth of the productive sectors.

It has been documented by a recent study done on the Bank's lendingfor power between 1965 and 1985 that, over the past two decades, mostcountries have failed in forecasting implementation schedules, investmentcosts and sales - all factors that affect significantly the economic viabilityof a project or program and may also impact on the finances of powerutilities and the public sector as a whole. This recent experience revealshow unpredictable the power sector can be and hence, the importance of theuncertainty problem in investment decisions.

The Energy Development Division of the PPR Industry and EnergyDepartment has therefore initiated a study, with Regional assistance, aimed atresearching the risk and uncertainty field and developing an appropriatemethodology for power system planning.

A main underlying assumption of the research project is that thetraditional deterministic approach to power planning leads towards inflexibleleast-cost programs which, taking advantage of economies of scale, typicallyinclude large generating plants and particularly large hydroplants - whenhydropower is an important resource - in spite of their inherent higher riskscompared to other alternatives. Furthermore, this approach does notexplicitly evaluate the risks of failure to achieve macroeconomic objectivesand the consequences of sub-optimal power investments. Although suchconstraints do not invalidate the basic principle of least-cost long termprogramming, they do cast doubt on the present methodology and call forimprovements to the treatment or risk and uncertainty in planning powerinvestments. A viable strategy for power system development should satisfythe overall objective of meeting power demand at least economic cost subjectto being consistent with a sound policy on risk management for the economy andthe power sector. This paper */ reports on she state of the art of riskanalytical techniques in power planning and the orn,oing work at the Bank.

*/ The present paper is an updated version of a paper presented in Tunis inlate 1988 during the UNDP-World Bank Seminar on Energy Planning forEuropean and Arab States.

Table of Contents

Page No.

1. INTRODUCTION . ............................................ 1

2. THE POWER PLANNING PROBLEM ........... *......* ............ 2

3. NATURE OF THE UNCERTAINTY PROBLEM ....... ..................... 3

4. CURRENT PRACTICES IN THE TREATMENT OF UNCERTAINTY ................. 6

5. POTENTIAL SOLUTIONS ..... .......................................... 8

6. CONCLUSIONS ........... ..... .... ... .. ... . 15

REFERENCES ................ *o.................... 16

ANNEX I ....................... ......... 27

List of Figures

1. Power Demand Forecast Experience - Deviation DistributionAfter Five Years ....... .......................... ....... . 17

2. Power Demand Forecast Experience - Deviation DistributionAfter Ten Years ............................ ... ........ .. 18

3. Electricity Consumption in 20 Largest LDCs . .1.............. il4. World Bank Oil Price Projections ............ .................. 205. Adjusted Cost Growth .......................................... 216. Distribution of Cost Overruns in Power Projects ............... 227. Schedule Slip ............ .* .............. ........... .. 238. Strategic Model: Tradeoff Example ............................ 249. Strategic Model: Illustration of Decision Sets ............... 2510. Strategic Model: Two Related Scenarios ....................... 26

INCORPORATING RISK AND UNCERTAINTY IN POWER SYSTEM PLANNING

1. INTRODUCTION

Over the last 15 years, the world has experienced an era of abruptchanges in energy prices and disruptions in economic growth. It has been aperiod of transition in which most developing countries had to adjust, or arestill adjusting, their en gy production and consumption patterns to reflect anew environment. Perhaps one of the most important changes has been thatduring this period, future events have proved to be more uncertain thanperceived before. Consequently, policy makers, managers and planners ofborrowing countries and development agencies, with the events of the last 15years in mind, are now more concerned about the long-term risks associatedwith current decisions.

In the power subsector, significant decisions are usually based onforecasts of major planning parameters such as power demand, capital costs,fuel prices and foreign exchange rates. These planning decisions are rarely,if ever, made with perfect information. Because of the uncertainties,elements of risk always surround these decisions, and the consequences of 'baddecisions' - those which lead to the failure to match the committed powerdevelopment program with the actual least-cost expansion program for meetingdemand - can sometimes be catastrophic. They can impose a substantial costpenalty on the host economy by disrupting the implementation of macroeconomicpolicies for public investment, pricing, balance of payments and growth of theproductive sectors.

Recent studies done by the World Bank (1989, 1988) have found thatover the past two decades, many developing countries have failed inforecasting implementation schedules, investment costs and sales - all factorsthat affect significantly the economic viability of a project and also impacton the finances of power utilities and the power sector as a whole.

The first reaction to this poor performance in forecasting the mainplanning parameters has been to invest in more sophisticated forecastingtools, while maintaining the essentially deterministic nature of the planningapproach (e.g. complex econometric models for power demand forecasts).However, these sometimes quite costly investments have so far proven to berelatively unproductive. For example, a survey on the forecast'ng experienceof 100 U.S. power utilities found that sophisticated models failed to providebetter results than the less sophisticated methods (Huss, 1985).

The issue is then that uncertainty is an unavoidable factor that hasto be addressed in the planning process. The need is to devise a planningprocess for dealing with uncertainty by developing strategies which minimizerisk, or do not lead to 'bad decisions', rather than strategies that focusexclusively on 'least-cost' solutions based on a deterministic - and henceoften times unrealistic - assumptions of future conditions and events. Thesestrategies, however, may require higher costs and therefore raise thefollowing question: how much should be paid to avoid, or reduce, the risks of

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incorrect planning? To analyze this problem, the World Bank ia undertaking aprogram designed to incorporate risk and uncertainty in power planning. Thepresent paper reports on the progress and findings to date of this program.

2. THE POWER PLANNING PROBLEM

Before addressing the problem of uncertainty in power development,its treatment and potential solutions, it may be convenient to review brieflysome basic concepts of the electric power system planning problem andmethodology. A more complete overview can be found in the final report of aWorld Bank study aimed to assess power expansion planning models (World Bank,1985).

The objective of expansion power planning studies is to determine asequence of capacity reinforcement in generation and transmission so as tomeet the future electricity demand complying with the following conditions:

- Lowest cost: it is sought to minimize the investment, operation andmaintenance costs.

- Reliability: to secure reliable supply of the load.

These requirements are to be achieved while meeting social,financial, political, geographical and environmental constraints. The powerplanning effort implies therefore the minimization of total costs plus theoptimization, or at least an adequate representation, of the power systemoperation (i.e. a sound simulation of the energy dispatch), while meeting anacceptable level of supply reliability.

In principle, the power planning problem is a typical exercise inoperations research which justifies the adoption of a systems approach. Thisapproach is necessary to assess both the expansion plan as a whole and, quitefrequently, the economic merit of any particular project 2J. Methodologiesfor addressing this problem were developed and refined largely during esixties and seventies, and are being used by most developing countries -These methodologies are fairly sophisticated since the overall optimizationproblem has the following characteristics (World Bank, 1985):

1/ Unless a particular project is "marginal" (e.g., a relatively smallexpansion project or rehabilitation program that will not impactsignificantly on the system's supply marginal costs), a simplifiedbenefit-cost analysis is not appropriate since it generally fails incapturing the project's impact on the system's operation, reliability andsubsequent investment decisions.

2/ IAEA's WASP generation planning model is probably the mo.Jt widely usedpower planning tool in developing countries.

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- Discrete decision variables: investments, maintenance and unitcommitment are "all-or-nothing" decisions (often times irreversible)that affect system capacity by indivisible amounts.

- Non-linear variations: load curve, thermal generation cost curvesand variation of hydro plant characteristics with reservoir levelare non-linear functions.

- Dynamic interactions: reservoir storage, capacity stock,availability of sites and economics of scale create strong linkagesbetween past and future decisions.

- Constraints: laws of physics and technical and economic limitationstranslate into mx7y equality and inequality constraints (although,in principle, reliability levels constitute a problem ofoptimization, they are usually treated as an additional constraint).

These characteristics, added to the problem size (large number ofdecision variables and constraints), determine that the optimization problemis hardly tractable without significant simplifications or a problembreakdown. The incorporation of random variables and uncertainty into thesealready complex models will therefore entail a major analytical challenge.

3. NATURE OF THE UNCERTAIhTY PROBLEM

Uncertainty means "not known with certainty', hence elements ofuncertainty are those upon which there is a lack of definite knowledge and canresult in the failure of achieving a sound development program. Risks are thechances of harm or losses to the investor (or consumer) inherent to decisionstaken within an uncertain environment. Thus, uncertainty refers to lack ofknowledge about future events and risk refers to the possible adverseconsequences of this uncertainty.

There are many different types of uncertainties. In some cases, theprobabilities of various outcomes can be derived from past observations (e.g.water availability when hydrological data is sufficient). However, in manycases uncertain future events are not related to well known historical data,but are rather events that are singular and do not repeat themselves. Inthese cases, any probabilistic prediction would be judgemental rather thanstatistical and would reflect the degree of confidence that an individual hasthat a particular event will occur (Raiffa, 1968). Uncertainties can differalso in regard to the amount of the variation (e.g. dispersion of forecastsdeviations), the magnitude of the risk associated, the frequency of risk (onetime or periodical risks), and whether the risks are limited to a particularproject or program, are correlated to other risks or are generic.

It is helpful to classify the uncertainties faced by power utilitiesinto two categories, namely external and internal factors, in order to designpossible measures for their management. External factors are those largelyoutside the control of the utility, while internal factors are those uponwhich the utility has at least a partial control. Table 1 displays the mostimportant factors of uncertainty, external and internal. In general, the

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degree of uncertainty related to internal factors can be reduced by moreefficient management in the implementation of projects and their operation.On the other hand, the only way to handle external factors is by incorporatingthese uncertainties in the planning process. This strategy will not reducethe degree of uncertainty, however it has the potential of reducingsubstantially the risks associated with investment decisions.

Table 1. Planning Uncertainties

Associated with external factors- Fuel prices- Economic and power demand growth- Inflation and interest rates- Exchange rates- Structure of relative energy prices- Structure of energy demand- Natural and cost of energy-use dependent facilities and equipment- Technological developments- Regulatory environment; tariff policy, financial incentives,

environmental regulations- Natural factors: hydrology, geological conditions, etc.

Associated with internal factors- Construction schedules- Operation and maintenance costs- Plant availability and output- Effectivenes3 of conservation and load management programs- System losses

The importance of the uncertainty problem in the power sector can beillustrated by comparing actual and forecast values for various keyparameters. The average, and in particular the distribution, of thesediscrepancies provide a measure of the risks associated with investmentdecisions based on a single deterministic view of the future. Several studiesevaluating World Bank financed power projects worldwide reached the followingresults (World Bank 1989, 1988, 1988a):

(a) Demand estimates

An ex-post evaluation of forecasts in 45 countries found that, ingeneral, forecasters have been too optimistic. Tt was found, on average,three forecast over-estimates for every under-estimate. Not surprisingly,forecast deviation and uncertainty increased with the forecast horizon.Demand estimates one year out from the time the forecasts were made show atypical deviation of +/- 5%, althot.gh some observed deviations were in therange of -20% to 75%. After five years, the deviations ranged from -10% to50% (Figure 1). After seven years, deviation increased to -50% to 100%, andafter 10 years the range was between -70% and 100% (Figure 2). In addition tothis increasing inaccuracy in demand forecasts, it was found tLat the degreeof correlation between electricity demand growth for subsequent time periodswas usually low, especially in developing countries with poor or declining

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economic performance (Figure 3). This last finding suggests that simpleextrapolations of past trends will fail to produce good forecasts.

(b) Oil prices

Track records of forecasting oil prices (the Bank's is shown inFigure 4 in constant prices) reveal that it has always been highlyunsuccessful in providing reliable predictions of price increases and declinesover the past 15 years. Due to cheir volatility, oil prices have become oneof the main sources of uncertainty in power planning. This uncertainty ismanifested in the great variations of forecasts undertaken (e.g. the range inestimates of future oil prices is much greater than that for coal prices) andthe magnitude of the associated risks. Technological choices based oninaccurate oil price forecasts can carry a high cost penalty to hosteconomies.

(c) Construction cost overruns

A recent study shows that, in nominal terms, the average costoverruns for about 40 hydroelectric projects was 40.7%, with isolated costoverruns of up to 200%. In real terms (constant values), the average overrunwas 9.3%, and the range of deviations observed ranged from -25% to 100%. Forall types of Bank power projects implemented during the period 1967-84, theaverage overruA in nominal terms was 19% (see Figures 5 and 6). In regard tothis sample, it was found that those projects approved before and completedafter the 1973 oil crisis were subject to the most serious cost overrunslargely due to the effects of unanticipated inflation.

(d) Implementation time

Adherence to project implementation schedule is a key measure ofproject performance. On average, power projects approved by the Bank between1967-1978 were estimated at appraisal to be completed in 46 months but actualaverage implementation time amounted to 66 months, an average delay of 20months (43%). For 41 hydroelectric projects the average delay was 30.4%, butwith a fairly uniform distribution from 0% to 100% (Figure 7).

These results on forecast performance of different planningparameters reveal two principal features. First, the average deviations are,for all variables, quite high and clearly biased in one direction. There isan optimistic bias reflected in the overestimation of demand growth and theunderestimation of costs and implementation time. Second and probably mostimportant, the great dispersion found in all variables indicates the degree ofuncertainty faced in making particular power sector investment decisions and,hence, the scope for misleading conclusions from the traditional de:erministicplanning techniques. It is also clear that the wide spread found in thedifferences between forecast and actual values is very seldom captared by theusually narrow margins for error adopted in sensitivity analysis.

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4. CURRENT PRACTICES IN THE TREATMENT OF UNCERTAINTY

Uncertainty can be handled in various ways. In practice, it issometimes ignored focussing on short-term strategies and assuming that long-term uncertain issues will resolve themse ves. There are however, variuusways of handling it directly, such as:

- Defer decisions: wait until additional information is available toreduce uncertainties, meanwhile purchase additional information toreduce uncertainty.

- Sell risks to other parties: conduct auctions for supply and demandresources, negotiate long-term fuel-supply and purchase-powercontracts. This, c' course carries the risk of foregone lowerprices in the future.

- Plan very carefully for all reasonabl- contingencies: co have aplan available for use if certain contingencies evolve; only usefulfor short-term commitments/plans.

- Adopt flexible strategies that allow for relatively easy andinexpensive changes.

All these strategies involve added costs. Utilities are thusconfronted with the problem of deciding how much is _ceptable to pay in orderto reduce risks? Decision-making under risk is best served when the bestavailable information is applied to the decision process. In this sense, asatisfactory planning tool should address this particulr- problem, i.e. thetrade-off between added cost and reduced risk. Although planners andresearchers are currently working on a number of new approaches, there is notyet a satisfactory and widely accepted tool to deal with the problem of riskand uncertainty in power planning.

In spite of the obvious need for address-ing the uncertainty problemin power planning, very little is being done, particularly in developingcountries, where deterministic least-cost models constitute the main, andsometimes only, planning tool. The objective of these models is to determinethe development program that will meet a forecast power demand at leasteconomic cost under a predicated set of assumptions for the planning,arameters. No consideration is given to an explicit evaluation ofdifferences in risk parameters between alternative investment sequences. Inpractice, the evaluation usually includes some sensitivity analysis only tcconfirm the robustness of the evaluation conclusion to arbitrary variations ina few planning parameters. However, this analysis is not made to change orimprove the development program, i.e. sensitivity analysis as applied impliesa descriptive approach instead of being prescriptive. Furthermore, in thecase of some of the parameters, the margin of variation examined has tended to

be much smaller than the ex-post difference between the actual trends and theoriginally forecast trends made at the time of investment appraisal. Suchshortcomings often disqualify the adopted development program from actuallybeing the 1 est cost means of meeting demand. The deterministic least-costapproach does not explicitly evaluate the risks of failure to achieve economicobjectives and the consequences of power investments being sub-optimal.Although such outcomes do not necessarily invalidate the basic principle of

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least-cost long term programming for power development, they do cast doubt onthe efficiency of the present methodology to achieve the basic least-lostobjective.

The traditional determ4 nistic approach, used by the World Bank andmany development agencies, often times results in leas:-cost programs which,taking advantage of economies of scale, typizally f.Rvor large generatingplants and particularly large hydroplants - when hydropower is a major energyresource - which inherently face greater economic, geological, hydrologicaland environmental uncertainties than other alternatives. These programs tendto be more risky than a power expansion based on smaller plants due to thefollowing reasons: (1) the selection of a small group of large plants resultsin a low diversification of investments, thus increasing overall risks; (2)large projects tend to have larger potential impacts; (3) large projects,particularly hydropower plants, reduce the flexibility of a program sincetheir long lead time decisions are hard to modify as external conditionschange; and (4) costs and energy supply of hydropower projects are moreuncertain due to their own geological and hydrologisal characteristics.Accordingly, inadequate consideration of uncertainty in the selection ofleast-cost power development programs often results in higher risks.

In industrialized countries, particularly in the U.S., many powerutility companies do not rely on least-t_.3st optimization models for systemplanning. This is partly due to the disappointments of the past and, partlybecause for many companies the choice is limited due to regulatory,environme,ntal and political considerations and the fact that demand is growingslowly 3'. A survey done on the planning practices of 14 US power utilitiesidentified the use of different techniques for dealing with uncertainty whichfit inco four major categories: scenario analysis, sensitivity analysis,portfolio analysis and probabilistic analysis (Hirst and Schweitzer, 1988).Table 2 provides a brief description of each of these methods.

In the U.S., many power utilities use at least one of these methodsfor their long-term planning, or a combination of two or more of them.

Most of the analytical techniques mentioned are applied, though notrrstricted, to supply policies. That is to say to the analysis of expansionpLans. There is however, a variety of demand-side policies which also cancontribute to meet future electricity demands. These policies, such as loadmanagement programs and conservation programs, are not widely applied indeveloping countries in spite of their potential cost effectiveness and theirinherent advantages over traditional supply programs in terms of uncertaintyreduction. The smaller size, shorter lead time, and opportunities to modifydemand-side programs during implementation are all factors which reduceuncertainty for utilities, however their implementation may sometimes beimpeded by institutional and other constraints.

3/ However, it is important to mention that deterministic least-costplanning is still being practiced in several industrialized countries,such as the U.K., France, Canada and Sweden.

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Table 2. Techniques Currently Used to Analyze Uncertainty.

Scenario analysis Alternative scenarios are first constructed andalternative plans are identified to meet each ofthese scenarios. Best alternative plans for eachscenario are then analyzed under o.her scenarios inorder to assess their performance (i.e. the risksinvolved) and also to identify those investmentdecisions that are appropriate under a large numberof scenarios.

Sensitivity analysis The preferred plan is identified for a most likelyscenario. Key factors (uncertain variables) are thenvaried to see how the plan responds to thesevariations.

Portfolio analysis Multiple plans are developed, each of which meetsdifferent objectives (economic, social,environmental). Often these plans are then subjectedto sensitivity analysis.

Probabilistic analysis Probabilities are assigned to different values of keyuncertain variables, and outcomes _ e obtainedthrough probabilistic simulation (e.g. Monte Carlotechniques). The result is an expected value andprobability distribution for key economic indicators.

5. POTENTIAL SOLUTIONS

The first stage of the Bank's analysis of the potential forincorporating risk and uncertainty in power planning consisted of a literaturereview of the existing techniques and the identification of suitableapproaches. Th, initial effort identified three different methods which, todiffering degrees, are potentially useful for assessing power projects underuncertainty (World Bank, 1989a). These are:

i) The use of a stochastic power planning optimization model which usesophisticated operational research techniques to internalize theuncertainty problem into these already complex - in a computationalsense - optimization models.

ii) The development of an informal strategic risk-tradeoff method whichaims to assess the robustness of different power expansion plans.

iii) The adaptation of finance valuation methods, particularly optionvalue methods, taking advantage of the existing .?nalogy betweenfinancial markets problems and project investment decisions.

The first two methods fit into the methodologica' categories ofstochastic programming and scenario analysis, respestively. Scenario analysishas been recently applied in the World Bank using simple conventionalmodels. Two interesting applications are IEN's studies on Thailand's EnergySector Investment (World Bank, 1988b) and a Power Planning Study for Congo(World Bank, 1989b).

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The following section includes a brief description of the threeidentified methods as presented at the S>minar on Risk and Uncertainty inPower Planning held by the World Bank in late 1988. In addition, a selectedannotated literature - extracted from the above mentioned review - is providedin Annex I.

Stochastic Optimization Model

This method considers the extension of the traditional capacityexpansion model of power planning based on a least-cost approach byincorporating uncertain (stochastic) variables (Bisthoven et.al., 1985).Thus, the idea is not to give up the existing approach because of uncertainty,but instead to accommodate it.

The method takes into account a set of scenarios and, instead ofanalyzing them successively (in the manner a traditional scenario approachwould), it directly takes all of them into account in the decision evaluationprocess. Technically, the method can also be seen as an extension of thestandard decision tree approach where the different branches - correspondingto different scenarios - bifurcate at the time when the uncertainty is assumedto be resolved. In practice, a few branches in the tree are generallysufficient to capture most of the effects of uncertainty. The key problem istherefore to structure scenarios into an event tree capturing the effects ofuncertainty while trying to minimize the optimization computational effort.Different scenarios are considered with associated discrete probabilities.

The model is usually formulated as a mathematical program tominimize total expansion and operating costs subject to demand and capacityconstraint . Solution techniques involve the application of decompositionmethods 4 . This model has been applied in industrialized countries onseveral energy planning problems with two or three uncertain variables.

The Search for Robust Solutions in Power Systems Expansion Plans:Strategic Risk-Tradeoff Model

This is a technique of trade-off analysis that compares multipleattributes of alternative solutions in order to identify those which are themost robust in the sense that they perform well in the greatest number oflikely scenarios (or with the greatest probability across the scenariospace). The following description of the method is taken from a presentationmade by Mr. Hyde Merrill in the above mentioned seminar.

4/ The "state-of-the-world decomposition approach" is a primal-dual methodthat solves the dynamic problem of power systems planning, i.e. theproblem of making decisions over an extended periou of time, using staticdeterministic solution techniques for specific sub-problems (e.g. energydispatch for an specific period). The main probLem (the dynamicoptimization problem) I.s decomposed into a set of linked staticdeterministic problems, where the linkages are enforced through Lagrangemultipliers. Each static problem represents one "state-of-the-world".Thus the method replaces a single complex problem with many simpleproblems.

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Definitions

A utility chooses from a set of options: build a new coal fired power plan,implement time of day rates, upgrade an interconnection, etc. Each option hasparameters (e.g., year or size or incentive) to be specified.

A plan is a set of specified options - for example, "publish residential timeof day rates in 1989, build a 600 MW coal plant in 1994, and add 350 MW oftransfer capability to the west in 1992."

Uncertainties are beyond the utility's foreknowledge or control; load growth,fuel prices, penetration of demand-side programs, etc. Each has parameters tobe specified like "3% per year" for load growth. Uncertainties can be modeledprobabilistically or as "unknown but bounded" variables without a probabilitystructure.

A scenario is a set of specified uncertainties, for example: "3%/year loadgrowth and 15/year real oil price increase."

Attributes are measures of the goodness of a plan. These measures may includerevenue requirements (total or by ratepayer class), fuel mix, reliability ofservice, financial burden (e.g., capital requirements), and environmentalimpacts. Attributes are functions of options and uncertainties. The plannerwants to minimize or maximize each attribute.

The consideration of alternatives in the process of power systemplanning involves setting up input uncertainties describing the states of theworld considered relevant for the planning process, and testing how optionswould perform in that context. This would yield tradeoffs in the attributespace. An example of this is shown in Figure 8, that shows the tradeoffbetween two attributes: reserve deficiency in MW-years and present value ofrevenue requirements. Each star in this figure shows a plan. The figure alsoillustrates the process whereby a decision set can be arrived at A decisionset consists of those plans which are not completely dominated" by others.In Figure 8, the plans that belong to the decision set are linked together bya line. It is obvious that there are no other plans which would be betterthan those on the decision set regarding the attributes shown. Hence, all ofthose outside the decision set can be dropped from future consideration.

Figure 9 shows how the knee set is defined. The knee set consistsof those plans which are at the limit of the areas of diminishing returns forthe attributes. For instance, in order to obtain a higher degree ofreliability, much higher costs are required, as shown in the group of optionswhere the system is overbuilt. Alternatively, reductions in present worth ofrevenue requirements beyond those obtained in the knee set could only beobtained at the cost of unacceptably high levels of unreliability.

5/ A plan dominates another if it is better with respect to all attributes.

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Uncertainty can be considered explicitly in this type of tradeoffanalysis by setting up a system of scenarios, which would cover the entireevent space by discrediting the relevant probability distribu:- 's if theanalysis is carried out probabilistically, or the region uc.ween theboundaries of possible values, if probabilities are not assigned. Figure 10shows how the decision set and its knee can be found in two related scenarios,in this case showing the present worth of revenue requirements versus the SO2emissions for 22 coal conversion plant. . Under one scenario a 1% per yearload growth is assumed, and under the other load declines at 1% per year.

As can be seen in the figure a number of the same plans belong tothe knee set regardless of the scenario chosen. This example serves toillustrate a special point, namely that it does not matter whether or not aparticular indicator (such as present worth of revenue requirements) issensitive to a particular uncertainty. What really matters is whether or notthe 4ecision to be taken is sensitive to the uncertainty. In the case of thefigure, all other things being equal, it is possible that the same projectwould be chosen regardless of the scenarios that were to prevail.

The example of Figure 10 is helpful in defining the notion ofrobustness. A plan is robust if it is in the conditional decision set forevery scenario. In other words, if regardless of the scenario assumed toprevail the plan were included in the decision set. When the analysis of thescenarios is carried out probabilistically it can be said that a plan isrobust with probability P if with probability P scenarios will occur for whichthe plan is in the conditional decision set. On the other hand, an option isconsidered flexible if its specified values are part of conditional decisionset plans for every scenario.

An advantage of the system proposed is that by examining thecharacteristics of the options which appear in certain scenarios, it might bepossible to construct hedges, i.e. to adjust the best options in order toreduce their risks. By combining the best features of various options orplans, new ones may be found that could be more robust.

No special software is required to use the approach described forthe search of robust solutions. A software package called RISKMIN (Bhavarajuet.al., 1987) is available to help, however, and one of its chief benefits isthat it can create additional options without the need for calculating themexplicitly. The procedure for finding robust plans is therefore as follows:

(1) Identify options, uncertainties and attributes.(2) Develop a data base using existing expansion planning software.(3) Identify critical and non-critical uncertainties.(4) Find decision sets and measure robustness.(5) Measure exposure, identify hazards and hedges.(6) Do additional simulations, step 2, and go to step 4.

This method has been applied by several U.S. power utilities.

As can be seen, this method was not developed to deal only with theproblem of uncertainty but to examine also the multiple (and oftenconflicting) objectives found in power planning. This implies a broaderapproach to power planning which provides very valuable information into thedecision making process allowing, for example, an explicit comparison of

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economic and environmental objectives. However, the application of thisapproach should be done with special caution since it may open the door forthe introduction of spurious non-economic factors into the decision process.

Finance Valuation Methods

Two finance valuation methods are considered potentially useful forincorporating risk in power planning models. These are: (1) risk-adjusteddiscount rates, and (2) option pricing methods.

A basic principle of corporate finance is that one should not paymore for an investment project than the price of a portfolio of securitiesoffering returns of comparable risk and scale. This principle is embodied inthe "Net Present Value" rule, in which one discounts the expected cash flowsof investment projects at a risk-adjusted rate. Net present value is ameasure of profitability. If the decision maker is choosing among mutuallyexclusive investments, then the project with the largest net present valuesshould be selected, since it is the most profitable.

It is essential to the use of the risk-adjusted discount rate methodthat the discount rate be the expected rate of return on assets of the samerisk. Here, the relevant risk is the systematic risk associated with theinvestment,-defining systematic risk as that which is correlated with the riskof all other assets or, more generally, with aggregate consumption.

In power system planning, cost minimization has traditionally beenthe objective, under the assumption that all alternative generation plans meeta common demand and thus provide the same benefits. The net present valueprinciple can nevertheless be applied, because if all benefits are the same,minimizing cost also maximizes value. Different cost streams have to bediscounted at different rates depending on their riskiness. For instance,fixed costs (with zero covariance with aggregate demand) should have a lowerdiscount rate, hence a higher present value than comparable costs which arepositively correlated with the returns of other assets; and should have ahigher discount rate t1an comparable costs negatively correlated with thereturns of other assets.- However, this risk adjustment on the discount rateis only valid under special circumstances where the degree of riskiness isexponentially distributed over time.

When costs will be determined by a series of decisions the directionof which depends on some uncertain economic factor, it can be very difficultto estimate expected cost or an appropriate risk-adjusted discount rate. Forsuch problems, the methods of option pricing are useful. Option theory cameout of the finance literature (Black and Scholes, 1973) and has proven to be

6/ This seemingly counter intuitive result can be clarified as follows: acost which is higher when all other assets are providing high returns andlower when the returns are low is easier to bear than cne which isinvariant; on the other hand, a cost which is higher when all otherassets are providing low returns and vice versa is more difficult tobear.

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useful for a broad range of problems involving contingent decisions. Thistheo,ry shows that the value of an option can be obtained from stock prices andthe cost of borrowing by replicating the payoffs to an option with acombination of stocks and borrowing. Flexibility in power system alternativesis often analogous to the flexibility in exercising a stock option. Forinstance, in addition to the investment cost of a particular power plant,there is an opportunity cost of exercising the option to invest in this plantresulting from the loss of flexibility as other expansion plans - presumablyless risky under certain scenarios - are no longer possible. For example, itmay be better to delay plant installation until avoided cost (i.e. the cost ofthe alternative plan) exceeds the investment cost by a margin greater than theopportunity cost of exercising the option to invest.

Option pricing methods can be used to measure the opportunity costof exercising an option to invest and hence develop decision rules fordetermining how big a margin is required to justify installation. In general,the greater the uncertainty associated with the project the larger this marginshould be. Thus, option pricing methods provide a way to value flexibility, adifficult task when using other approaches.

Option pricing methods have some limitations at their present stateof development. One concern is the computational difficulty of handling morethan one risk factor. Another limitation is the fact that it addresses onlyone type of decision problem, e.g. the time to build a specific project.

Preliminary Evaluation of Alternative Methods

The following preliminary evaluation is based on operationallyoriented criteria considering the following aspects:

(a) Modelling Capability. The models' ability to capture the possibleconsequences of multiple uncertainties inherent to alternativeinvestment plans. The importance of this attribute depends on thecomplexity of the decision problem at hand. Hence, simple modelscould be more appropriate when facing simple decision problems.

(b) Transparenc rid Contribution to Decision Making. The method shouldbe readily u. .erstood by decision makers. The criteria for judgingalternatives should be easy to understand and the consequences ofdiffering judgemental inputs should be reviewed without excessiveeffort.

(c) Practical Applicability. The method should be amenable for use bypower planners without excp-sive time inputs for the transitionprocess, training and appl:....A.on. A low cost practical decisiontool should be preferred.

Although the criteria considered is admittedly subjective, the exercise isuseful because it brings into focus important considerations of the powerplanning practice and the incorporation of risk analysis.

A summary of this evaluation is shown in Table 3. The comparison ofthese techniques is itself a multiattribute problem with three criteria.However, none of the techniques clearly dominates the others.

- 14 -

While the stochastic optimization model is quite promising in termsof its modelling capability, it provides poorer information compared tostrategic planning since it does not make explicit the trade-off betweenhigher cost and reduced risk. The risk-tradeoff model appears to be a veryuseful technique since it is simple, lacks the computational sophistication ofstochastic optimization, and is understandable and addresses directly thetrade-off problem. However, its power relies on the planner's skills forformulating the problem and capturing the dynamic characteristic inherent tothe expansion of power systems. Both methods have been applied with successin industrialized countries, though there has been no practical experience indeveloping countries.

The option valuation model has not been applied to analyze theexpansion of complex power systems. Its limited modelling capability -apparently restricted to one investment decision and one uncertain variable -would constrain its application to small and simple power systems whereinvestment choices are limited to two or three alternative technologies.However, its strength relies in its theoretical appeal and the fact that thedata base and the computational effort required for its application are farless demanding than in more complex traditional decision models. Whetherthese advantages are offset by a lack of modelling capability is a questionthat needs to be tackled at the empirical level.

Table 3 Summary of the Evaluation

StochastingOptimization Risk-Tradeoff Option Pricing

Modelling Capability Captures dynamics of Skills in formulation Handles only one

decision problem. Can of scenarios investment decisionhandle several determines capability and one uncertain

uncertain variables. of modelling dynamic variable. OtherOther attributes are decision problems, attributes are

assessed externally. Can handle several assessed externally.

uncertain variablesand attributes.

Contribution to Provides optimized Provides explicit Measures value of

Decision Making solution. No explicit information on trade- flexibility comparing

data on trade-offs, offs between two alternative plans.unless compared to attributes and risk-

deterministic cost. Allowsapproach. improvement of

strategies.

Practical Training in problem Data on non-economic Training in options

Applicability modelling. attributes. method is required.

Substantial Support of Low cost application.standard planning

models is required.Training in risk-

tradeoff softwarecould be required.

- 15 -

6. CONCLUSIONS

Power system planners face the challenge of determining the type andtiming of major investments under conditions of great uncertainty inpredicting the future trends of major planning parameters such as powerdemand, capital costs and international fuel prices. Failure to matchreasonably closely the ex ante selected development program wiith the ex postmost desirable least-cost expansion program for meeting demand can impose asubstantial cost penalty on the host economy, whLch could disrupt theimplementation of macroeconomic policies for public investment, pricing,balance of payments and growth of the productive sectors.

The traditional deterministic approaches to power planning followedin developing countries fail in addressing the significant differences in theuncertainties attached to alternative projects and often-times lead towardsinflexible least-cost programs which typically include large generating plantsin spite of their inherently higher risks compared to other alternatives.Furthermore, this approach does not explicitly evaluate the risks of failureto achieve economic objectives and the consequences of sub-optimal powerinvestments. Although such constraints do not invalidate the basic principleof least-cost long term programming, they do cast doubt on the presentmethodology and call for improvements to the treatment and explicit evaluationof differential risk in planning power investments.

In industrialized countries, many power utilities do not rely onleast-cost optimization models for system planning. Instead, a certain numberof alternative plans are compared using scenario analysis and other methodsfor assessing the robustness of these plans. Although the application of thesemethods implies substantial progress in the treatment of uncertainty, it iswidely recognized that much more remains to be accomplished.

Three promising methods have been identified for addressing risk anduncertainty in power planning. These are (a) a stochastic optimization powerplanning model; (b) an strategic risk-tradeoff model for assessing therobustness of power expansion plans; and (c) the adaptation of financevaluation methods. Nevertheless, a preliminary comparative evaluation ofthese methods does not provide an adequate basis for identifying any one ofthem as clearly superior over the others. There is therefore the need ofapplying these methods in case studies in order to test them foreffectiveness, acceptability and policy implications.

A useful analytical tool for addressing the uncertainty problemshould emphasize simplicity of use and be able to simulate the decisionprocess itself, i.e. the effects of frequent decision making and thepossibility of modifying decisions over time. When dealing with risk anduncertainty, there is always a trade-off between risk and cost. A soundmethodology should therefore provide clear and meaningful informationregarding the risk associated with a particular decision and the abovementioned trade-offs, preferably in an explicit manner, as alternative plansare compared. The decision criteria may vary according to the type ofinformation at hand. However, the final choice of this criteria will alwaysreflect the decision maker's subjective preferences regarding risk avoidance.

- 16 -

REFERENCES

Bhavaraju, M.P., Chamberlain, T.C. and Nour, N.E., 1987. An Approach toRisk Evaluation in Electric Resource Planning, Research Report 2537-1,2. Public Service Electric and Gas Company, prepared for EPRI, December.

Bisthoven, O.J., Schuchewytsch, P. and Smeers, Y., 1985. "Dealing withUncertain Demand in Power Generation Planning", from Energy Markets inthe Long-Term: Planning Under Uncertainty. S. Kydes and D.M. Geraghty(editors), Elsevier Science Publishers, B.V. IMACs.

Black, F. and Scholes, M, 1973. "The Pricing of Options and CorporateLiabilities, "Journal of Political Economy, May.

Hirst, E and Schweitzer, M., 1988. Uncertainty in Long-Term ResourcePlanning for Electric Utilities, Oak Ridge National Laboratory. Draftreport, October.

Huss, William, 1985. "Can Electric Utilities Improve Their ForecastAccuracy? The Historical Perspective",, Public Utilities Fortnightly.December 26.

*Raiffa, Howard, 1968. Decision Analysis: Introductory Lectures onChoices Under Uncertainty. Addison-Wesley, Reading, MASS.

World Bank, 1989. A Review of World Bank Lending for Electric Power,Industry and Energy Department Working Paper. Energy Series Paper No. 2,March.

World Bank, 1989a. Preliminary Stage of a Research Program on ImprovedMethodology for Incorporating Risk and Uncertainty in Power SystemPlanning, Literature Review and Survey of Current Practices. Reportprepared by Information for Investment Decisions Inc., February.

World Bank, 1989b. Congo Power Development Study, Energy Efficiency andStrategy Unit.

World Bank, 1988. Review and Evaluation of Historic Load ForecastingExperience (1960-1985). Draft report prepared by RCG/Hagler Bailly,Inc., August.

World Bank, 1988a. Cost Growth and Schedule Slippage in World BankHydroelectric Projects. Preliminary draft prepared by IndependentProject Analysis Inc., June.

World Bank, 1986b. Thailand - Impact of Lower and Uncertain Oil Priceson Energy Sector Investments, Energy Efficiency and Strategy Unit.

World Bank, 1985. Assessment of Electric Power System Planning Models,Energy Department Paper No. 20, March.

FIGURE 1

POWER DEMAND FORECAST EXPERIENCEDeviation Distribution After Five Years

PERCENT (%)

35

30

25

20

15

10

5

0

-50 -20 -10 -5 0 5 10 20 50 100

Forecast Sales -Actual SalesDEVIATION X 100

Actual Sales

FIGURE 2

POWER DEMAND FORECAST EXPERIENCEDeviation Distribution After Ten Years

PERCENT (%)

35

30

25I-

20

15

10

5

0-50 -20 -10 -5 0 5 10 20 50 100

Forecast Sales -Actual SalesDEVIATION X 100

Actual Sales

- 19 -

FIGURE 3

ELECTRICITY CONSUMPTION IN 20 LARGEST LDCs

Distribution of Growth Variation

from period 1970-75 to 1975-80

._ 7

0 414

Z 2

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 %

from period 1975-80 to 1980-85

rn 7

6~

4.14

Z 2

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

FIGURE 4

WOIRLD BANK OIL IPRICE IPROJECTI'IONSIN CONSTANT 1987 US$ P'ER1 B3ARIREfLJ

100

90

80-

70- ~ ~ ~ ~~~ 960 PRO)JECTION192POCIN60-

(I)-- - *-~19114 jimJECriON

50 -

4-ACTUAL PRICES

30 -

20 - - - - - -1986 PROJECITION

1978 PRIOJECTION 198 ROJECTION10

0

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992o 1994 1996 19911 12000

YEAR

FIGURE 5

Adjusted Cost Growth39 Hlydroelectric Projects

Ratio of Actual to Appraisal Estimate InConstant US$

Percent of ProjectXs30

25

20

15

10

5~~~~~~ ~ ~ ~ .*..

0

< 0.75 0.75 - 0.99 1.00 - 1.24 1.25 - 1.49 1.50 2o00

Range of Cost GrowthMean 1.093Median = 1.023Stondard Deviation = 0.316 IPA. ltc.

FIGURE 6

DISTRIBUTION OF COST OVERRUNS IN POWER PROJECTS

PERCENT (%)

35

30

25 -

20

15

1o

5

0-60 -40 -20 0 20 40 60 80 100 120 140 %

Average = 19%p .

FIGURE 7

Schedule Slip41 hlydroelectric PIrojeCtsRatio of Actual to Appraisal Estinrate

Percent of Projects30

25

20

i5 -.

10

5

0

~.00 .9 1 1.'20 .1 30 -. 5 1.60 -. 2.00

Range of Schedule SlipMean 1.304Median = 1.214Standard Deviation = 0.273 IPA. Inc.

- 24 -

FIGURE 6

Strategic Model: Tradeoff Example

1750 *

_ 0

- ~~~~~~~*-_

*

1500 +RESERVE -

DEFICIENCy(XW-YEARS) *

_ 0 *0

1250 +

_ I * *

1000 + - 0

_- - 0= s. * 0

0.750 +

e e + e...-- -- --- -- -- -- - -- -- ----- ---… --

1600 1750 1900 2050 2200 2350REVENUE REQUtREMENTS t$ MILLtONS)

Sum of annual reserve deficiencies (CI below reserveobligation versus present worch of revenue requiremenrs,20 year horizon.

- 25 -

FIGURE 9

Strategic Model: Illustration of Decision Sets

System isRISK OF ,,--w<Unaccepcab1Y

RISK OF UnreliableINSUFFICIENTGENERATINGCAPACITY TRADE OFF CURVE SET(e.g., LOLP)

KNEE SET

Best Risk/Cost_ / I~radeoff

System is_ Overbuilt

PRESENT WORTH OFREVENUE REQUIREYENTS

- 26 -

FIGURE 10

Strategic Model: TWQ Related Scenarios

44{ 1 { r | | r g X | I [ I g |~~~~~~~ * a S r r. I r r as. W

$9 *(10 )

42 ~\\

I, 1

40 ~0 I..| 2t 1% loadh//r . growth

_ -1% load growth

cA §~~~~~ I t L I t I I I " t I l I L I I I I t I

o ICc IScO 2X0 2500 3000 35c0 4000

GRA/ S ECOND

Present worth of revenue requirements versus SO, for 22 coal

conversion plans

- 27 -

ANNEX I

ANNOTATED BIBLIOGRAPHY

Introduction

This annex reviews articles found in the literatureof OperationsResearch,Systems Engineering,Economics and Finance.It is organized as follows: Section A presents the stochastic optimization approach, Section B presents the ideas derivingfrom the options analysis literature, Section C reports on what we have called the search for robustness and presentsrecent work completed at EPRI, and Section D includes a selected biliography.

A.Stochastic Optimization Approach

Stochasticoptimization techniques attack the problem of decisions under uncertaintysquarely by modelling the existinguncertainty and choosing the strategy which is optimal in the light of that uncertainty. Although the articles reviewedin this Section usually do not explicitly include this feature, it is conceptually possible to specify utility functions andhave the stochastic optimization method find the optimal strategy taking into account a given degree of risk aversion.

The major problem of stochastic optimization methods has been the computationalburden it imposes. The number ofcombinationsthat have to be examined in order to arrive at the global optimum increases exponentiallywith the numberof scenarios considered, the number of time periods and the number of capacity additions considered. For this reason,often drastic simplifications of reality need to be made to prevent the methods from absorbing inacceptable amountsof computer time. As shall be seen in the following reviews, however, progress has been made in decomposing largeproblems into combinations of smaller but equivalent problems, hence making the overall problem more tractable andexpanding the size of the problem that can be realistically solved.

A survey of the existing literature of er the last twenty years shows that uncertaintiesare often modeled using some formof decision tree. Various algorithmic approaches can be used to treat the problem numerically. Generalized Bendersdecompositionand related techniques are the most frequentlyused approach. Different variations of this basic techniquehave been used in all the recent papers.

Rcvicw of the analytical techniques used

Mathematical programming techniques have been proposed for electric utility capacity expansion problems as early asthe work of Masse and Gibrat (1957). The papers surveyed by Anderson (1972) were deterministicin nature and moreaccurate probabilistic approaches were proposed later. These include the state of the art Benders' methodology ofBloom (1983). Deterministic and probabilistic models usually refer to the way plant outages are modeled, althoughprobabilisticmodels can model other sources of uncertainty,such as hydrologyor total demand. In deterministicmodels,the plant capacities are multiplied by the expected availability factor to get the derated capacity. These are then usedin the production cost function. This simple technique produces biased results and does not guarantee a good solution.In the probabilistic model, each of the availability states is considered based on the (discrete) probability distributionof the plant outages. The solution is obtained by using a technique known as probabilistic simulation (see the sectionon Bender's decomposition below), developed by Baleriaux et.al(1967), Booth (1972) and also described by Vardi andAviltzhak(1981). This techniqueis computationallyburdensomeand Rau et.al.(1979)and Stremel and Rau (1979) haveproposed an approximating alternative known as the method of moments. Both these methods are used in the contextof Benders' decomposition for solving the subproblems that the main problem is decomposed into. The over/undermodel, first developed by Calazdet et.al.(1977) and later used by Sanghvi and Limaye (1979) focuses on the target reservemargin or the excess of total capacity over expected peak demand as the decision variable. Other papers, including the

- 28 -

one by Sanghvi et.al (1981) consider a range of uncertainties, but concentrate more on simulating the behavior ofproposed solutions, and not on explicit optimization. The state of the world approach by Borison et.al. (1983), usesa scenario approach to model demand and fuel price uncertainties.

Benders' decomposition technique

This approach models the optimization problem as a mathematical program, which has an objective function that hasto be minimized subject to constraints. The usual objective is to minimize costs, which are of two types: fixedinvestment costs and operating costs. The constraints are mainly of two types: the first type requiring that theprobability of demand not being met be less than some specified number at any given instant of time. This is knownas the reliability constraint. The second type of constraints requires that the level of operation at any instant of timebe less than the installed capacity.

Time is discretized and the planning horizon is divided into time instants 1,2,3,...,T. Some of the models haverefinements like including upper and lower bounds on capacity installation. Some of the models assume that caracityis available in any size whereas some others assume that capacity is available only in prespecified discrete sizes, whichrequire the use integer variables. In other models, the probabilistic reliability constraints are non-linear. The problemsthus posed cannot be solved by the standard linear programming simplex algorithm. Hence the need for an approachlike Bender's decomposition,under which the problem is decomposed into a 'master problem" and a set of subproblems,one for each time period. Each subproblem and its solution technique may be illustrated by the following example.

The objective is to minimize the operating costs during one of the time periods t, and the constraints are the same asthose for the original problem with two important differences: each subproblem for time period t has constraints forthat time period only and not for other time periods. Thus, the capacities are not variables as far as the subproblemis concerned but are known, fixed quantities. The planning problem is therefore decomposed into a set of subproblems,each representing the optimal operation of a set of generating plants of fixed capacity. The reason why the problemcan be decomposed into a set of subproblems is because of the structure of the constraints: the operating cost duringa time period depends only on the level of operation of each plant during that time period and not on other timeperiods.

The subproblems, which include non-linear probabilistic reliability constraints, are solved by using a technique calledprobabilistic simulation. In this technique, the load duration curve is first considered, which gives for any load level,the percentage of time that the load during that time period (which is typically of 1 year) exceeds that level. Next, theplants are ordered in a "merit order" in which the plant with the lowest operating cost is first in the order and the plantwith the highest operating cost is the lasL Using a mathematical procedure called convolution, the load duration curveis convolved with the outage distribution of each plant taken in merit order. This procedure gives for each plant thefraction of total demand served by it, and the so called equivalent load duration curve faced by each plant. Theprocedure also gives the expected unserved energy for that period. The associated fraction of time for which thisunserved energy prevails is called the loss of load probability. The solution of the subproblem gives the expectedunserved energy, the expected cost of operation and the dual multipliers for the subproblem. These dual multipliersare the value of adding an additional unit of capacity at each plant, and are fed back to the "master problem".

The master problem consists of finding an optimum set of investments for the entire planning horizon. Since this isdifficult to solve, almost all the constraints are dropped, and a "relaxed" version of the problem is solved using anystandard linear programming technique. A trial solution consisting of a set of capacities to be installed and the timeat which they are added is obtained. This is used by the subproblems which generate dual multipliers. These are fedback to the master problem. Using duality and polyhedral theory, the constraints of the master problem are writtenin terms of these dual variables. These constraints are checked one by one. As soon as a violated constraint has beenfound, it is included in the relaxed master problem. If none of the constraintsof the master problem is violated by thedual multipliers, an acc. ptable solution has been found. Otherwise, the master problem is solved again for a new trial

- 29 -

solution. This is used by the subproblems to generate new dual multipliers, which are fed back to the master problem,where constraint violations are again checked for. The procedure is repeated until a trial solulion that satisfies all theconstraints has been found.

This is a generic techniqueand has been used in all the optimizationapproaches. Slight variations in the model do notaffect its applicability. The basic idea of decomposition can always be used, provided the two sets of constraintsdescribed earlier are such that constraints for one time period do not affect constraints for another time period. Thedifferent papers vary mainly in two ways: the precise problem modelled, and the nature of special techniques used tomake the Benders' decomposition run faster. These differences do not significantly affect the relative merits of thepapers. Moreover, they have not been converted into commercial code and it is not possible, therefore, to say whichof them would perform better.

Review of articles surveyed

The papers reviewed in this section differ in two ways: the type of model used and the solution technique. These donot vary in a significantway and do not affect the essential solution technique. Some of the models specify that capacityis available only in certain prespecified sizes. In such models, slight modifications to the solution technique are madeto take care of the additional constraints. Other models include upper and lower bounds on the capacity installations.Some models include the option of using renewable energy resources like wind and solar energy. Models also differ onthe way plant outages are modeled. One approach is to use a reserve margin capacity to take care of demandfluctuations. Another approach is to use a constraint stating that the fraction of time over which the demand is notmet is less than some specified number, say, 1 day in ten years. Some models include uncertainties in demand growthrates and fuel prices, others only model the uncertaintydue to plant outages. In.all of them, Benders' decompositiontechnique is used to solve the problem. Which particular model is suitable depends on the particular situation.

There are minorvariationsin the solution techniqueas well. These are essentiallyimplementationdetails. For example,one of the methods uses a deterministicapproximationto the problem to get a good startingsolution and then arrivesat an optimum solution to the actual problem in fewer iterations. In any case the models have not been commerciallvdeveloped to the extent that a ready made package be available.

In the pages that follow we present brief reviews of the articles considered most relevant in the recent literature.

a. Models for Determining Least Cost Investments in Electric Supply, D. Anderson, The Bell Journal of Economics,Spring 1972.

This is one of the earliest papers on this subject. All the formulations presented in it are deterministic, Allowancesfor uncertainty in demand and plant availability are made in the form of spare capacity. But this does not vield leastcost solutions. Though this was an important addition to the literature at that time (1972), better models incorporatinguncertainty are now available.

Three approaches to solving the problem are presented. In the first method marginal analysis is used. An initialarbitrary but reasonable investment plan is proposed. Suppose the plan includes a thermal plant. The cost ofsubstituting this by a hydro plant is computed. If favorable, the hydro plant is included and the thermal plant dropped.This analysis is done for all alternatives. This approach is not practical, however, because of the number of requiredcomputations.

The second method uses simulation models. Here a 'merit order" rating of the available plants at any given time isobtained, in order of increasing operating costs. Plants are put into operation in their merit order to meet the demand.Thus lower cost plants are put into operation before higher cost plants. The problem with this approach is that it givesgood operating schedules but does not give an investment plan.

- 30 -

The third method uses straightforwardlinear programming. Speed up techniques like Benders' decompositionare notused.

In summary, the models proposed in this paper are deterministic and not suitable for the ptlrpose of the present study.The idea of merit order operation is used in the other papers, but faster implementation of the mathematical programsis done using Benders' decomposition.

b. Planning Electric Power Generation: A Non-linear Mixed Integer Model Employing Benders Decomposition, F.Noonan and R.J. Giglio, Management Science, May 1977

This is a fairly comprehensive model and incorporates uncertainty in demand and plant availability using sophisticatedconstraint equations. Uncertainties due to fuel price changes and those due to supply side variations have not beenconsidered. The general solution technique is the same as those used in the latest linear programmingbased methods,namely, Benders decomposition. An algorithm based on this paper was used as an aid to decision making in the NewEngland states.

c. Planning Future Electric Generation Capacity A.P. Sanghvi and D.R. Limaye, Energy Policy, June 1979.

This paper contains the over/under model and considers the trade off between over or under building capacity. Theobjective is to provide a decision simulation framework. The model is based on the supply and demand curves forelectricity. The average cost curve of electricity for a specified demand growth rate and expansion rate is determined.Different such supply cost curves are obtained for different demand growth rates. Next, a demand curve of cost versusdemand is determined from the expected demand growth rate and the demand elasticity. An equilibrium is the pointof intersection of the supply and demand curves. The model then analyses the situation at each point in time. In somecases there will be excessive capacity, i.e., more capacity than required has been built. In other cases there might notbe capacity, and the demand in the target may not be met. The costs of over and under building capacity are computedfor each time period and printed in the report. This information is used by the decision maker to choose an expansionplan. The model also has a provision for revising expansion plans in case actual demand growth rates become availableat a later date. The model was applied to the Pacific. Northwest region in the United States and concludes that thesocial cost of over building is lower than the social cost of under building.

d. Solving and Electricity Generating Capacity Expansion Planning Problem by Generalized Bender's Decomposition,J.A. Bloom, Operations Research, Jan-Feb 1983.

This paper provides the theoretical background to the method proposed by Sherali et. al. The problem considered hereis to determine a minimum cost capacity expansion plan which meets forecast demands for electricity over a long range(20 to 30 years) with a specified level of reliability. lwo types of costs are considered: the initial capital cost ofbuilding the generation plants and the continuing cost of operating the generating system to meet the demands ofcustomers. There are random load fluctuations and plant failures (outages). Hence it is not possible to guarantee thatcustomer demand will always be satisfied. The standard service is specified by probabilistic reliability measures.

The model assumes that the capacity costs increase linearly with size and that operating costs increase linearly withoutput. In reality, capacitycosts exhibit economies of scale, and operations have decreasingmarginai costs at low outputlevels and increasing marginal costs as output approaches capacity. However, these assumptions are commonly used inplanning models. The techniques used to relax these assumptions can be adapted from combinatorial or integerprogramming. They would quickly make the problem computationallyintractable, however.

The rapidly varying nature of demand is represented by a load duration function over a period of one year. This givesfor each level of load, the expected Dime during which the load exceeds that level. It is assumed that this is a continuousfunction. The only uncertainty considered is that due to plant failures (outages). A probabilistic simulation methodas proposed by Baleriaux et. al. and Booth is used. It is assumed that plant outages are independent of the load andof the failures of other plants. Using a convolution technique between the load duration curve and the outage rates

- 31 _

of various plants, they obtain an equivalent load duration curve. The reliability constraint is derived from this andspecifies that the expected unserved energy is less than some level, say, the number of MWh not served in that period.

The problem is decomposed into a set of subproblems, representing the operation of a set of plants of fixed capacityin one year, and a master problem representing optir-al capacity investments over the entire planning horizon. Themaster initially proposes a plan of investments. This is passed onto the first subproblem. The subproblem is solvedusing a procedure called probabilistic simulation. This gives the expected cost of operating the system, the reliabilityand the marginal costs (or dual multipliers) of the plant capacities. The master problem is a linear program that usesthese marginal costs to determine a new trial capacity plan. The problem as a whole is solved iteratively by alternatelysolving the master problem and the subproblems until an optimum is found.

Computational testing on this method has not been done. However it seems that without any speed up modificationslike the one proposed by Sherali et. al., it would be computationally burdensome. The main disadvantage is theconvolution process which has to be performed for various mixes for equipment.

e. A State of the World Decomposition Approach to Dynamics and Uncertainty in Electricity Utility GenerationPlanning, A.B. Borison, P.A. Morris and S.S. Oren, Operations Research, Sept-Oct 1984.

This paper addresses the problems created by uncertainty. This could be uncertainty in demand, fuel costs or fuelavailability, economic conditions or Government regulations. It takes into account what it calls "dynamics," or theproblem of making decisions over an extended period of time as opposed to a one time "static" problem. Thecombination of uncertainty and dynamics introduces an additional complication and makes the problem much moredifficult than the static, deterministic expansion problem.

There are many straightforward methods for solving the static deterministic expansion proble. .a, where the objective isto determine the technologypurchases that minimize the cost of providing energy under fixed conditions. However, sincethe dynamic probabilistic expansion problem is much more intractable, methods have focused on one of the followingas mnentioned earlier:

(1) look at only a small subset of purchase decisions

(2) address uncertainty in a Umited fashion

(3)generate solutions that are not truly optimal.

The state-of-the-world decomposition approach introduced here is a primal-dual method that solves the dynamicprobabilistic problem using static deterministic solution techniques. The main problem is decomposed into a set oflinked static deterministicproblems, where the linkages are enforced through Lagrange multipliers. Each static problemrepresents one "state of the world" or a time and outcome scenario, for example a low fuel price in 1990. The methodreplaces a single complex problem with many simple problems. Each of the simple problems are solved efficientlythrough a simple dynamic programming procedure.

The main value of the method is that it solves a difficult dynamic probabilistic problem using simple static deterministictechniques. The technique has been tested out on problems involving 5-15 states of the world, 10-20 existing units, and5-10 new technology types.

f. Dealing with Uncertain Demand in Power Generation Planning, O.J. Bisthoven, P. Schuchewytschaxtd Y. Smeers,Core Reprint No. 652, (1985), Center for Operations Research and Econometrics,Universite Catholiquede Louvain,Belgium.

This paper represents a good combination of linear programming techniques and statistical decision making. It alsoevaluates the option of waiting for more information, and postponing decision making till this information becomes

- 32 -

available. The model is formulated as a mathematical program and is solved by decomposition. It models uncertaintyin plant availability by a reliability function. The uncertainties in demand growth and fuel prices is modeled by ascenario approach. Different scenarios of demand growth rates and fuel prices are considered each with an associatedprobability. For example, a 2.7% growth rate with a low fuel price may have a probability of 30%. These scenariosare captured in a decision tree. The model is a mathematical program that is solved by the standard decompositiontechnique.

The example cited in the paper is illustrative. The basic issue is to decide on the pattern of investments in nuclear orcoal generation plants over 5 time periods or 12 time periods. Traditional analysis of the 5 period problem does notassociate probabilitieswith different scenarios. It recommends investing right away in large nuclear plants, having longlead times for completion. When probabilities are associated with the scenarios, the recommendation is to postponeinvestment for a time period and then invest in a series of smaller coal based plants. The example also illustrates theeffect of changing the planning horizon. With a longer time horizon, the size of investments goes up significantly, andthe recommendationis to go for nuclear plants after two time periods. The reason for this is that because the priceof fuel is rising, after a certain length of time the nuclear option becomes more attractive compared to the coal basedplants.

This model combinesdiscreteprobabilitiesof scenarioswith continuousplant capacities. It can includecostand demanduncertainties and it embeds the classical loss of load probability reliability constraints. In practical applications thecomputationalburden appeared to be acceptable.

g. An Integer Programming Approach and Implementation for an Electric Utility Capacity Planning Problem withRenewable Energy Sources, H.F. Sherali, Konstantin Stachus and J.M. Huacuz, Management Science, July 1987.

This paper considers the problem of an electric utility concerned with long range capacity expansion planning. Analgorithm is presented to solve problems faced by relatively small systems.(less than 5000MW). It considers uncertaintyin plant availability due to forced outages. A load duration function is used which gives, for each level of load, theexpected time during which the load exceeds that level. The model considers conventional energy sources like hydro-electricity, coal, oil, gas or nuclear energy, as well as renewable energy sources like wind or solar energy. It also takes

into account the fact that capacity is available in certain specified sizes.

Earlier methods like the probabilistic simulation method of Baleriaux et. al. (1967) cannot be used when we considerrenewable energy sources because of the statistical interdependencycreated by the weather between renewable energyproduction and the load. This is overcome by a simulation method in which the energy net of renewable energy isobtained. The alternative method proposed by Caramanis et. al. (1982), code named EGEAS, cannot be used in thiscase because the system is small.

The method proposed here is an improvement over Bloom's (1983) Generalized Bender's algorithm. The renewableenergy output is simulated or derived from historical data for every hour of the year, and is subtracted from the overallload on an hour by hour basis. The reSulting load curve net of renewable energy is thus obtained. This is used in aphase 1 deterministic model to get a (hopefully) near optimal solution. The deterministic model is relatively easy tosolve. In phase 2, the solution from phase 1 is used in order to obtain a faster convergence to the optimal solutionof the more accurate probabilistic model. The phase 2 method is similar to that of Bloom's Generalized Bender'sdecomposition. The computational innovation that this model offers is that fewer phase 2 Iterations are needed andit conserves nearly 80% of the effort needed compared to the method where phase 1 is not used.

Discount rates for money can be fixed as desired. Forced outage rates for the existing plants were obtained fromavailable data. Additional runs witih different outage rates can also be made. A growth rate in demand of 3% wasassumed, but any future demand pattern could be specified. Two types of reliability constraints were imposed. Oneis based on the policy of the utility that the purchased capacity be 20% more than the peak load. The second constraintis that the fraction of time for which load is not served (also called the loss of load probability) be less than somespecified amount, for example 3 days in 10 years.

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Computational results for the Tijuana-Mexicalisubsystem in Mexico are presented. The model has 5 existing plants and4 expansion options. A 20 year horizon is used. Two types of renewable options are considered: solar cooling systemsand conservation measures in the form of roof insulation and installation of storm doors anid windows. The level ofuncertainty is based entirely on the outage rates of the existing plants and has not been reported. The procedure took1400 cpu seconds on an IBM 3084 computer.

h. Optimi7ingResourceAcquisitionDecisionsby StochasticProgrAmming,D.B. Bienstockand J.F. Shapiro, ManagementScience, February 1988.

This paper addresses the strategic problem faced by an electric utility of acquiring resources or capacity over a long timehorizon. It looks at the benefits of acquiring these resources and at the uncertainties in the external environment. Themodel proposed considers uncertainties in demand, environmental restrictions and fuel costs. It also providescontingency plans to be put into effect as the uncertainties are revealed over time. The technique used is stochasticprogramming which combines deterministic mathematical programming with decision analysis models for determiningoptimal hedging strategies in an uncertain environment.

The model presented is an extension of an earlier model (Wagner, 1969). The model has two stages, and can beextended into many stages. At each stage we have uncertainty, in the sense that one of a given number of scenariosmay occur. Each scenario would reflect some combination of demand, fuel cost or environmental condition. Acontingency plan is proposed for each scenario. Generalized Bender's decomposition is used to solve the problem. A"fmaster" problem is constructed an a set of subproblems, one for each scenario. The master problem consists of thefirst stage constraints and the capacity expansion decisions for each stage. The subproblems consist of the operationalconstraints and variables for each scenario. These relate to the optimal operation of the system given a fixed capacityfor each plant. The master problem passes on a trial set of capacities to a subproblem. This is solved and the marginalcosts of the resources are passed back to the master problem. This is used to update the trial solution by the masterproblem, and a new set of capacities passed onto the next subproblem, which in turn passes back revised marginal coststo the master problem.

Revenue is assumed to increase linearly with output. Expansion of a facility is constrained to be within a certain range,for example between 100MW and I000MW. Long term contracts for fuel purchases are built into the model and is auseful feature. A computational study was carried out on a problem with 1 1 existing plants, and 5 expansion optionis.Non- conventional or renewable energy resources have not been considered. There are three scenarios for demandgrowth (1%, 2% or 3% per year) and two scenarios for environmentalstandards (due to sulphur emissions) at the endof the first stage. The model was implemented on a PRIME 800 computer using the LINDO package. A prior analysisof the subproblems was done before running the model. This yielded the bounds on the capacity needed for eachsubproblem and were fed into the master problem. Various arbitrary plant constructionstrategies were also consideredand input into the subproblems which in turn generated cuts for the master problem. This prior analysis significantlycut down on the running time and solutions within1% of optimality were reached in 5iterations. Explicit running timeswere not mentioned.

Advantagesof the model include modeling uncertaintiesin demand and fuel costs. but uncertaintydue to plant outageshave not been considered. Moreover demand in a given stage is assumed to be fixed whereas earlier models haverecognized randomn fluctuation within a period (of say 1 year). Renewable energy sources have not been considered.Supply contracts-for fuel acquisition have been explicitly considered and have been built into the plant constructiondecisions.

B. Options Analysis

Generally speaking, an option is the temporary or perpetual right to undertake a transaction for which the returns(costs) are fixed, while the costs (returns) are unknown in advance. In finance, where the option pricing theme was

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developed first, attention has focussed on puts and calls, i.e. eptions to sell or buy stock shares. In a broader context,there may exist options to trade assets, commodities or contracts, to invest in projects, to switch technologies, etc.

Option pricing techniques are designed to assess the ex-ante value which can be attached to the scope for more flexibledecision making, thus accounting for the possible losses related to a decision (say, to undertake an investment ; -oject)made within an uncertain environment. Options are a means of insuring against uncertainty. The central message ofoption pricing theory is that options can be used to create a riskless hedge, i.e. a portfolio that yields the same returnsas a riskfree asset (project). This only requires that the option is contingent on another l isky asset which, combinedwith a riskfree asset, mirrors the dynamics of the option, then the value of the option (relative to its "exercise price"and the actual price of the asset that replicates its dynamics) can be determined in terms of the equilibrium solutionto a portfolio choice problem. Standard option valuation formulas are fairly easy to apply. Several applications of theoption pricing model to investment decisions have been recently formulated.

Review of articles surveyed

a. Options, Flexibility and Investment Decisions, R.S. Pindyck, Workshop on New Methods for Project and ContractEvaluation, Center for Energy Policy Research, MIT

This article illustrates the application of the options approach to the problem of whether to invest in a large coal plant(high capital cost, but relatively low fuel cost) or a series of small oil based turbines (low capital cost but high operatingcosts). Traditional discounted cash flow analysis would recommend to undertake the coal plant project if its net presentvalue exceeds that of the turbines alternative. However, the option pricing method recommends to abstain frominvesting in the coal project taking into account, in addition, the opportunity cost of exercising the option to build thatplant, i.e. the resulting loss of flexibility as the alternative solution, presumably less risky, is no longer possible. Theexample considers fuel prices to oe the only uncertain variable assuming that they follow a random walk :.ound anexpected growth rate.

TMe example also analyzes the sensitivity of the decision to the degree of fuel price uncertainty,discount rate, coal plantsize, random behavior of fuel prices (a mean-revertingprocess) and the correlation between oil and coal prices (partiallycorrelated instead of perfectly correlated), always focussing on a single option with a single source of uncertainty.

The approach offers the advantages of requiring a limited data base and being very easy to handle computationally.However, these advantages strongly depend on the assumptions made regarding the stochastic process that drives thebehavior of the random variable, i.e. that the random variable is (log) normally distributed with a constant mean andvariance. Furthermore,its appeal also depends on the number of options or the number of uncertainvariables. In casethat the former assumption does not hold or that the problem at hand involves more than one option choice (or morethan one uncertain variable) the option valuation approach would no longer render a simple analytical solution thusloosing much of its elegance and tractability.

b. Tlme to Build, Option Value, and Investment Decisions, Saman Majd and R.S. Pindyck, Journal of Financial

Economics 18 (1987).

This paper uses the option pricing approach to derive optimal investment decision rules and to value such investments.It analyzes the effects of time to build, opportunity cost and uncertainty on the investment decision, showing that asimple deterministic net present value rule can be considerably misleading.

The specific problem addressed here is the one faced by a firm before investing in a major project like the constructionof a new underground mine or the development of a large petrochemical plant. Investment decisions and associatedcash outlays occur sequentially over time. There are constraints on the rate of construction and on the outlays, and itis often the case that the project yields no return until it is completed. The paper considers a project that costs S6million and'has a maximum investment rate of $1 million per year. Such a project is viewed as a "compound option":

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each unit investment gives us an option to invest in the next unit. Evaluating the project requires a decision rule thatdetermineswhether an additional dollar should be spent given a cumulative amount already spent. This decision ruleis formulated as a standard option pricing model which relates the value of the project to the expected return, the timefactor and the opportunity cpst of delaying the completion. The assumptions regarding the stochastic process of therandom variable are the same as those mentioned for the previous paper; hence, the above mentioned limitations applyas well.

The interaction between the various elements in the formulated model may be described as follows. As expected, whenuncertainty related to the value of the project increases, the critical value of the project (cutoff value below which itis not attractive to invest) also increases. The interaction between the project value, maximum rate of investment andthe opportunity cost of delaying completion is rather complicated. For high maximum investment rates, cutoff valuesare lower (thus making the project more attractive) becoming even lower if the opportunity cost of capital is higher.However, as maximum investment rate decreases (i.e. for projects where the minimum time to build is long), the cutoffvalue increases, and could increase even more for higher opportunity costs. This apparently contradictory result isattributed to the counterbalancingeffect of the foregone cash flows during construction.

Being a standard option pricing formulation, the model only addresses the problem of coming up with a strategy fora single project, considering only one random variable that is assumed to be lognormally distributed.

Value of flexibility

The following four papers were reviewed on this subject:

(1)The Strategic Value of Flexibility: Reducing the Ability to Compromise, N. Kulatilaka and S.G. Marks, Departmentof Finance and Economics, School of Management, Boston University.

(2) Valuing the Flexibility of Flexible Manufacturing Systems, N. Kulatilaka, Working Paper No; MIT-EL 88- 006WP,Center for Energy Policy Research, MIT.

(3)The Value of Flexibility, N. Kulatilaka, Working Paper No. MIT-EL 86-014WP, Energy Laboratory, MIT.

(4) A General Formulation of Corporate Real Options, N. Kulatilaka and J. Marcus, School of Management, BostonUniversity.

These papers address the following problem. Consider a firm that is faced with an investmentdecision. There are threetypes of technology available. One is technology A, another is technology B, and the third is a flexible technology thatcan operate in either of two modes, A or B. For example, there may be a thermal power plant that can operate eitheron coal or gas. Depending on the price of fuel, the firm may choose to run the plant either on coal or gas. The mostsignificant value of flexibility is to provide the production process with an ability to modify itself in the face ofuncertainty. The papers address this problem in terms of the option value of flexibility: the option to switch from onemode to another, thus providing methods to place a value on the flexibility option.

The approach developed by the authors is based on a standard option pricing model. However, it extends this basicframework to more complex formulations that allow for the analysis of more complex problems (multiple option choiceproblems). A main point argued by the authors is that most real options (such as those presented in Pindyck's papers)can be viewed as special cases of a general flexibility option that enables firms to switch operation modes at severaldecision points in the life of the project.

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C Search For Robust Solutions

Many practitioners and researchers in the field of power system planning, having realized that elaborate deterministicmodelling is likely to give the wrong solution, and having been frustrated by the inability of making accurate long-termforecasts, have turned their attention to the problem of searching for "robust" solutions, whose chief characteristicwouldbe to be reasonable under most, if not all, foreseeable scenarios.

One excellent example of how to search for robust solutions is that of the recent EPRI research project which isreviewed below in this section. Not only has EPRI developed a methodo.ogy to do this, but it has also implementedit in a computer program called RISKMIN, which is available from the EPRI. This model is the result of an effortdescribed at the end of Section 2 below. All other papers in this section culminate in that model.

Review of artides surveyed

a. Multiple Objective Trade Off Analysis in Power System Planning, F.C. Schweppe, MIT and H.M. Merrill, PowerTechnologies Inc., USA

This paper is very similar to the one by Bhavaraju et.al. on "An approach to risk evaluation in electric resourceplanning." A basic premise of the paper is that there is no one criterion that would define an optimum plan. This isan organizing approach that can be used by an experienced planner to help solve the problem.

Some key definitions used (they are also used in the paper by Bhavaraju et. al.) are:

(1) Attributesare measures of the goodness of the plan. They include the revenue requirements,loss of load expectation,etc. These attributes are functions of options.

(2) Options are the investments and include building a new coal fired plant, or building a small turbine based generator.

(3) A plan is a set of specifled options. For example, build a 600MW coal plant in 1994 and add 350MW of transfercapability.

(4) Uncertaintiesare beyond the utility's control and include load growth, fuel prices, regulatory changes, etc.

(5)A future is a set of specified uncertainties, for example a 3% load growth and a 1% per year oil price increase.

(6) A scenario is a single plan with a single future.

(7) Risk is the variation of attributes to which a utility is exposed because of uncertainties.

The planning process consists of identifying options and uncertainties, developing pians, calculating attributes for plansand uncertaintiesand finally, identifying the best plans. The method used is the trade-off/risk method. It does not findan optimum plan. It is a way of eliminating many possible plans that are inferior, and leaving a small set of plans whichare reasonable compromises between conflicting objectives. The main steps in the method are the same as that usedin the Bhavaraju paper. A set of plans is analyzed using trade off concepts. A plan is picked and checked against theother plans to see if any of them dominates it. If so, it is dropped from the decision set. If not, it is included in thedecision set, which is the set of plans that under no scenario were significantly inferior to other plans. This procedureis repeated for all the plans. At the end we obtain a decision set, which is the set of plans that under no scenario weresignificantly inferior to other plans. This is further analyzed by the planner to obtain a final decision.

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The important issues raised in the paper are as follows:

(1)Robust plans Are there any plans that almost always look good, independentlyof what future occurs, in the senseof not being excessively costly, over oi under dimensioned?

(2) Uncertainty. Are there any uncertainties that are important or unimportantwhen considering a particular plan?

In principle it is similar to the report by Bhavaraju et.al. and basically consists of analyzing a set of different scenariosto come up with a small set of 'good' ones.

b. StrategicPlanning for Electric Utilities: Problems and Analytic Methods, H.M. Merrill, Power Technologies Inc. andF.C. Schweppe, MIT, Interfaces 14, Jan-Feb 1984.

This paper introduces a method for the problem based on multi-objective decision analysis as opposed to simulationor optimization. It is based on trade off analysis :nd is similar to the ones by Schweppe et.al. and Bhavaraju et.al. Theme.hod is outlined below:

First, key variables are identified. Decision variables represent decisions over which the utility has control, such aswhether to build or retire a plant. Exogenous variables represent those over which there is little or no control andinclude load growth and fuel price and availability. Attributes measure the goodness of a particular strategy, such ascost of electricity to the customer and environmental impact.

A range of values for the exogenousvariables is specified. For example, demand growth may be expected to be within -2% and +3% and values of -2, -1, 0, 1, 2 and 3 pcrcent chosen to span the uncertainty range. Similarly, a range ofvalues is specified for the decision variables. Using these, the attribute values are calculated. This is done by using thealready existing analytical and computer tools in the utility industry. A set of SMARTE functions are then developedthat relate the attributes to the decision and exogenous variables. Basically, this is done by u'sing regression techniques.Here again, standard computer packages are used to come up with the functions.

In the next step, trade off analysis is done to identify the good plans. If the initial range of values for the decisionvariables or the uncertainty variables is found to be inadequate, then we specify new values and re-evaluate the plans.

c. An Approach to Risk Evaluationin Electric ResourcePlanning, M.P. Bhavaraju,T.C. Chamberlainand N.E. Nour,Research Report 2537-1,2. Public Service Electric and Gas Company, December 1987. Prepared for EPRL

The primary objective of this report was to develop a method to trade off multiple, conflicting attributes and to identifyplans that are robust under specified uncertainties. It builds on a previous EPRI report RP1960 entitled "An Apprcao:%to Determining Transfer Capability Objectives,' and culminates with the RISKMIN software mentioned in theintroductorysection.

Different investment plans are evaluated, two at a time, and the better plan is included in a decision set. If neither planis clearly better (as happens when one plan is better in one attribute, say cost, but worse in another attribute like risk),both are included in the decision set. After comnparing all plans, a set of "good" plans remain in the decision set. Thisset of plans can then be evaluated by the user to decide the desirable plan considering any concerns not included in themodel.

Uncertainties are considered by two different approaches. One is to use explicit probability distributions for all of theunceztainties. The other approach is to specify upper and lower bounds on the uncertain values and study someintermediatevalue. Only feasible scenarios are considered. For example, high fuel cost is associated with low demand,and a situation where both price and demand are high may not be considered.

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The overall methodology involves three main steps:

(1) Evaluate the attributes arising from all possible investment plans and uncertainties. Attributes are used to evaluatean expansion plan. For example, financial attributes are capital requirements and interest costs, capital requirements,interest costs, revenues, operating expenses and average cost of electricity; performance attributes are loss of loadprobability; environmental attributes might quantify pollution, etc.

The report states that a primary input to the model is the list of plans with the uncertainty values. It seems that thisis a drawback, because coming up with reasonable plans without the aid of a model is a difficult task.

(2) Identify the decision set, which is the set of all plans that are not worse than some other plan. A plan is evaluatedand its attributes are calculated. Plan 1 is said to "strictly dominate" Plan 2 if all its attributes are better than theattributes of Plan 2. Plan 1 is said to "significantly dominate" Plan 2 if at least one attribute of Plan 1 is much betterthan the correspondingattribute of Plan 2, and no attribute is much worse than an attribute of Plan 2. Tolerance limitsfor much better or much worse are set by the user. For example, a difference of investment cost of $100,000 may beconsidered insignificant, whereas a difference of S1 million may be considered significant.

Plans are evaluated two at a time. If one plan strictly or significantly dominates the other, it is included in the decisionset and the other plan is discarded. If neither plan dominates, both are included in the decision set. A plan in thedecision set is them compared to another plan that has not yet been considered. When the process is completed, a finalset of plans is obtained.

(3) Diagnostic analysis of the plans in the decision set. The model generates the following four special reports:

- Trade off analysis report This lists the plans in the final decision set, and the demand and price scenarios thatsupport each plan. For example, for Plan 1 (which is a specified set of investments), it may be stated that Plan 1is good under 1% or 2% demand growth and low fuel price. This gives an idea of the "robustness of the plan, i.e.,under how many different uncertainty scenarios it is reasonable. Similarly, it also gives the set of favorable plansfor each demand and price scenario.

The report also gives the percentage of scenarios that support a particular plan. For example, if a plan is supportedby 80% of possible uncertaintyscenarios, it can be said to be more robust than a plan that is supported by only 40%.

- Robustnessof individual investments. Considers an inyestment in a particular plant. The report tells all the differentplans which include this plant.

- Extreme and Expected Attribute Values Report Reports the high and low values of some attribute, say cost. Thisreport provides the extreme values for each attribute and the demand and price scenario under which they wouldoccur. If probabilities are assigned to the uncertainties, the report also gives the expected value and the standarddeviation of each attribute. Large differences between extreme values or large standard deviations indicate high risk.

- Comparison of pairs of plans. This report provides a comparison of the attribute values that differ most for twoselected plans. It indicates the demand and price scenario under which this difference occurs. This report makesit easier to compare two plans.

While the word strategy is not mentioned in the report, it could be said that the model could provide the outlines ofa possible investment strategy, defined as an initial course of action and a set of responses to varying future scenarios.Since the model provides an indication of "robusters"of individual investments (or options), clearly an investmentwhichis dominant under most scenarios (i.e., is very robust) would be a good initial investment with which to start anexpansion plan. Once this decision has been taken, the model could be re-run, presumably at a later time when a newdecision would be required and in the possession of newer information and forecasts, to see how the remaining capacityrequirementscould be met.

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The model has much to commend it. Firstly, it is user friendly and makes interactive decision making easier. Secondly,it specifically assumes that there is no one "optimum" plan, and provides the user with a set of good plans which canbe further evaluated. By providing the robustnessof each plan and investment, it enables the user to choose plans thatwould work under a wide variety of uncertainty scenarios. Tolerances for different attributes can be set by the user tomeet his specific needs. These tolerances are then used by the model to compare different plans.

Some of the difficulties with the model are as follows. Firstly, the user has to provide a set of plans as input to themodel. A comprehensiveset of feasible plans that does not exclude any good plans for a large complex problem is verydifficult to arrive at. There is also the need to carry out simulation studies of selected plans and uncertainty scenariosto calculate the attributes for each plan. It can generate additional scenarios by using linear interpolation betweencomputed scenarios, however.

D. Selected Bibliography

General

Albouy, Y. and Systems Eurape Consultants.Assessmentof Electric Power System Planninn Models, Energy DepartmentPaper No.20. The World Bank, March 1985.

Anderson, D. Models for Determining Least Cost Investment in Electricity Supply, Bell Journal of Economics andManagement Science (3), 1972.

Anderson, J.R. Forecasting. Uncertainty and Public Project Appraisal, Commodities Division Working Paper No.1983-4. The World Bank,July 1983.

Calazet, E.G., Judd, B.R. Miller, A-C. and Rassmussen, E.S. Decision Analysis of California Electrical CapacityEnpansion. Stanford Research Institute, Menlo Park, California, 1977.

Masse, P. and Gibrat, R. Application of Linear Programmingto Investmentsin the Electric Power Industry, ManagementScience No.3, 1957.

Sanghvi, AXP. and Limaye, R.L. Planning Future Electrical Generation Capacity, Energy Policy. June 1979.

Stochastic and Probabilistic Analysis

Baleriaux, M., Jamoulle, E. and de Guertechin, F.L. Simulation de l'exploitation d'un Parc de Machines Thermiques deProduction d'Electricite couple a des Stations de Pompage, Revue E No.5, 1967.

Bienstock, O.J. and Shapiro, J.F. Optimization Resource Acquisition Decisions by StochasticProgramming,ManaeementScience Feb. 1988.

Bisthoven, O.J., Schuchewytsch,P. and Smeers, Y. Dealing with Uncertain Demand in Power Generation Planning. FromEnergy Markets in the Long-Term: Planning Under Uncertaintv S.Kydes and D.M.Geraghty (editors), Elsevier SciencePublishers, B.V. (North-Holland) IMACs 1985.

Bloom, J.A. Solving an Electric Generating Capacity Expansion Planning Problem by Generalized BendersDecomposition, Operations Research Jan-Feb 1983.

Booth, R. Power System Simulation Model Based on Probability Analvsis, IEEE Transactions on P.AS.. Vol. 91, 1972.

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Borison, A.B.,Morris, P.A. and Oren, S.S. A State of the W',orld DecompositionApproach to Dynamics and Uncertaintyin Electric Utility Generation Planning, Operations Research Sep-Oct 1984.

Nissan, L. and Zahavi, J. Electricity Equilibrium Models Witt. Stochastic Demands, Energy Economics Oct. 1987.

Noonan, F. and Giglio, R.J. Planning Electric Power Generation:A Non-linear Mixed Integer Model Employing Bender'sDecomposition, Management Science No.23, 1977.

Rau, N.S., Schenk, N. and Toy, P. Expected Energy Production Cost by the Method of Moments, 1EEE PES 1979Summer Meeting, F79.

Sherali, H.D., Staschus, K. and Huacuz, J.M. An Integer Programming Approach and Implementation for an ElectricUtility Planning Problem With Renewable Energy Sources, Mana2ement Science, July 1987.

Stremel, J.P. and Rau, N.S. The Cumulant Method of Calculating LOLP, IEEE PES Summer Meeting, A79.

Vardi, J. and Avi-Itzhak, B. Electric Enerav Generation, MIT Press, Cambridge MA, 1981.

Trade-off Approach

Bhavaraju, M.P., Chamberlain, T.C. and Nour, N.E. An Approach to Risk Evaluation in Electric Resource Planning,Research Project 2537-1,2. Dec. 1987. Public Service Electric and Gas Company, prepared for EPRI.

Keeney, R.L., Lathrop, J. and Sicherman, A. An Analysis of Baltimore Gas and Electric Company's Technology Choice,Operations Research No.34. 1986.

Keeney, R.L. An Illustrated Procedure for Assessing Multiattribute Utility Functions, Sloan Management Review, 14,1972.

Lo, E., Campo, R. and Ma, F. Decision Framework for New Technologies: A Tool for Strategic Planning of ElectricUtilities IEEE P.A.S, Vol. PWRS-2, Nov.1987.

Merrill, H.M. and Bhavaraju,M. Transfer CapabilitvObjectives: A StrategicApproach, IEEE P.A.S, Vol. 104, May 1985.

Merrill, H.M. and Schweppe, F.C. Strategic PI nning for Electric Utilities: Problems and Analytical Methods. Interfaces14, Jan-Feb 1984.

Merrill, H.M., Schweppe, F.C. and White, D.C. Enerev Strategy Planning for Electric Utilities (SMARTE methodologyv)IEEE Transactions on P.A.S. Vol. 101, No.2, Feb.1982.

Mukherjee, S. and Ma, F. Utility Investment in New and Emerging 'fechnologies: Multi-attribute Dynamic Model forSequential Decision Making Under Risk and Uncertaintv. EPRI report.

Schweppe, F.C. and Merrill, H.M. Multiple Objective Trade Off Analysis in Power System Planning. 9th Power SystemsComputation Conference, Cascais, Portugal, Aug-Sep. 1987.

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Finance Valuation Methods

Jacoby, H.D. and Laughton, D. Energv Project Evaluation Usine Derivation Asset Valuation. [AEE papers andProceedings of the 8th Annual North American Conference, Nov.1986.

Kulatilaka, N. and Marks, S.G. The Strategic Value of Flexibilitv: Reducing the Abilitv to Compromise, School ofManagement, Boston University. 1988.

Kulatilaka, N. Valuing the Flexibility of Flexible ManufacturineSvstems, Center for Energy Policy Research, WorkingPaper No. MIT-EL 88-006WP. 1988.

Kulatilaka, N. The Value of Flexibilitv. Energy Laboratory, MIT. Working Paper No. MIT-EL 86-014WP, 1986.

Majd, S. and Pindyck, R.S. Time to Build, Option Value and Investment Decisions, Journal of Financial EconomicsNo.18, 1987.

Pindyck, R.S. Options, Flexibilitvand InvestmentDecisions Center for EnergyPolicy Research,MIT. Workshopon NewMethods for Project and Contract Evaluations, March 1988.

ENERGY SERTES PAPERS

No. 1 Energy Issues in the DeveLoping WorLd, February 1988.

No. 2 Review of World Bank Lending for F ctric Power, March 1988..

No. 3 Some Considerations in Colleccing Data on Household EnergyConsumpcion, March 1988.

No. 4 Improving Power System Efficiency in the Developing Countriesthrough Performance Contracting, May 1988.

No. 5 Impact of Lower Oil Prices on Renewable Energy Technologies, May1988.

No. 6 A Comparison of Lamps for Domestic Lighting in Developing Countries,June 1988.

No. 7 Recent WorLd Bank Activities in Energy (Revised September 1988).

No. 8 A Visual Overview of the World Oil Markets, July 1988.

No. 9 Current International Gas Trades and Prices, November 1988.

No. 10 Promoting Investment for Natural Gas Exploration and Production inDeveloping Countries, January 1989.

No. 11 Technology Survey Report on Electric Power Systems, February 1989.

No. 12 Recent Developments in the U.S. Power Sector and Their Relevance forthe Developing Countries, February 1989.

No. 13 Domestic Energy Pricing Policies, April 1989.

No. 14 Financing of the Energy Sector in Developing Countries, April 1989.

No. 15 The Future Role of Hydropower in Developing Countries, April 1989.

No. 16 Fuelwood Stumpage: Considerations for Developing Country EnergyPlanning, June 1989.

No. 17 Incorporating Risk and Uncertainty in Power System Planning, June1989.

Note: For extra cooies or these papers olease caLl Ms. Marv Fer.andez onextension 33637.

INDUSTRY SERIES PAPERS

No. 1 Japanese Direct Foreign Investment: Patterns and Implicationsfor Developing Countries, February 1989.

No. 2 Emerging Patterns of International Competition in SelectedIndustrial Product Groups, February 1989.

No. 3 Changing Firm Boundaries: Analysis of Technology-SharingAlliances, February 1989.

No. 4 Technological Advance and Organizational Innovation in theEngineering Industry, March 1989.

No. 5 The RoLe of Catalytic Agents in Entering International Markets,March 1989.

No. 6 Overview of Japanese Industrial Technology Development,March 1989.

No. 7 Reform of Ownership and Control Mechanisms in Hungary and ChinaApril 1989.

No. 8 The Computer Industry in Industrialized Economies: Lessons forthe Newly Industrializing, February 1989.

No. 9 Institutions And Dynamic Comparative Advantage ElectronicsIndustry in South Korea and Taiwan, June 1989.

No. 10 New Environment for Intellectual Property, June 1989.

Note: For extra copies of these papers please contact Ms. Wendy Youngon extension 33618.