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Energy Policy. Vol. 24, No. 2, pp. 129-136. IYY6 Copyright 0 1996 Elsevier Science Ltd

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Valuing the flexibility of alternative sources of power generation

Chris Chapman and Stephen Ward Centre,fbr Risk Research, Department qf Accounting and Management Science, University qfSouthampton, Highfield. Southampton SOI 7 I BJ, UK

Solar and other renewable technologies can provide increments to an existing energy system which are small in capacity with a short lead time. Such power generation units provide more flexibility in incremental provision than large, long lead time units such as nuclear power stations. However, small, short lead time units are not normally given explicit credit for the flexibility these attributes provide. This additional flexibility can be valued by assessing the costs arising from the relative in- flexibility of large, long lead time units. Numerical examples illustrate the proposed approach and the scale of the values involved. Failure to consider such values provides a built-in bias against the selection of sources of energy available as units with a small capacity, short lead time, and other flex- ibility attributes, including mobility and modularity. The approach outlined in this paper can elimi- nate this bias in a manner which is transparent and open to effective sensitivity analysis. K~LWW& Renewables; Selection bias; Flexibility

In his summary paper for the recent renewable energy paper series in Energy Policy, Jackson (1992) is optimistic, but points to some significant impediments to be overcome, in- cluding institutional obstacles with specific economic mani- festations, citing discount rates (Awerbuch, 1991, 1995) as one example. Another example, considered in this paper, is the valuation of flexibility.

In a management context, the term ‘flexibility’ is gener- ally used to describe the ability to do something other than that which was originally intended (Evans, 1991). Similar terms to ‘flexible’ are ‘adaptable’ and ‘versatile’ (defined respectively by the Concise O.xford Dictionary as ‘capable of modification and ‘able to turn readily from one activity to another’).

Flexibility is sometimes confused with diversification. For example, Ansoff’s concept of ‘defensive external’ flex- ibility (Ansoff, 1987) is concerned with minimization of the impact of threats, which leans towards the notion of re- silience based on diversification -the ability to withstand shocks - rather than the ability to actively do different things. Ansoff emphasizes the importance of diversification

in customer base, market segments and product related technologies in order to reduce dependence on any one business area and minimize ‘cross vulnerabilities’ between business areas.

Given the high levels of uncertainty about future demand and supply in the energy industry, some researchers have ar- gued for identifying an optimal degree of diversification, via the concept of entropy, as a way of determining an ap-

propriate level of flexibility for the system (Stirling, 1994). A difficulty with this approach is that entropy is a ‘black box’ measure which values diversity per se without refer- ence to any objective. The possibility of positive or negative correlation between power source risk is ignored.

There is a difference between flexibility and diversifica- tion. However, diversification in sources of power genera- tion may well lead to flexibility, in the sense of the set of sources available and used to generate electricity, and this flexibility can include attributes associated with resilience.

Other things being equal, one position is more flexible than another if:

(1)

(2)

(3)

It leaves available a larger set of future positions (Marschak and Nelson, 1962; Jones and Ostroy, 1984; Slack, 1983). It allows the attainment of new positions in a shorter pe- riod of time (Slack, 1983). It requires less additional cost to move to another posi- tion (Marschak and Nelson, 1962; Jones and Ostroy, 1984; Slack, 1983; Stigler, 1939).

These measures imply a multidimensional concept of flex- ibility. However, the above dimensions may not always be compatible: for example, a position that is preferable in terms of the time taken to reach other positions may not be prefer- able in terms of the cost of reaching the other positions. Therefore, developing a strategy of appropriate flexibility may involve trading off the dimensions as necessary.

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130 Valuing.flexibili[v: C Chapman and S Ward

Flexibility is not necessarily desirable. There is a need to match the approach to flexibility with the kind of uncer- tainty which organizational planning addresses. For ex- ample, a willingness to change objectives at short notice, or a preference for short-term rather than long-term contracts (with customers or suppliers), while evidence of flexibility, may be extremely disruptive and strategically inadvisable. The existence of slack resources or spare capacity may allow organizations to absorb shocks or exploit opportun- ities rapidly without disrupting existing operations, but may be grossly inefficient if this slack is rarely used. Flexibility should only be adopted in a form and to an extent that brings net benefits. Assessing this requires an appreciation of both the costs and benefits.

The design of an organizational undertaking usually starts from an appreciation of purpose and the need for ac- tivities which achieve the purpose efficiently and effect- ively. In this context, the incorporation of flexibility requires a deliberate departure from conventional design and planning philosophy, and a clear appreciation of the ad- vantages that a flexible posture offers. Unfortunately, this appreciation is often limited to a hazy recognition of a sub- set of the problems, threats and opportunities that may con- front the organization in the future, and an equally hazy awareness that a rigid posture is likely to be dysfunctional in dealing with them.

The body of this paper begins with an overview of the relationship between diversification and flexibility devel- oped by the first author for risk management by Ontario Hydro (Chapman, 1992) in terms of three interdependent but separable planning horizons. It then uses a numerical example to quantify the value of flexibility in this particular context. This example highlights two key issues which are then discussed, before a final concluding section.

Three planning horizons

Planning for an electric utility can be usefully decomposed into three separate planning horizons and processes. They are interdependent but separable, in the sense that they can be considered one at a time in an iterative process, with earlier analysis in one informing the others. It is important to impose separability, not just to make the overall process tractable, but because the issues of concern in the three dif- ferent horizons are very different, requiring different forms of modelling. However, it is also important to recognize the interdependencies. Additional (four or more) horizons might be usefully explored, but less than three will cause difficulties.

Short-term planning is concerned with which units to operate (on load, as spinning reserve, and as standby or near-term reserve) to meet current demand, the ongoing ‘real time’ end of the business. The focus is rapid fluctua- tions in demand and sudden short-term plant failures, which are only partially predictable, working on a minute to minute basis up to a maximum horizon of about a year. Maintenance planning is part of this process. Robustness is the key concern. It is important to avoid letting the lights go out.

Medium-term planning is concerned with which new units of each energy source to build and bring on stream, and which existing units to mothball or retire. The focus is medium-term (l-15 years) swings in demand, medium- or long-term (catastrophic) plant failures, and the total margin of available reserve to meet these swings and failures. New unit go ahead decisions need to be made using a pool of op- tions defined and preplanned by the long-term planning process, with due regard to medium- and short-term needs, but without revisiting long-term strategic analysis. Flexibil- ity in choice of power source is a key concern. It is import- ant to avoid cost generated by rigidity.

Long-term planning is concerned with the mix of energy sources the system should be aiming for in the long term, say I5 years out and beyond, and the pool of probable additions to the system ready for a medium-term planning ‘go’ decision. The focus is on long-term strategy. A key concern is to avoid fundamental strategic errors, going down a blind alley with the whole system, or failing to develop a key new source of energy. Diversification is attractive in so far as it reduces the chance of such errors, as well as fostering flexibility.

Long-term planning in this three horizon framework re- quires the selection of an appropriate conceptual basis. We do not have to prespecify a particular modelling frame- work, but we do have to select a paradigm or mind set. The paradigm ‘predict and prepare’ is common to the planning philosophy of a wide range of organizations. In a stable en- vironment it can work reasonably well. Ontario Hydro’s re- cent Demand/Supply Plan (DSP) (I 990) could be associ- ated with this perspective. Demand forecasts with tight confidence bands were the starting point for a largely deter- ministic planning process which assumed that the base load source of power selected on a lowest base cost basis would prove to be the lowest cost option. Recent experience sug- gests this is not a viable strategy for energy planning in the 1990s. Actual demand fell outside the confidence bands be- fore the hearings to approve the DSP were complete, and Ontario Hydro subsequently withdrew their plan.

Shell and others have developed scenario analysis, now widely adopted by utilities, for long-term planning (Beck, 1982; Schnars, 1987; Helmer, 1983; Schoemaker, 1991). Scenario analysis abandons trying to make long term predic- tions which depend upon political and economic forces too complex to yield a confidence band of practical value when looking ahead IO years or so. Instead, it first concentrates on representative ‘high’ and ‘low’ scenarios, identifying the combinations of features and events which might lead to the widest range of extremes worth trying to plan for. It then concentrates on planning corporate developments which could survive these extremes in an effective manner, recog- nizing that influencing future events may be possible. It fol- lows the paradigm ‘prepare for the best and the worst, having first understood what these terms mean’.

In this paper we employ portfolio theory’ as the concep- tual basis for long-term planning, an approach to diversilica-

‘A useful introduction in the present context is Chapter 22. ‘Portfolio analysis and the spreading or transferring of risk’ in Chapman r/a/ (I 987).

Valuing,fkxibility: C Chapman and S Ward 13 1

tion developed for Ontario Hydro (Chapman, 1992). With this approach covariance is the key to diversification, linked to the concept of efficient diversification (minimizing the increase in expected cost associated with moving away from the predict and prepare paradigm to one taking ex- plicit account of the need to manage risk) and the concept of taking as much risk as practicable (stopping diversifica- tion as soon as the risk is acceptable). From this perspective the predict and prepare paradigm is a special case when risk is not an issue, and the scenario approach is effective but not efficient.

Making a portfolio approach operational is not an easy task. The first trick is to establish an expected value frame- work which makes sense as a long-term planning primary objective, based on all relevant sources of uncertainty: tech- nology, market, regulatory, health impacts, other environ- mental impacts and so on. Risk is then associated with departures from this expected value, with various possible measures of risk (like variance) being secondary objectives. A plausible primary objective is expected cost per kilowatt hour of electric energy at the horizon, say 25 years out, which includes all relevant costs. All relevant costs include capital costs, fuel costs, other operating costs and disposal costs-all the usual financial considerations. Relevant costs also ought to include the costs of considerations not nor- mally included, such as the cost of inflexibility (of interest here) and the cost of unreliability both of which are driven by the choice of power unit type. Taking a wider perspec- tive could require the inclusion of various externalized costs which political processes may internalize, like the possible cost of legislation on emissions, and externalities which are not likely to be internalized, like the cost of dealing with a Chernobyl type nuclear disaster. Issues like national inde- pendence and reducing exposure to miners’ strikes could also be embedded in this value function as well, in a will- ingness to pay sense. This range of cost issues is considered in more detail elsewhere (Chapman, 1992).

The second trick is to establish that while such expected values and their associated probability distributions will be contentious as soon as they are given a numeric form, this makes such definition more important, not less important, and certainly not an excuse for giving up. Authors who have been very clear on how and why such issues can be ap- proached with subjective probabilities have been around for some time, but there is scope for further developments in this area.2

The third trick is to develop a form of modelling which can use separability to build up an understanding of parts of the overall portfolio, without losing the important impacts of correlation. The bare bones of such an approach have been suggested (Chapman, 1992), but considerable development is required. Complexities like economics of scale with or without modularity which are not part of normal portfolio

There are many texts which deal with modern portfolio theory, including Levy and Samat, 1984; Brealey and Myers, 1984. 2A useful classic starting point is the appendix of Raiffa (I 968). A current example is considered in Chapman and Howden (I 995).

analysis need to be accommodated within this framework, in addition to issues like reversibility of decisions.

The fourth trick is to keep the whole approach flexible and transparent, open to sensitivity analysis and testing al- ternative perspectives, with solutions generated by the ana- lysis depending upon assumptions which are clearly visible and subject to robustness analysis if appropriate. That is the flavour of the suggested approach, illustrated to some ex- tent by the approach taken in this paper.

Making a portfolio approach operational is a topic be- yond the scope of this paper. However, it is important to ap- preciate that the approach to flexibility developed here assumes such an approach, with the expected cost of inflex- ibility and associated risk feeding into the long-term plan- ning process (Chapman, 1992). If long-term planning is approached via a predict and prepare, scenario or entropy based approach the flexibility concept developed here is not made invalid, but it may be weakened.

Valuing flexibility in a medium-term planning context

Making a medium-term planning approach operational given the kind of long-term planning approach just de- scribed is much easier, but not simple. The answers pro- vided by the long-term planning process should be of the form ‘the target in 25-years time is about 35% energy source A, 30% energy source B, 20% energy source C, and so on’. The gap between the units currently constructed which are expected to be operational in 1 O-1 5 years and these targets define a ‘possible requirements pool’ of units. Analysis of this pool should lead to a ‘probable require- ments pool’ of units, the first or first few units of each type, with a priority ordering. These units need to be preplanned to the stage where they can be given a ‘go’ status by medium-term planning with a minimum economic time to completion. Medium-term planning then reduces to making these go decisions (or not), in relation to decisions to moth- ball or retire (or refurbish) units, using all the techniques and models available.

This section illustrates how modelling can help with the timing issues of medium-term planning, and the nature of some of the issues involved. We suppose that little can be done to improve estimates of future demand, or to manage future demand, so that our concern is meeting future de- mand at the lowest cost per kilowatt hour of electricity, with cost broadly defined as noted earlier.

Inability to forecast precisely when power is needed in- volves a cost which is a function of the size and lead time of the units being considered and the relative flexibility pro- vided by other units which the system can call on to bridge demand/supply gaps. Other things being equal, the larger the units, and the longer the construction lead times, the greater this cost will be, because it becomes more difficult to synchronize new power generating capacity with the growth in demand. in practice demand growth equivalent to the capacity of the new units may either wholly or partially lead or lag the availability of those units.

132 Valuing,flexibiliv: C Chapman and S Ward

Period1 Period 2 Period3 Growth GW Probablility

0 0.3 x 0.2 x 0.1 = 0.006 1 0.3 x 0.2 x 0.4 = 0.024 2 0.3 x 0.2 x 0.5 = 0.030

0.3 x 0.4 x 0.3 = 0.036 0.3 x 0.4 x 0.4 = 0.048 0.3 x 0.4 x 0.3 = 0.036 0.3 x 0.4 x 0.4 = 0.048 0.3 x 0.4 x 0.4 = 0.048 0.3 x 0.4 x 0.2 = 0.024 0.4 x 0.3 x 0.2 = 0.024 0.4 x 0.3 x 0.4 = 0.048 0.4 x 0.3 x 0.4 = 0.048 0.4 x 0.4 x 0.3 = 0.048 0.4 x 0.4 x 0.4 = 0.064 0.4 x 0.4 x 0.3 = 0.048 0.4 x 0.3 x 0.4 = 0.048 0.4 x 0.3 x 0.4 = 0.048 0.4 x 0.3 x 0.2 = 0.024

2 0.3 x 0.4 x 0.2 = 0.024 3 0.3 x 0.4 x 0.4 = 0.048 4 0.3 x 0.4 x 0.4 = 0.048 3 0.3 x 0.4 x 0.3 = 0.036 4 0.3 x 0.4 x 0.4 = 0.048 5 0.3 x 0.4 x 0.3 = 0.036 4 0.3 x 0.2 x 0.5 = 0.030 5 0.3 x 0.2 x 0.4 = 0.024 6 0.3 x 0.2 x 0.1 = 0.006

Figure 1 Example load growth probability tree for 3 three-year periods

To the extent that load growth leads the availability of new units, the cost of meeting this load would be based on the use of existing shoulder period plant for base load, ex- isting stand by for peak load, deferred retirements and/or new plant. To the extent that load growth lags the availabil- ity of new units, there will be an excess of generating ca- pacity and a higher cost per kilowatt hour as units are underutilized, shut down completely, or units under con- struction are held in abeyance. The cost of meeting leading load growth and the increased cost per kilowatt hour due to lagging load growth are costs which arise because of the in- flexibility of new units in terms of their size and lead time. A set of small units with short construction lead times in- volves much less cost of this kind for the same total amount of power because the gap between required power and available power can be very much less. This additional flex- ibility can be valued by assessing the costs arising from the relative inflexibility of large, long lead time units.

To demonstrate the valuation process, the inflexibility associated with a 3 GW nuclear power station is considered in this section, assuming that the long-term planning pro- cess has made such a unit a probable choice, and it has been developed to the point of a go decision. Any other large power station with a long lead time would involve the same issues (a large hydro-electric power station for example).

Assume that the minimum construction period for a 3 GW nuclear power station is nine years, given design is complete and updated, permissions are in place, and so on. Assume we want to model the implications of committing now to construction of this nuclear power station.

Modelling load growth

Assume that the tree of Figure 1 represents our current view of load growth over the next nine years, which could incor- porate planned retirements and mothballing, plus un- planned retirements and catastrophic failures. Figure I illustrates a probability tree model of uncertain load growth, a three period semi-Markov process. It portrays load growth in each of three 3-year periods in terms of probability tree branches associated with load growth of 0, 1 or 2 GW. It assumes some correlation over time: if load growth is zero in the first period, the chance that it will be zero in the second period is lower than it was in the first (0.2 rather than 0.3), and lower than it would be if first pe- riod growth were 1 or 2 GW (0.3 or 0.4). This extends to third period relationships in a similar manner. It reflects random shocks which may or may not be sustained over time, as we would expect in practice. That is, over time there is some tendency to return to an underlying trend, al- though such returns may not occur.

The net effect over nine years of the three levels of branches is computed by summing the growth over the branches. For example, zero growth in all 3 three-year periods yields zero growth over the nine years. The probability of each outcome is the product of the associated branch probab- ilities. For example, the probability of zero growth over the nine years is

0.3 x 0.2 x 0.1 = 0.006

Table I shows the probability of each possible load growth after nine years derived by simply allocating each of the probabilities associated with an end point of the Figure 1 tree to its gigawatt value in the Table I ‘probability calcula- tion components’ columns, and summing across rows. What is involved is repetitive addition of conditionally spe- cified dependent probability distributions. The symmetry of the dependence pattern results in an expected growth in each time period of I GW per three years, 3 GW over the nine years, as indicated in Table I.

More precision could be used, and different numbers ar- gued for. The authors would not wish to defend the num- bers used here for illustrative purposes. However, the order of magnitudes of the confidence bands look reasonable for illustrative purposes in terms of a system the size of Ontario Hydro’s, if possibly on the optimistic side: a one in three chance of the 3 GW forecast being correct to the nearest gi- gawatt; a 25% chance of the out-turn being 1 GW on the high side or 1 GW on the low side of the 3 GW forecast; a IO% chance of the out-turn being 2 GW on the high side or 2 GW on the low side; a less than I % chance of the out-turn being 3 GW on the high side or 3 GW on the low side.

Modelling the cost of uncertainty about demand

Suppose that contingency plans to cope with a departure from the expected load growth of 3 GW are reflected in the cost per kilowatt hour in present value terms associated with load growth outcomes from 0 to 6 GW as shown in

Valuing.jltxibiIit_v: C Chapman and S Ward 133

Table I Load growth probability distribution for nine years' Growth Probability calculation components,coiumns associated with successive (GW) setsofthreevaiuestaken fromtheprobabiiitycoiumnofFigure 1

0 0.006 I 0.024 0.036 0.024 2 0.030 0.048 0.048 0.048 0.048 0.024 3 0.036 0.048 0.048 0.064 0.048 0.048 4 0.024 0.048 0.048 0.048 5 0.024 6

0.036 0.048 0.036

0.030 0.024 0.006

Probability Cumulative (density) probability

0.006 0.006 0.084 0.090 0.246 0.336 0.328 0.664 0.246 0.910 0.084 0.994 0.006 I .ooo

“Expected growth after nine years 3 GW, I GW every three years

Table 2. The costs per kilowatt hour for different levels of load growth are illustrative, the pattern of the costs being the point of interest rather than the individual values. This pattern arises from the following assumptions.

Assumption I. The cost figures in Table 2 reflect average growth patterns to reach the various nine-year growth lev- els. For present modelling purposes we are not concerned with detailing cost differences related to the alternative ways of achieving each of the growth levels portrayed by Figure I. In practice there are differences, which could be modelled directly by avoiding the simplification of Figure I in Table I. For present purposes it is assumed that these dif- ferences largely cancel out and are not important in the pre- sent context.

Assumption 2. A load growth of 3 GW is associated with a cost per kilowatt hour of 8 cents, taken as a base cost for ex- ample purposes. This reflects the direct costs associated with running the nuclear station at full capacity over its life including all capital, maintenance and decommissioning costs, expressed as a cost per kilowatt hour. In addition, it includes the marginal costs associated with meeting an av- erage growth pattern of I GW every three years over the nine-year horizon (Figure I ). on an interim basis before the new nuclear plant is available, a cost which arises because of the inflexibility of this unit.

Assumption 3. A load growth of 2 GW is associated with a cost per kilowatt hour of 9 cents. This includes the same costs as the 3 GW outcome, with smaller costs associated with meeting the 2 GW load growth over the nine-year hori- zon on an interim basis. However, it also includes the cost of running the new unit only two-thirds of the time initially, or the equivalent cost of reduced usage of other system units

Table 2 illustrative costoutcomesiinkedtoioad growth outcomes

Probability cost Growth(CW) from Table 1 (cents/kWh) Product

0 0.006 14 0.084 I 0.0x4 II 0.924 2 0.246 9 2.214 3 0.328 8 2.624 4 0.246 8.5 2.091 5 0.0x4 9 0.756 6 0.006 9.5 0.057 Expected cost, cen&/kWh x.75

where this is more efficient. For example. if baseload gas tired plant is shut down because the nuclear unit is ready be- fore it is needed, the cost implications should be borne by the nuclear unit, because it is the inflexible timing of the nu- clear unit in relation to uncertain demand which gives rise to these costs. A 13% increase in through life cost may be too severe if demand recovers quickly after the end of the nine- year period, but more appropriate if no growth is anticipated beyond the nine-year horizon. However, the 9 cents is a con- venient round number for illustrative purposes, as are all the other costs. It is the pattern of the costs which is the point of interest rather than the individual values.

Assumption 4. A load growth of 1 GW is associated with a cost per kilowatt hour of 1 I cents. This includes the same costs as the 2 GW outcome, with smaller costs associated with meeting the I GW growth over the nine-year horizon on an interim basis, but much larger costs associated with running the new unit only one-third of the time initially, or the equivalent cost of reduced usage of other system units where this is more efficient.

Assumption 5. A load growth of 0 GW is associated with a cost per kilowatt hour of 14 cents to reflect the same cost pattern, the geometric cost increase from 3 to 2 to I to 0 GW growth reflecting the non-linear impact of a decline in load growth as it approaches zero.

Assumption 6. A load growth of 4 GW is associated with a cost per kilowatt hour of 8.5 cents to reflect the same costs as the 3 GW outcome, the extra half cent being attributed to a more rapid rise in demand over the nine-year period to the 3 GW level. It is assumed that any interim costs arising from the additional fourth gigawatt would be associated with the next unit of power, which would be initiated via re- vised forecasts, and bear interim costs in the same way as the unit being considered here. A 6% increase may be se- vere, but a convenient round number for illustrative pur- poses.

Assumption 7. A load growth of 5 GW is associated with a cost per kilowatt hour of 9 cents to reflect the same costs as the 3 GW outcome, the extra cent being attributed to a much more rapid rise in demand over the nine-year period to the 3 GW level. It is assumed that any interim costs aris- ing from the additional fourth and fifth gigawatt would be associated with the next unit of power.

134 Valuingflexibility: C Chapman and S Ward

Assumption 8. A load growth of 6 GW is associated with a cost per kilowatt hour of 9.5 cents for reasons similar to as- sumption 7.

Normal practice would not involve attributing the addi- tional costs associated with interim use of other units to a nuclear power station as assumed for Table 2. Nor would normal practice attribute the full costs of overcapacity due to a new nuclear power station in the manner assumed for Table 2. But if such costs must be borne by the system, and they stem from the nuclear power station decision, they need to be considered in the context of long-term planning if alternative sources do not involve such costs. Many types of solar and renewable power (like small hydro units) or small gas fired units, which could be constructed very quickly, do not involve such large additional cost and risk of this kind. In the case of small gas fired units, relatively low capital cost and savings in fuel costs if the gas fired units are not operated contribute to a reduction in penalty costs, over and above the shorter construction period.

The cost qf’i+xibility

Given an expected load growth of 3 GW over nine years, Table 2 shows that the expected cost per kilowatt hour with a 3 GW facility available in nine years is 8.75 cents per kilowatt hour. This increase in cost per kilowatt hour from the base cost of 8 is clearly very important. It implies an ex- pected cost per kilowatt hour of 0.75 cents associated with imperfect knowledge of demand growth (and loss of other supply) in conjunction with a commitment to a 3 GW nu- clear power station with a nine-year lead time. This addi- tional cost arises because the 3 GW, long lead time. nuclear power commitment is not sufficiently flexible to obtain the base cost of 8 cents per kilowatt hour in the presence of un- certainty about demand. The 0.75 cents per kilowatt hour can be regarded as the cost of inflexibility associated with this commitment. It is not far short of IO% of the total cost.

This cost of inflexibility does not include further inflex- ibility costs embedded in the 8 cents per kilowatt hour base cost, as noted in assumption 2. These costs arise because of the need to meet interim growth in load before the 3 GW unit comes on stream. They occur even if the predicted 3 GW growth over nine years follows a I -1-l pattern, but different load growth patterns may reduce or increase these costs. This further cost of inflexibility needs to be meas- ured, and managed as part of the medium-term planning process. The costs associated with alternative load growth paths could be modelled if the simplification from Figure 1 to Table I was avoided. However, costs not attributable to uncertainty about load growth would need to be considered outside the proposed model.

Even if the cost increases over base cost in Table 2 should be 10% of those used, 0.08 cents per kilowatt hour as a cost of inflexibility arising from uncertainty about de- mand, I% of the total cost, is by no means trivial. The linear rate of increase in cost per kilowatt hour for load growth in the range 4 to 6 GW is modest relative to the geometric rate of increase in costs associated with slower growth rates, but probably more overstated than the geometric rate. In prac-

Table 3 Cost outcomes llnked to different levels of planned growth

Load growth Probability Cost (cents/kWh) given a (GW) from Table I planned growth In CW of

2 3

0 0.006 II 14 I 0.084 9 II 2 0.246 8 9 3 0.328 8.5 8 4 0.246 9 8.5 5 0.084 9.5 9 6 0.006 9.5 9.5 Expected cost, cents/kWh 8.7 8.8

tice, the linear rate might be reduced by a factor of a hundred, and the geometric rates by a factor of ten, if flexibility is properly managed within an approach like that outlined here.

Lagging new capacity behind demand

Whatever the appropriate scaling, the asymmetry of the costs in Table 2 suggests a policy for the medium-term planning process which involves never attempting to meet the whole of anticipated load growth with nuclear power stations, meeting such anticipated load growth at least in part with non-nuclear, and then bringing in nuclear stations to take over established base load. That is, deliberately lag the introduction of new nuclear plant, or build plants which are smaller than the expected load growth.

Table 3 illustrates what the modelling of such a policy might imply for various possible assumed load growth tar- gets, assuming for simplicity that the unit can be scaled in- stead of delaying construction, and assuming a base cost of 8 cents whenever actual growth equals the planned for growth rate.

In the 2 GW planned growth case costs are drawn from Table 2, except that for growth to 6 GW, there is assumed to be no additional cost impact over the 5 GW growth scen- ario. This yields an expected cost per kilowatt hour of 8.7, which is less than the expected cost with a 3 GW provision. This result suggests a planned growth in capacity of 2 GW after nine years (despite an expected demand of 3 GW), corresponding to a lag of about four years behind expected load growth of 2 GW (see Table I). This lag would involve an expected cost saving of about 0. I cents relative to intro- ducing capacity to meet the expected demand increase in nine years’ time. This is only about I % of the total cost per kilowatt hour, but it is about 14% of the cost of inflexibility associated with imperfect knowledge as portrayed by Table 3, 8.7 - 8.0 = 0.7 cent per kilowatt hour.

Even with this lag policy, the long lead time involved in conjunction with demand uncertainty still adds nearly 10% to the base cost. An important issue is whether this ex- pected cost and risk should be considered in the long-term planning process. If a short lead time option with an ex- pected cost of I 10% of base cost of nuclear power is avail- able, it is comparable in expected cost terms, using the example numbers. The approach to long-term planning out- lined earlier could consider these additional system costs and risks associated with new supply implementation lags

Valuingjlexibilitv: C Chapman and S Ward 135

without embedding them directly in the cost per kilowatt hour distribution of individual sources. However, the effect would be a shift in the preferred mix away from sources with large capital costs and long lead times towards sources with low capital costs and short lead times.

Even if the absolute magnitude of the cost penalties as- sumed in Table 3 are less by an order of magnitude or more. this issue remains significant. To justify ignoring it would require a demonstration that the absolute magnitude of the cost penalties is many orders of magnitude less, and/or the uncertainty is orders of magnitude less.

Ontario Hydro’s corporate intuition appeared to suggest bringing on units early, that is planning for (temporary) overcapacity, as part of an understandable corporate con- cern to avoid ‘letting the lights go out’ (Ontario Hydro, 1990). In this context it is counterintuitive to deliberately plan to be late. However, the asymmetry of Table I penalty costs warrants deliberate planning to be late. This asymme- try is realistic, even though more precision could be used, and different numbers could be argued for. The authors would not wish to defend the numbers used here for illus- trative purposes. Doubling the cost per kilowatt hour for a nuclear unit which it turns out is not needed at all when it comes on stream is modest in full cost terms from some perspectives, although it may seem contentious from oth- ers. Even if the actual costs are less by an order of magni- tude or more, on either side of the distribution, the issue illustrated remains important.

Essentially, if being late is less expensive than being early, it pays to be late, although there are costs involved. The ex- tent to which it pays to be late is a function of the relative penalties associated with being early or late. In general. an asymmetry of the penalty function means that it is sensible to set a target for new generating capacity which will not match expected load growth, but leads or lags expected growth de- pending upon the direction and degree of asymmetry.

The load growth distribution used for this example was assumed to be symmetric, to focus attention on the asym- metric penalty costs. If the load growth distribution were not symmetric, this would complicate the situation, but the same principles would apply. In practice, it would be im- portant to demonstrate how changes in the central values, spread and skew of the assumed distribution of Table I, de- rived from Figure I, affected results. Similar comments apply to Tables 2 and 3. It would be desirable to test and demonstrate the robustness of only three branches at each of three levels in the tree structure of Figure I, and its simplifcation in Table I. However, in practice very little is gained by increasing the level of detail beyond that pro- vided in Table I until decisions are clear at a strategic Ievel.3

Nevertheless, to assist an electric utility with medium- term system planning, models of this kind would have to examine reasonably complex decision rules associated with exploiting flexibility, both to develop appropriate

See the example assessment in Chapman et al ( 1987. pp 208-2 IO).

rules and to provide a basis for the illustrative numbers of Tables 2 and 3. The attributes of flexibility considered di- rectly in the last section arc the ability to add small incre- ments of energy with short lead times, to counterbalance the large increment, long lead time difficulties raised by the nuclear power station example. However, other forms of flexibility could be incorporated. For example, if exist- ing units which are due for retirement can be run on to meet a shortfall in energy due to an unexpected demand in- crease, this can contribute to the lowering of the cost of in- flexibility for the nuclear power units. Further, if reasonably portable solar or wind power units purchased to meet a shortfall can be sold on to other utilities after major nuclear or hydro projects come on stream, as the most cost effective way of bridging a shortage and then disposing of a surplus, this aspect of flexibility will be valued by the proposed approach. That is, the reversibility of decisions to add new units, or to retire old units, is part and parcel of the overall system flexibility package which this approach considers. An obvious additional source of flexibility may be provided by buying or selling energy from neighbouring utilities. In this case the cost of inflexibility will be influ- enced by purchase and selling prices which will depend in turn on the surplus/deficit situations of neighbouring utili- ties (Hirst, 1990). There is no reason why any aspect of flexibility which is relevant to the management of the sys- tem cannot be incorporated in this approach. While more precision might be useful, the basic model form would not require modification, and it is both simple and transparent (Ward, 1989).

Conclusion

The approach outlined in this paper provides a model for considering medium-term planning decisions related to the large capacity and long lead time units which are normally the basis of planning new base load capacity. Related plan- ning to cope with inability to forecast demand accurately is part of this process, including the assessment of target lead times, and the more effective this process is, the smaller the cost of inflexibility.

The inflexibility of large, long lead time units is relative to the flexibility afforded by the availability of small, short lead time units, the link operating through the medium-term planning process itself. Within this framework it is simply not possible to value flexibility without looking at the in- flexibility of alternatives which might be preferred on an exclusive basis were it not for their inflexibility. We would not be interested in large, long lead time sources of power unless they were desirable for reasons other than flexibility. Flexibility is valuable in so far as it is able to reduce the cost of inflexibility. The availability of flexible alternatives to reduce the inflexibility cost of large, long lead time units will directly reduce the cost of this inflexibility for long- term mix of power sources planning purposes. Any ap- proach to flexibility which does not include this depend- ence is clearly missing a key ingredient if not the key ingredient.

136 Valuing.flexibility: C Chapman and S Ward

Acknowledgements

This paper is based on work undertaken on behalf of the In- dependent Power Producers Society of Ontario, in particu- lar exhibit #748 for the Environmental Assessment Board considering Ontario Hydro’s Demand and Supply Plan Hearings.

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