The Risk of Early Retirement of U.S. Nuclear Power Plants under Electricity Deregulation and...

Geoffrey S. Rothwell [*]

During the next decade, most states in the USA will deregulate electricity generation. Nuclear power plants that were ordered and built in a regulated environment will continue to be regulated as nuclear facilities. However, under state deregulation the price

they receive for their electricity will be set largely in non-regulated markets. This paper examines the competitiveness of the nuclear power industry with a probabilistic model to identify which nuclear power units face the highest risk of early retirement under deregulation. Projected outputs under both average-cost and marginal-cost pricing are compared with expected generation under continued rate-of-return regulation. Nuclear units at risk of early retirement are in regions with the lowest forecast prices or are old plants. But, if [CO.sub.2] regulation targets an emission reduction to 9% below projected 2010 levels (projected to be 24% obove 1990 levels), there are only a few units at risk of early retirement after 2015.

1. ELECTRICITY DEREGULATION, THE KYOTO PROTOCOL, AND NUCLEAR POWER

Although it is unlikely that Congress will pass legislation on either the issue of electricity deregulation or carbon dioxide emission reductions in the 106th Congress, the Clinton Administration backed initiatives to address both issues. See, for example, CEA (1998) and U.S. DOE (1999). By comparing low-cost and high-cost electric utilities, the Council of Economic Advisors (CEA) presumes that competition will force high-cost electricity providers to become more efficient, leading to cost reductions of $25 billion (1996$); see CEA (1998, Appendix 3). With increases in dispatch efficiencies, improved capital utilization, and reduced capital additions, cost reductions could range between $26 and $32 billion (1996$). Also, with these changes, carbon dioxide ([CO.sub.2]) emissions could drop by 40 to 60 million metric tons (U.S. DOE, 1999).

The Kyoto Protocol requires the US to reduce greenhouse gas (GHG)equivalent emissions, including [CO.sub.2], by 7% below 1990 levels between 2008 and 2012, on average. In 1990, total GHG emissions in the US were about 1600 million metric tons of carbon equivalent (MMTCE), inferring a reduction of about 1500 MMTCE to meet the Kyoto Protocol. From 1990 to 1996, US emissions rose about 150 MMTCE, and continue to rise. Assuming a rise in emissions of 33% above 1990 levels by 2008-2012 (see US DOE/EIA, 1998a), adherence to the Protocol could require a reduction of more than 600 MMTCE. If the CEA's conclusions regarding the influence of electricity deregulation are correct, up to 10% of the 600 MMTCE reduction could come from introducing competition into the electricity market.

This conclusion depends in part on assumptions regarding nuclear power plant (NPP) retirements. In the 1990s nine nuclear units retired prematurely in the US; see Table 1. Generally, these were old, single-unit plants. All began commercial operation before the accident at Three Mile Island in 1979. Westinghouse supplied most of the reactors. Many plants are in the Northeast.

To investigate whether other NPPs are at risk of early retirement, this paper describes a probabilistic model of NPP economic viability under electricity deregulation and carbon dioxide emission reductions. The paper begins by forecasting operating costs and output at US NPPs through the end of their initial licensed lifetimes. The forecasting technique used here also yields estimates of the forecasting errors for costs and output. Using a Monte Carlo simulation of these distributions and the distribution of expected market prices, it is found that one to three dozen nuclear power units are at risk of early retirement with the introduction of competition into electricity generation. Units particularly vulnerable to early retirement are old plants, single-unit plants, and plants in specific regions of the US. But if regulations target a [CO.sub.2] emission cut, there are only a few units at risk of early retirement after 2015.

Although it is not known when states will introduce competition into electricity markets, in this analysis, it is assumed that if an owner of a nuclear power unit can purchase power at a price below the unit's cost of production, the unit is at risk of early retirement. The closure decision will rest on other factors, such as whether capital costs can be recovered if the plant is not "used and useful," i.e., whether stranded assets can be recovered. Therefore, this analysis does not predict whether particular nuclear power units will retire, but suggests how the probability of early retirement changes under different deregulation and [CO.sub.2] emission reduction scenarios. [1]

2. ANNUAL AVERAGE VARIABLE EXPENSES AT NPPS

To forecast NPP retirements, this paper relies on the neoclassical economics model in which a firm will cease production if its average variable cost (AVC, equal to total variable cost divided by output) is greater than the output's price. [2] To determine whether a particular NPP is likely to cease production, this section discusses average variable cost; Section 3 discusses output; and Section 4 discusses price. Section 5 examines the influences of deregulation on the probability of retirement. Section 6 examines the influences of [CO.sub.2] emission reductions.

Variable cost includes all costs that vary with additional units of output. But NPPs are continuous production facilities where costs vary little with the production of an additional kilowatt-hour (kWh), see Rothwell (1996). Therefore to distinguish annual NPP costs from the traditional definition of AVC, this paper refers to these costs as Annual Average Variable Expenses (AVE). Three costs that vary annually are fuel expenses (FUEL), operating and maintenance costs (O&M), and capital additions (CAPADD). [3]

[TVE.sub.t] = [FUEL.sub.t] + [O&M.sub.t] + [CAPADD.sub.t], (1a)

[AVE.sub.t] = ([FUEL.sub.t] + [O&M.sub.t] + [CAPADD.sub.t]) / [Q.sub.t], or (1b)

[AVE.sub.t] = [AveFUEL.sub.t] + [AveO&M.sub.t] + [AveCAP.sub.t], (1c)

where [TVE.sub.t] is total annual variable expenses; [Q.sub.t] is electricity generated in year t; and [AveFUEL.sub.t], [AveO&M.sub.t], and [AveCAP.sub.t], are annual average fuel, O&M, and capital additions per kWh (here the time subscript is dropped to simplify notation). [4]

Figure 1 graphs these average costs during the last decade. [5] NPP expenses have declined in the US since 1988. (These expenses are reported by plant, not by unit, so plants define samples in this section; in the next section, which discusses productivity, nuclear power units define the samples.) AveFUEL has steadily declined from its highest level in 1984 with declines in uranium prices. [6] Also, AveO&M and AveCAP declined during the 1990s. These latter declines were due to major increases in productivity and minor decreases in costs.

Figure 2 presents the cumulative distribution of AVE across plants for 1990 and 1998. In 1990, 23% of the plants had average operating expenses above 35 mills/kWh, similar to projected national average cost prices; see Beamon (1998). By 1998, only 7% of the plants were above 35 mills/kWh and only 14% were above 30 mills/kWh. [7]

Figure 3 presents AVE from 1987 to 1998 for two large, single-unit plants that came into commercial operation in 1985 in the same region. The rises and falls in cost per kWh are due in part to 18-month refueling cycles, i.e., in some years the plants experience an extensive outage to refuel (decreasing productivity and increasing cost per kWh) and in other years there is no refueling outage. NPP1 has been (on average) more expensive to operate than NPP2. (I will refer to these two plants later.)

While fuel expenses vary directly with output, many O&M expenses and capital additions are predetermined in annual budgets. Variations in the annual averages for these expenses are a function of unanticipated cost and variations in annual output. To account for changes in annual output, I substitute Q [equivalent] CF [cdotp] MAX into Equation (1b), where CF is the capacity factor and MAX is the nuclear power unit's annual maximum dependable production of kWh. [8] So,

AVE = AveFUEL + (O&M/CF [cdotp] MAX) + (CAP/CF [cdotp] MAX) , (2a)

AVE = AveFUEL + (MinO&M / CF) + (MinCAP / CF), (2b)

where MinO&M (= O&M/MAX) would be the average O&M cost at full capacity (i.e., running at a 100% capacity factor) and MinCAP (= CAPADD / MAX) would be the average capital addition at full capacity. Although AVE have decreased at a rate of 4.8% per year, there has been little change in industry MinO&M (0.5 %/year). Increases in capacity factors have accounted for much of the decline in AVE.

This approach (1) explicitly acknowledges the importance of plant productivity (as measured by the capacity factor) in observed annual average variable expenses and (2) reduces the variance in the measures of O&M and capital additions by accounting for the variance in annual output. Following this approach, forecasting AVE requires forecasts of AveFUEL, MinO&M, MinCAP, and CF. Next, the paper describes the estimation of statistical forecasting equations for each expense. Section 3 discusses forecasting the capacity factor.

Previous analyses of NPP costs (including Maidment and Rothwell, 1998) have found significant differences in cost trends for 8 cohorts of plants, defined by three characteristics: (1) by reactor type (Pressurized vs. Boiling Water Reactors, PWR vs. BWR), (2) by vintage (commercial operation before 1982, "old," and after 1982, "new"), and (3) whether the plant had one ("single") or more units ("dual"). Table 2 presents descriptive statistics of expenses by cost cohort, where "Units" is the number of nuclear power units in the cohort, 'Ohs" is the number of observations in the panel, "Mm" is the minimum observation, "Max" is the maximum observation, and "SD" is the standard deviation. Between 1987 to 1998, old, single-unit plants have been the most expensive to operate. This is primarily because of the high O&M expenses, see Table 2, cohorts 1 and 5 (in columns under MinO&M). The most striking aspect of Table 2 is the high variance within cohorts (see the column labeled SD) and between cohorts (compare mean va lues).

With these data the following forecasting equations are estimated for AveFUEL, MinO&M, and MinCAP for each plant by cohort (for estimation results, see Rothwell, 1998a.):

[AveFUEL.sub.it] = [Y.sub.lit] = [a.sub.li] + [b.sub.lj](1/[TIME.sub.i]) + [e.sub.lit] (3a)

[MinO&M.sub.it] = [Y.sub.2it] = [a.sub.2i] + [b.sub.2j](1/[TIME.sub.i]) + [e.sub.2it] (3b)

[MinCAP.sub.it] = [Y.sub.3it] = [a.sub.3i] + [b.sub.3j](1/[TIME.sub.i]) + [e.sub.3it] (3c)

where t indexes the year of the observation, i indexes the plant, j indexes the cohort, a and b are parameters to be estimated, TIME is years since 1986 (the year before the beginning of the sample period), and e is the error term. [9] As TIME increases, the influence of the second term in Equations (3a)-(3c) decreases; so the [a.sub.ki], (k = 1,2,3) can be interpreted as asymptotic values of the dependent variables for each plant.

Under the appropriate assumptions, an approximation of the forecasting error (ignoring the diminishing influence of TIME and the covariances) is

Ferror([Y.sub.kit]) = Var([A.sub.ki]) + Var([E.sub.kit]) (4)

where FError is Forecast Error, Var is Variance, [A.sub.ki] is the estimated value of [a.sub.ki], and [E.sub.kit] is the residual. The forecast error depends on the error in estimating the plant-specific constant and the variance of the residual. A similar forecasting distribution can be defined for capacity factors.

3. FORECASTING NUCLEAR POWER PLANT PRODUCTIVITY

During the 1980s and 1990s, productivity at US nuclear power units improved dramatically. Nuclear power industry average annual capacity factors (CFs) increased from 60% in 1983 to 70% in 1988 to 73% in 1993 to 85% in 1998. See Rothwell (1998b). The cumulative distributions of unit-specific capacity factors for 1990 and 1998 are shown in Figure 4: while only 35% of the nuclear power units experienced CFs above 75% in 1990, 80% of the units had CFs above 75% in 1998.

But improvements have not been uniform across all nuclear unit types. Because of the differences among average CFs for Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs) from different manufacturers and NPPs of different sizes, I follow Thomas (1990) and consider eight cohorts: (1) Westinghouse PWRs smaller than 700 Mw (all came into commercial operation before 1982); (2) Westinghouse PWRs between 700 and 1000 Mw; (3) Westinghouse PWRs larger than 1000 Mw; (4) Babcock & Wilcox PWRs (all between 700 and 1000 Mw); (5) Combustion Engineering PWRs (all larger than 700 Mw); (6) General Electric BWRs smaller than 700 Mw (all came into commercial operation before 1982); (7) General Electric BWRs between 700 and 1000 Mw; and (8) General Electric BWRs larger than 1000 Mw. Table 3 presents descriptive statistics for each of these cohorts. The mean CF for each cohort improved between 1982-1989 and 1990-1998. [10] In particular, capacity factors for Babcock & Wilcox (the designers of Three Mile Island) units increased from 57% to 80% and capacity factors for large General Electric units increased from 46% to 71%.

Rothwell (1998b) estimated forecasting equations and forecasting errors for unit-specific CFs by cohort:

[CF.sub.it] = [a.sub.4i] + [b.sub.4j] (1/[TIME.sub.i]) + [e.sub.4it] , (5)

FError([CF.sub.it]) = Var([A.sub.4i]) + Var([E.sub.4it]) , (6)

where TIME is years since 1982, when productivity started to improve following declines after the accident at Three Mile Island. [11]

Using the model from Rothwell (1990) and data from 1982 through 1998, Rothwell (1998b) found that while some single-unit plants have been chronically unproductive (i.e., had capacity factors below 75% throughout the 1990s), older, multiple-unit plants have also been chronically unproductive. Forecasts of expenses and productivity must be combined to determine the distribution of AVE. For example, Figure 5 presents the first simulation (of 100) for each year from 2000 to 2020 of the forecast distributions of AVE for the two NPPs in Figure 3. NPP1 (AVEl) is forecast to be more expensive to operate than NPP2 (AVE2), and NPP1's expenses have a higher forecast variance than for NPP2. Figure 5 also shows expected electricity prices (average annual revenues per kWh) for these two NPPs. The next section discusses these prices.

4. DEREGULATED ANNUAL AVERAGE REVENUES AND CARBON CONTENT PRICES

Forecasting electricity prices under deregulation is inherently difficult. I rely on forecasts of average-cost prices and marginal-cost prices for each year from 2000 to 2020 for 13 regions in the US underlying Annual Energy Outlook 1999 (US DOE/ETA, 1998b). It is assumed here that the real price in 2020 (converted to 1996$) is constant to 2040. Beamon (1998) discusses these prices, updating US DOE/EIA (1997) with the National Energy Modeling System (NEMS); see, for example, US DOE/EIA (2000a). [12] These forecasts are for NEMS regions, which are either North American Electricity Reliability Council (NERC) regions or subdivisions of these regions. (See Table 1 for NERC regions.) Almost one-third of the units are in the Southeastern Electric Reliability Council (SERC), which includes Alabama, Florida, Georgia, North and South Carolina, Tennessee, and parts of Mississippi and Virginia.

This paper considers two sets of prices (p, defined as average annual revenues): (1) average cost (AC) pricing that begins in 2000 and continues to 2040 with the real price after 2020 equal to the forecast AC price in 2020, and (2) prices that converge linearly to marginal-cost (MC) prices as a function of state-level electricity deregulation, where prices in some states converge in 2005 and in other states in 2010, as a function of the current deregulation status in the state. Table 4 presents the mid-2000 status of deregulation by state. Here it is assumed that states listed in the first two columns experience marginal-cost pricing by 2005 and states in the last column experience marginal-cost pricing by 2010. Because some states (such as California) have already deregulated generation and some states (such as Alabama) are only investigating deregulation, it is reasonable to presume more than one date for convergence to marginal cost pricing.

Of course, the electricity market prices are uncertain. Ideally, the NEMS model would forecast price distributions, rather than expected prices. Because of the lack of characteristics of forecast electricity price distributions, I proxy expected standard deviations for these (annual average) prices using the standard deviation of average revenue for residential customers for each state with a lognormal distribution using information from Energy Information Administration Form 826 for 1990-1997. [13] (The calculated standard deviation can be interpreted as a percentage deviation from the mean.) With the first two moments of this distribution (the mean from the NEMS forecast and the variance from Form 826 data) I simulate real electricity prices from 2000 to 2040. Figure 5 presents two price paths associated with the two representative NPPs. (These price paths assume convergence to MC pricing in 2005.) NPP1 is in a state where the standard deviation in average revenue has been 5.5% per year in the 1990s and NP P2 is in a state with a standard deviation of 3.2% per year. NPP2 is competitive in all years, while NPP1 is competitive in all but 4 years in this simulation.

To investigate the influence of [CO.sub.2] emission reductions, carbon-content prices (the increases in energy prices due to [CO.sub.2] reduction regulation) can be added to the expected regional kWh price, see US DOE/EIA (1998a, Table B8, p. 184). This paper considers seven cases: (1) no carbon regulation, assumed to be 1990-level carbon emissions plus 33%, (2) 1990-level emissions plus 24%, (3) 1990-level emissions plus 14%, (4) 1990-level emissions plus 9%, (5) 1990-level emissions, (6) 1990-level emissions minus 3%, and (7) 1990-level emissions minus 7%; see Table 5. For example, under the assumptions and analysis of US DOE/EIA (1998a), to bring average emissions between 2008 and 2012 to 1990 levels (Case 5) would require an equilibrium price of $250 per metric ton of carbon content, implying national average increases in the price per kWh of 1.3 cents (1996$) in 2005, 2.9 cents in 2010, and 2.1 cents in 2020. [14] These metric tons of carbon prices are similar to many analysts' projections; see Weyant and Hill (1999, Figure 10A).

5. THE INFLUENCE OF DEREGULATION ON NUCLEAR POWER PLANTS

Before discussing [CO.sub.2] reduction regulation, this section examines electricity generation deregulation by discussing (1) AC (Average Cost) versus MC (Marginal Cost) pricing and (2) regional differences in the influence of deregulation. [15]

First, Table 6 compares "AR Regulation" with deregulation involving AC or MC pricing. (Under the "AR Regulation," nuclear power plant owners would receive average revenues per kWh in their state as experienced in 1996; this mimics rate-of-return regulation before the introduction of deregulation.) Table 6 presents retirements of nuclear units from 2000 to 2020. For each pricing assumption, Monte Carlo results are summarized with the maximum (MAX), the mean (MEAN), the minimum (MIN), and the standard deviation (SD) of 100 samples from forecast distributions of AveFUEL, MinO&M, MinCAP, and CF for each plant in each year. [16] For example, in Table 6 MAX is the maximum number of competitive units (i.e., AVE [less than] p) in any of the 100 samples.

Comparing "AR Regulation" with "AC Pricing," in the year 2000, there are on average 18 (= 101.6 - 83.3) units at risk of early retirement. [17] This increases to 23 units by 2012, then declines. Comparing "AR Regulation" with "MC Pricing" in 2005, there are on average 33 units at risk of early retirement. [18] This increases to 34 units in 2006 and then declines with scheduled retirements. In 2005 on average 14 (= 82.6 - 68.6, at the mean) more units are at risk of early retirement under MC Pricing than under AC Pricing. [19] These unit retirements could be translated into nuclear power industry electricity generation. There is a 100 TWh (terawatthours) difference between "AR Regulation" and "AC Pricing" in 2000 and close to a 200 TWh difference between "AR Regulation" and "MC Pricing" in 2005. [20]

These results do not imply that particular units will retire because (1) different units are non-competitive in different simulation samples, (2) each unit is represented by an imperfect statistical model, and (3) this statistical model is based on historical data that do not reflect NPP management response to the competitive pressures of deregulation. Therefore, these results represent "worst-case" scenarios of the influence of deregulation.

While this model ignores cost reduction measures, 38 (= 103 - 65) units are expected to retire under current licenses by 2015 (i.e., without license renewal). See the first column in Table 6 for years 2000 and 2015. Thus, if all units at risk of retirement actually retire, "MC Pricing" accelerates retirements by 12 years (compare 76.2 in 2014 under "AR Regulation" with 77.5 in 2002 under "MC Pricing"). "AC Pricing" accelerates retirements by six years (compare 76.2 in 2014 with 77.5 in 2008 under "AC Pricing").

Table 7 presents results by NERC region. The first column for each region is the forecast output in TWh assuming "AR Regulation." The second column is the percentage change in output assuming "MC Pricing." The influence of regulation is not evenly distributed across the US. Looking at results for 2005 and 2010, regions can be grouped into three categories: (1) the highest impact is on Regions I (ECAR), 3 (MACC), 5 (MAPP), and 6 (NPCC); (2) there is a moderate impact on Regions 4 (MAIN), 7 (SERC), and 8 (SWPP); and (3) there is a small impact on Regions 2 (ERCOT) and 9 (WSCC). Of course, the impact of deregulation depends on competitive electricity prices in each region and the competitiveness of each region's NPPs. Projected MC prices for 2010 are lowest in Regions 1, 2 and 5. See Beamon (1998). Prices are highest in Regions 7, 8, and 9. Marginal-cost prices explain why NPPs in Regions 1 and 5 are at risk of retiring early and why there might be a small impact on NPPs in Region 9, but prices do not explain w hy deregulation has a smaller influence on NPP competitiveness in Region 2. In Region 2 cost is more influential than price. In both Regions 2 and 9 most plants are large, new Westinghouse PWRs at multiple unit sites with the low MinO&M, see Table 2.

To summarize the influence of deregulating electricity generation, nuclear power units at the highest risk of early retirement are in regions with the lowest projected marginal costs (ECAR, which includes Ohio and Michigan, and MAPP, which includes Iowa, Minnesota, Nebraska, and Wisconsin). The other units should remain competitive with deregulation. [21] However, this analysis ignores cost cutting measures that NPP owners and operators could implement in the face of competition. [22] So, it is unlikely that all units at risk of early retirement will retire.

6. CARBON DIOXIDE EMISSION REDUCTION REGULATION

As discussed above, [CO.sub.2] emission reductions from generating electricity presume an increase in price to discourage consumption and encourage investment in non-[CO.sub.2] emitting generation. Whether this is done through "carbon taxes" or through a "cap-and-trade" program, under [CO.sub.2] regulation the marginal cost of generating electricity will reflect the increased cost of carbon-content (CC) pricing. Although each region will experience increases in electricity prices that reflect the regional composition of [CO.sub.2] emitting sources (primarily from burning coal and natural gas) and non-[CO.sub.2] emitting sources (primarily nuclear and hydro power), this paper assumes that all US electricity markets experience increases in market prices equal to those in Table 5.

US DOE/EIA (1998a) assumes the introduction of [CO.sub.2] regulation in 2005 to achieve reduction targets between 2008 and 2012. Table 8 examines the influence of CC pricing for six levels of [CO.sub.2] reduction, all assuming MC pricing. There is no change in the mean number of competitive units before the introduction of CC prices in 2005 (US DOE/EIA, 1998a). In Table 8 the first column is the difference between the mean under "AR Regulation" and "MC Pricing"; see Table 6. The second through eighth columns give the number of units at risk of early retirement under the seven cases outlined in Table 5. For example, the second column gives results under the assumption of a CC price of 0.1 cents/kWh in 2005, gradually increasing to 0.9 cents/kWh in 2010, and to 1.2 cents/kWh in 2020 (and continuing through 2040). This paper assumes a linear increase in equilibrium CC prices from 2005 to 2010. An increase of 0.26 cents/kWh (2.6 mills/kWh) in 2006 reduces the average number of nuclear power units at risk of earl y retirement from 34 to 27. On average only four nuclear power units are at risk of early retirement in 2015 with a CC price of 1.2 cents/kWh (note, 38 units are now scheduled to retire by 2015, see Table 6). As the CC price increases in Cases 3 through 7, the number of units at risk of early retirement decreases but at a decreasing rate. [23] The nuclear power industry response depends on the shape of the cumulative cost curve (see Figure 2): small increases in price reduce most, but not all, of the nuclear units at risk of early retirement.

7. DISCUSSION AND FURTHER RESEARCH

Between 2006 and 2016, unless licenses are renewed, 50 nuclear power operating licenses will expire. The NRC has finalized license renewal regulations. However, if there is not sufficient experience to forecast life extension costs (i.e., the costs of aging) by 2006 (when nuclear power unit operating licenses begin to expire), some units at risk of early retirement will retire before these costs are understood. [24] A complete model should incorporate the license renewal decision and life extension investments. [25] This can be done by calculating the distribution of the net present value of each nuclear power unit in each year and comparing it with projected life extension investments. Also, other influences on a utility's decision to retire a nuclear power unit should be considered. These include the number of nuclear units operated by the utility, the availability and reliability of alternative fuel sources, and the expected treatment of outstanding liabilities (including potential decommissioning costs) by state regulators. [26]

During the next decade, electricity generation in many US states will be deregulated. Deregulation involves (1) the creation of electricity markets where the cost of the marginal producer will determine the competitive price and (2) the restructuring of electricity generator ownership. [27] During the institutional transition from the current system to a deregulated one, NPP operators will face increasing uncertainty regarding the price they receive for their product. Because of the capital intensity of the nuclear power industry, the real and financial costs of continuing to operate and maintain NPPs will rise in a risky environment unless steps are taken to reduce expenses, particularly those for labor, which account for a large fraction of O&M costs. If costs are not reduced, some units at risk of early retirement will actually retire. However, whether costs are reduced or competitive markets are established in electricity generation, with [CO.sub.2] emission reduction regulations, few units will be at ri sk of early retirement.

ACKNOWLEDGMENTS

Previous versions of this paper were presented to the American Nuclear Society International Conference on Future Nuclear Systems ("Global '99"), the Center for Clean Air Policy, Center for International Security and Arms Control (Stanford University), Department of Nuclear Engineering (UC Berkeley), Electricity Working Group (EIA), Energy Institute (UC Berkeley), Energy Modeling Forum, International Association for Energy Economics, Lawrence Livermore National Laboratory, and Massachusetts Institute of Technology Security Studies Program. Funding has been provided by Department of Energy/Energy Information Administration. I thank A.J. Beamon, B. Biewald, C. Braun, T. Butler, J. Carroll, L. Church, S. Cohn, J. Conti, R. Eynon, D. Fennell, M. Fertel, S. Gander, R. Graber, R. Hagen, D. Hale, C. Heising, N. Helme, J. Hewlett, H. Huntington, D. Jackson, D. Johnson, E. Kahn, W. Kastenberg, D. Korn, J. Lewis, A. Macfarlane, J. Maidment, M. May, N. Meshkati, G. Motl, Z.D. Nikodem, R. Noll, R. Norgaard, B. O'Brien, C. Perin, P. Peterson, D. South, J. Stewart, J. Turnure, G.C. Watkins, B. van der Zwaan, R. Wood, and three anonymous referees at The Energy Journal for their comments, data, encouragement, or financial support. Of course, any errors are my own.

(*.) Stanford University. Department of Economics, Stanford, California 94305-6072 USA. E-mail: rothwell@stanford.edu

(1.) Nordhaus (1997) considers a similar set of issues. Nordhaus concludes, "Sweden has much to lose and little to gain from an early retirement of its nuclear power industry." (p. 159). This conclusion is based on a dynamic, macroeconomic model, unlike the model in this paper. For a dynamic programming model of nuclear power plant retirements, see Rothwell and Rust (1997).

(2.) See, for example, Mas-Colell, Whinston and Green (1995, pp. 143-147). Future research will compare the AVC decision rule with other rules, including the Net Present Value and Real Options approaches. The latter would lead to later shutdowns, if future profits are stochastic and above a lower limit. See Dixit and Pindyck (1994, pp. 213-244).

(3.) "Capital additions" are expenditures for durable equipment that could be avoided by retiring the nuclear power unit. They do not include financial expenses associated with capital investment. See the discussion of "Going-Forward Costs" in Raber and Hasell (1997).

(4.) Nuclear fuel accounting is very complex given that NPP operators own the fuel from fuel fabrication through fuel utilization to spent fuel disposition. In cost data this capital accounting is simplified as an expense per kWh.

(5.) These data do not include insurance and administrative overheads, as discussed in US DOE/EIA (1995, p. 4). Also, units that were retired before January 1, 1999, are excluded in this analysis; as is Browns Ferry 1, which has not operated since March 1985.

(6.) Average fuel prices have been high for new, single-unit Boiling Water Reactors because fuel contracts at four of these plants were signed when uranium prices were particularly high in the late 1970s and early 1980s. See Table 2. These costs should decline to industry averages as new uranium is purchased, making new BWRs more competitive.

(7.) Because labor costs account for a large fraction of annual average variable expenses, much of the cost-cutting effort at nuclear power plants is focused on reducing labor requirements. See International Atomic Energy Agency (1999).

(8.) There are several definitions of NPP size, including nameplate rating, designed electrical rating, and licensed thermal power. Maximum dependable capacity in MW (MDC) is used here because it is most compatible with international conventions. See, for example, International Atomic Energy Agency (1998, p. 19). MAX equals MDC * 1,000 * 8,760 (or 8,784 in leap years).

(9.) While these forecasting equations look simplistic, they are equivalent to estimating a fully interacted, fixed-effects model that controls reactor type, reactor vintage, and number of units at the plant site. Unlike other empirical models of NPP costs that focus on hypothesis testing, the primary purpose here is forecasting, in particular, forecasting expectations of NPP operators regarding the mean and variance of NPP cost. For a discussion of richer models to test hypotheses, see Rothwell (1998a).

(10.) As discussed in Rothwell (1998a), because of the definition of maximum dependable capacity, it is possible to observe capacity factors greater than 100%.

(11.) Again, while these forecasting equations look simplistic, they are equivalent to estimating a fully interacted, fixed-effects model that controls for reactor type, reactor manufacturer, and unit size. For a discussion of richer models, see Rothwell (1998b).

(12.) The average and marginal-cost based prices used in this analysis are available from the author upon request. Email: rothwell@standord.edu.

(13.) Although deregulated hourly electricity markets are much more volatile than prices in Form 826, there is not enough experience with average annual revenues for base-load generators to calculate a price variance. Future research will examine the distribution of annual revenues to determine whether the standard deviations used here are appropriate.

(14.) Although carbon-content prices in each year from 2005 to 2010 to 2020 are not linear interpolations of the prices between these years, I assume weighted averages for each year between them; see the Executive Summary, Figure ES-2 in US DOE/EIA (1998a). Also, white marginal regional Carbon Content (CC) prices would be more appropriate, these are not now available. However, in regions where natural gas will be the fuel of the marginal generator, these CC prices are too high. In regions where coal will be the fuel of the marginal generator, these CC prices are too low.

(15.) A deterministic version of the model, in which Var(AVE) = 0, was also explored for the MC pricing scenario. Comparing the deterministic and probabilistic versions of the model, the deterministic results were greater than the mean of the probabilistic distribution before 2005 and less than the mean from 2005 to 2017, after which they were similar. The deterministic output was greater than the mean until 2006 and was less than the mean until 2017. So, the deterministic version of the model (where some units are always competitive and other units are never competitive, as in Biewald and White, 1999, and US DOE/EIA, 1998b) was more optimistic than the probabilistic model before convergence to MC pricing and more pessimistic afterward.

(16.) In comparing these and other results, the standard error ([SE.sub.1]) of the mean is equal to the standard deviation ([SD.sub.1]) divided by the square root of the sample size, i.e., [(100).sup.0.5] = 10. To test the equivalence of two means, the difference, divided by [([[SE.sup.2].sub.1] + [[SE.sup.2].sub.2]).sup.0.5], follows a t-distribution with degrees of freedom equal to the sample size.

(17.) A unit is retired in the simulation only if it is non-competitive in all simulation samples, otherwise it is assumed that the owner maintains the option to retire. There are only two units (at single-unit sites) that are non-competitive in all simulations presented in Table 6.

(18.) Under long-run marginal cost pricing, DRI (1998) forecasts five units retiring between 1998 and 2001 and 20 at risk of early retirement. Under deregulation, Biewald and White (1999) forecast the closure of 34 units by 2003. With higher NPP operating costs (increasing at 0.5% per year) and lower market prices (7% less than MC prices in 1996 and 15% less than US DOB/EIA forecasts after 2005), Biewald and White (1999) find 90 units at risk of early retirement. In the Annual Energy Outlook 2000 (US DOE/EIA, 1999, p. 68) 13 units are expected to retire early by 2010.

(19.) The influence of the timing of deregulation was addressed by exploring different dates of convergence to MC pricing: (1) all states experience MC pricing by 2005, (2) all states experience MC pricing by 2010, and (3) some states are assumed to deregulate by 2005 and other states by 2010. Either because more nuclear units are in states actively deregulating generation markets or because more non-competitive units are in these states, the third approach yeilds results that are closer to the "2005" results than the "2010" results.

(20.) Generation forecasts are based on data from 1982-1998. Forecasts through 2035 are available from the author. Because nuclear power generation has been increasing, the forecasts are lower than nuclear industry output in the latter 1990s. In particular, in 1999 the industry generated 727 TWh, an increase of 8% over 1998. See US DOE/EIA (2000b). In 1999 the US nuclear industry generated more electricity than the nuclear industries of France (375 TWh) and Japan (306.9 TWh) combined.

(21.) A similar conclusion is reached in International Energy Agency (1998) regarding NPPs in other countries.

(22.) This analysis also ignores differences between the scenarios analyzed here and the NPP retirement assumptions underlying the NEMS price projections. Ideally, the model used here should be run as NEMS sub-module. If these interactions could be incorporated, it is likely that fewer plants would be at risk of retirement than found here: As more NPPs retire, regional prices would rise, making the remaining NPPs more competitive and less likely to retire.

(23.) For analysis of the avoided emissions of carbon dioxide, sulfur dioxide, nitrogen oxide, and ozone from nuclear power generation, see South (1999).

(24.) On March 23, 2000, the Nuclear Regulatory Commission approved the license renewal application for Calvert Cliffs Units 1 and 2, extending their licensed lifetimes to 2034 and 2036. On May 23, 2000, the NRC extended the licensed lifetimes of Oconee Units 1, 2, and 3 to 2033, 2033, and 2034. Draft Environmental Impact Statements have been submitted for two plants: Arkansas Nuclear 1 (2014), and Edwin Hatch 1(2014) and 2 (2018). By mid-2000 owners of 13 other plants had expressed interest in submitting a license renewal application. See http://www.nrc.gov/NRC/REACTOR/LR.

(25.) DRI (1998) assumes that if the net present value of a nuclear unit is greater than $500 million, the owner will make the necessary espenditures to renew the license for 20 years. Under this assumption, DRI predicts that 39 of 54 units will be granted the license renewals before 2020. Costs of license renewal by the NRC are likely to be low ($10-20 million), so the licenses at most units will be extended. But costs associated with plant aging are uncertain. So DRI forecasts of granted license renewals could be too low, but their forecast of the number of units operating for 60 years could be too high. Further research is required.

(26.) For more on decommissioning costs, see Pasqualetti and Rothwell (1991).

(27.) By mid-2000 several NPPs had been sold or were being sold and mergers of several nuclear utilities were proposed. AmerGen (a joint venture of PECO Energy, operator of Limerick and Peach Bottom, and British Energy, operator of NPPs in the UK) has negotiated the purchase of Three Mile Island Unit 1, Clinton, Oyster Creek, and Vermont Yankee. PECO and Unicom (Commonwealth Edison with 13 units) are merging to form Exelon. Entergy (operator of Arkansas One, Grand Gulf, River Bend, and Waterford) completed the purchase of Pilgrim in July 1999. In March 2000 the New York Power Authority approved the sale of Indian Point 3 and Fitzpatrick to Entergy. Sales of other units in New York are being negotiated. Further, it is likely that the owners of non-competitive units will either (1) try to sell their units to or merge with more efficient managers rather than retire them early or (2) organize themselves into coordinating management groups, as in the upper mid-west (the Nuclear Management Company with 7 units) an d in the southwest (with 8 units). For up-to-date information, see Nuclear News, "Nuclear plant dealings--completed, underway, and in negotiation" (monthly issues).

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